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Primordial black holes (PBHs) are hypothetical objects formed at the early epoch of the universe, which could be a type of dark matter (DM) candidate without the need for new particles. The abundance of PBH DM has been constrained strictly by many observations.In this work, with the radio observations of Fornax and Segue I, we constrain the abundance of PBH in dwarf spheroidal galaxies through the synchrotron self-Compton (SSC) effect of Hawking radiation electrons. By selecting optimal sources, we obtain the constraints on the fraction of PBH DM down to $\sim10^{-3}$ for Segue I and $\sim10^{-5}$ for Fornax at asteroidal mass. We also predict that, with 100 hours of future observation by the Square Kilometer Array, the SSC approach could place constraints comparable to the current strictest results for PBHs of $<5\times10^{15}\,{\rm g}$. Better projected constraints can be obtained by including the inverse Compton scattering on cosmic microwave background photons., Comment: 9 pages, 6 figures, accepted for publication in PRD

Dark photon is a new gauge boson beyond the Standard Model as a kind of dark matter (DM) candidate. Dark photon dark matter (DPDM) interacts with electromagnetic fields via kinetic mixing, implicating an approach to give a constraint with extragalactic very high energy (VHE) sources. In this work, we attempt to constrain the kinetic mixing from the photon-dark photon scattering process in the host galaxy of blazar, the intergalactic medium and the Milky Way. The VHE photons from a blazar would pass through a dense DM spike around the supermassive black hole where the absorption from DPDM is dramatically enhanced. The kinetic mixing is constrained to be $\epsilon \sim 10^{-7}$ at a 95$\%$ confidence level with $m_{\rm D}\sim 0.03 - 1$ eV mass range from the observations of Markarian (Mrk) 421 and Mrk 501., Comment: 16 pages, 10 figures, 3 tables

Many years ago, G.-C.~Rota discovered a close connection between symmetric functions and Rota-Baxter algebras, and proposed to study generalizations of symmetric functions in the framework of Rota-Baxter algebras. Guided by this proposal, quasisymmetric functions from weak composition (instead of just compositions) were obtained from free Rota-Baxter algebras on one generator. This paper aims to generalize this approach to free Rota-Baxter algebras on multiple generators in order to obtain further generalizations of quasisymmetric functions. For this purpose and also for its independent interest, the space $\mathrm{MQSym}$ of quasisymmetric functions on multiple sequences of variables is defined, generalizing quasisymmetric functions and diagonally quasisymmetric functions of Aval, Bergeron and Bergeron. Linear bases of such multi-quasisymmetric functions are given by monomial multi-quasisymmetric functions and fundamental multi-quasisymmetric functions, the latter recover the fundamental $G^m$-quasisymmetric functions of Aval and Chapoton. Next introduced is the even more general notion of multi-quasisymmetric functions $\mathrm{MQSym}^E$ with exponents in a semigroup $E$, which also generalizes the quasisymmetric functions with semigroup exponents in a recent work. Through this approach, a natural Hopf algebraic structure is obtained on $\mathrm{MQSym}^E$. Finally, in support of Rota's proposal, the free commutative unitary Rota-Baxter algebra on a finite set is shown to be isomorphic to a scalar extension of $\mathrm{MQSym}^E$, a fact which in turn equips the free Rota-Baxter algebra with a Hopf algebra structure., Comment: 27 pages

The study of kagome materials has attracted much attention in the past few years due to the presence of many electron-electron interaction-driven phases in a single material.In this work, we report the discovery of intrinsic spin-polarized p-wave superconductivity in the thin-flake kagome material RbV$_3$Sb$_5$. Firstly, when an in-plane magnetic field is swept in opposite directions, we observe a unique form of hysteresis in magnetoresistance which is different from the hysteresis induced by extrinsic mechanisms such as flux-trapping or superheating and supercooling effects. The unconventional hysteresis indicates the emergence of an intrinsic time-reversal symmetry-breaking superconducting phase. Strikingly, at a fixed magnetic field, the finite-resistance state can be quenched to the zero-resistance state by applying a large current. Secondly, at temperatures around 400 mK, the re-entrance of superconductivity occurs during an in-plane field-sweeping process with a fixed sweeping direction. This kind of re-entrance is asymmetric about the zero field axis and observed in all field directions for a fixed current direction, which is different from the re-entrance observed in conventional superconductors. Moreover, the angle-dependent in-plane critical field measurements reveal a two-fold symmetry that deviates from the original, centrosymmetric D$_{6h}$ point group symmetry of the crystal. These findings put very strong constraints on the possible superconducting pairing symmetry of RbV$_3$Sb$_5$. We point out that the pairing symmetry, which is consistent with the crystal symmetry and all the observed novel properties, is a time-reversal symmetry-breaking, p-wave pairing with net spin polarization. Importantly, this p-wave pairing gives rise to a nodal topological superconducting state with Majorana flat bands on the sample edges., Comment: 21 pages, 4 figures

We suppose that a Cooper pair (CP) will experience a damping force exerted by the condensed matter. A Langevin equation of a CP in two dimensional condensed matter is established. Following a method similar to Nelson's stochastic mechanics, generalized Schr\"{o}dinger equation of a CP in condensed matter is derived. If the CPs move with a constant velocity, then the corresponding direct current (DC) electrical conductivity can be calculated. Therefore, a Drude like formula of resistivity of CPs is derived. We suppose that the damping coefficient of CPs in two dimensional cuprate superconductors is a linear function of temperature. Then the resistivity and scattering rate of CPs turn out to be also linear-in-temperature. The origin of linear-in-temperature resistivity and Planckian dissipation in cuprate superconductors may be the linear temperature dependence of the damping coefficient of CPs., Comment: 10 pages, 0 figures, Latex

Since the general theory of relativity (GR) meets some difficulties, it seems that new considerations on the ether theories of gravitation in the history are needed. A theory of gravity based on some new concepts of ether and particles is briefly reviewed. In this theory, the universe is filled with a kind of fluid which may be called the $\Omega(0)$ substratum, or we say the gravitational ether. Particles are modeled as sink flows in the $\Omega(0)$ substratum. Newton's law of gravitation is derived by methods of fluid mechanics. Thus, gravity is interpreted as attractive force between sinks in the $\Omega(0)$ substratum. The theoretical calculation of the cosmological constant (CC) based on a mechanical model of vacuum is briefly reviewed. A proposed solution of the cosmological constant problem (CCP) is discussed. Inspired by the association of the gravitational wave (GW) event GW170817 and the gamma-ray burst (GRB) event GRB 170817A, we propose a theoretical calculation of the mass density of the electromagnetic ether., Comment: 6 pages, 0 figures, Latex. Keywords are revised. arXiv admin note: text overlap with arXiv:2209.10525

Nonlocality is the defining feature of quantum entanglement. Entangled states with multiple particles are of crucial importance in fundamental tests of quantum physics as well as in many quantum information tasks. One of the archetypal multipartite quantum states, Greenberger-Horne-Zeilinger (GHZ) state, allows one to observe the striking conflict of quantum physics to local realism in the so-called all-versus-nothing way. This is profoundly different from Bell's theorem for two particles, which relies on statistical predictions. Here, we demonstrate an integrated photonic chip capable of generating and manipulating the four-photon GHZ state. We perform a complete characterization of the four-photon GHZ state using quantum state tomography and obtain a state fidelity of 0.729(6). We further use the all-versus-nothing test and the Mermin inequalities to witness the quantum nonlocality of GHZ entanglement. Our work paves the way to perform fundamental tests of quantum physics with complex integrated quantum devices., Comment: 10 pages, 3 figures

Copy-move forgery detection aims at detecting duplicated regions in a suspected forged image, and deep learning based copy-move forgery detection methods are in the ascendant. These deep learning based methods heavily rely on synthetic training data, and the performance will degrade when facing new tasks. In this paper, we propose a Transformer-style copy-move forgery detection network named as CMFDFormer, and provide a novel PCSD (Pooled Cube and Strip Distillation) continual learning framework to help CMFDFormer handle new tasks. CMFDFormer consists of a MiT (Mix Transformer) backbone network and a PHD (Pluggable Hybrid Decoder) mask prediction network. The MiT backbone network is a Transformer-style network which is adopted on the basis of comprehensive analyses with CNN-style and MLP-style backbones. The PHD network is constructed based on self-correlation computation, hierarchical feature integration, a multi-scale cycle fully-connected block and a mask reconstruction block. The PHD network is applicable to feature extractors of different styles for hierarchical multi-scale information extraction, achieving comparable performance. Last but not least, we propose a PCSD continual learning framework to improve the forgery detectability and avoid catastrophic forgetting when handling new tasks. Our continual learning framework restricts intermediate features from the PHD network, and takes advantage of both cube pooling and strip pooling. Extensive experiments on publicly available datasets demonstrate the good performance of CMFDFormer and the effectiveness of the PCSD continual learning framework., Comment: 12pages,7 figures

We study the hadronic coupling constants in the two-body strong decays of the fully-charm tetraquark states with the $J^{PC}=0^{++}$, $1^{+-}$ and $2^{++}$ via the QCD sum rules based on rigorous quark-hadron duality. Then we obtain the hadronic coupling constants and partial decay widths therefore total decay widths, which support assigning the $X(6552)$ as the first radial excitation of the scalar tetraquark state. And other predictions can be used to diagnose exotic states in the future., Comment: 17 pages, 3 figures

Electrons and positrons produced in dark matter annihilation can generate secondary emission through synchrotron and IC processes, and such secondary emission provides a possible means to detect DM particles with masses beyond the detector's energy band. The secondary emission of heavy dark matter (HDM) particles in the TeV-PeV mass range lies within the Fermi-LAT energy band. In this paper, we utilize the Fermi-LAT observations of dwarf spheroidal (dSph) galaxies to search for annihilation signals of HDM particles. We consider the propagation of $e^+/e^-$ produced by DM annihilation within the dSphs, derive the electron spectrum of the equilibrium state by solving the propagation equation, and then compute the gamma-ray signals produced by the $e^+/e^-$ population through the IC and synchrotron processes. Considering the spatial diffusion of electrons, the dSphs are modeled as extended sources in the analysis of Fermi-LAT data according to the expected spatial intensity distribution of the gamma rays. We do not detect any significant HDM signal. By assuming a magnetic field strength of $B=1\,{\rm \mu G}$ and a diffusion coefficient of $D_0 = 3\times10^{28}\,{\rm cm^{2}s^{-1}}$ of the dSphs, we place limits on the annihilation cross section for HDM particles. Our results are weaker than the previous limits given by the VERITAS and IceCube observations of dSphs, but extend the existing limits to higher DM masses. As a complement, we also search for the prompt $\gamma$-rays produced by DM annihilation and give limits on the cross section in the 10-$10^5$ GeV mass range. Consequently, in this paper we obtain the upper limits on the DM annihilation cross section for a very wide mass range from 10 GeV to 100 PeV in a unified framework of the Fermi-LAT data analysis., Comment: 11 pages, 9 figures; add the KN effect for IC and model the secondary emission around dSphs as extended

Integrated microresonator facilitates the realization of quantum frequency comb (QFC), which provides a large number of discrete frequency modes with broadband spectral range and narrow linewidth. However, all previous demonstrations have focused on the generation of energy-time or time-bin entangled photons from QFC. Realizing polarization-entangled quantum frequency comb, which is the important resource for fundamental study of quantum mechanics and quantum information applications, remains challenging. Here, we demonstrate, for the first time, a broadband polarization-entangled quantum frequency comb by combining an integrated silicon nitride micro-resonator with a Sagnac interferometer. With a free spectral range of about 99 GHz and a narrow linewidth of about 190 MHz, our source provides 22 polarization entangled photons pairs with frequency covering the whole telecom C-band. The entanglement fidelities for all 22 pairs are above 81%, including 17 pairs with fidelities higher than 90%. Our demonstration paves the way for employing the polarization-entangled quantum frequency comb in quantum network using CMOS technology as well as standard dense wavelength division multiplexing technology., Comment: 11 pages, 9 figures

In this work, we systematically investigate the singly-charmed pentaquark molecular states $D^{(*)}N$, $D^{(*)}\Xi^{(*)}$ and $D_s^{(*)}\Xi^{(*)}$ with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension 13 and taking fully account of the light-flavor $SU(3)$ breaking effects. The numerical results favor assigning the $\Omega_c(3185)$ as the $D\Xi$ molecular state with the $J^P=\frac{1}{2}^-$ and $| I,I_3 \rangle=| 0,0 \rangle$, assigning the $\Omega_c(3327)$ as the $D^*\Xi$ molecular state with the $J^P=\frac{3}{2}^-$ and $|I,I_3 \rangle=| 0,0 \rangle$, assigning the $\Sigma_c(2800)$ as the $DN$ molecular state with the $J^P=\frac{1}{2}^-$ and $| I,I_3 \rangle=| 1,0 \rangle$, and assigning the $\Lambda_c(2940)/\Lambda_c(2910)$ as the $D^*N$ molecular state with the $J^P=\frac{3}{2}^-$ and $| I,I_3 \rangle=| 0,0 \rangle$. Other potential molecule candidates are also predicted, which may be observed in future experiments. For example, we can search for the $D\Xi$ and $D^*\Xi$ molecular states with the isospin $| I,I_3 \rangle=| 1,\pm1 \,\rangle$ in the $\Xi_c^+\bar{K}^0$ and $\Xi_c^0\bar{K}^-$ mass spectrum respectively in the future, which could shed light on the nature of the $\Omega_c(3185/3327)$., Comment: 23 pages, 6 figures

In this paper, we first introduce the notion of an extending datum of a Rota-Baxter Lie algebra through a vector space. We then construct a unified product for the Rota-Baxter Lie algebra with a vector space as a main ingredient in our approach. Finally, we solve the extending structures problem of Rota-Baxter Lie algebras, which generalizes and unifies two problems in the study of Rota-Baxter Lie algebras: the extension problem studied by Mishra-Das-Hazra and the factorization problem investigated by Lang-Sheng., Comment: 19 pages

Integrated quantum photonics has recently emerged as a powerful platform for generating, manipulating, and detecting entangled photons. Multipartite entangled states lie at the heart of the quantum physics and are the key enabling resources for scalable quantum information processing. Dicke state is an important class of genuinely entangled state, which has been systematically studied in the light-matter interactions, quantum state engineering and quantum metrology. Here, by using a silicon photonic chip, we report the generation and collectively coherent control of the entire family of four-photon Dicke states, i.e. with arbitrary excitations. We generate four entangled photons from two microresonators and coherently control them in a linear-optic quantum circuit, in which the nonlinear and linear processing are achieved in a chip-scale device. The generated photons are in telecom band, which lays the groundwork for large-scale photonic quantum technologies for multiparty networking and metrology., Comment: 19 pages, 4 figures in the main text and 13 figures in the Supplemental Material

In this research, we tentatively assign the $T_{c\bar{s}}(2900)$ as the $A\bar{A}$-type tetraquark state, and study the mass spectrum of the tetraquark states with strange and doubly strange, which have the spin-parity $J^P = 0^+$, $1^+$ and $2^+$, in the framework of the QCD sum rules in details, where the $A$ denotes the axialvector diquark state. The predicted mass $M=2.92\pm0.12\,\rm{GeV}$ is in consistent with the experimental values $M=2.892\pm0.014\pm0.015\,\rm{GeV}$ and $2.921\pm0.017\pm0.020\,\rm{GeV}$ from the LHCb collaboration and supports assigning the $T_{c\bar{s}}(2900)$ to be the $A\bar{A}$-type scalar $c\bar{s}q\bar{q}$ tetraquark state. The predictions for other tetraquark states can be confronted to the experimental data in the future to diagnose the nature of the fully open flavor exotic states., Comment: 20 pages, 7 figures

The quantum internet -- in synergy with the internet that we use today -- promises an enabling platform for next-generation information processing, including exponentially speed-up distributed computation, secure communication, and high-precision metrology. The key ingredients for realizing such a global network are the distribution and storage of quantum entanglement. As ground-based quantum networks are likely to be based on existing fiber networks, telecom-wavelength entangled photons and corresponding quantum memories are of central interest. Recently, $\rm^{167}Er^{3+}$ ions have been identified as a promising candidate for an efficient, broadband quantum memory at telecom wavelength. However, to date, no storage of entangled photons, the crucial step of quantum memory using these promising ions, $\rm^{167}Er^{3+}$, has been reported. Here, we demonstrate the storage and recall of the entangled state of two telecom photons generated from an integrated photonic chip based on a silicon nitride micro-ring resonator. Combining the natural narrow linewidth of the entangled photons and long storage time of $\rm^{167}Er^{3+}$ ions, we achieve storage time of 1.936 $\mu$s, more than 387 times longer than in previous works. Successful storage of entanglement in the crystal is certified by a violation of an entanglement witness with more than 23 standard deviations (-0.234 $\pm$ 0.010) at 1.936 $\mu$s storage time. These results pave the way for realizing quantum networks based on solid-state devices., Comment: We have improved the storage time of quantum entanglement to over 1.9 $\mu$s with a efficiency of about 2%, using partial nuclear spin polarization as well as better frequency locking for the laser system. We have also enhanced the coherence of signal photons, which are generated from an entangled photon-pair source based on an integrated microring resonator with a quality factor exceeding 10^6

A typical imaging scenario requires three basic ingredients: 1. a light source that emits light, which in turn interacts and scatters off the object of interest; 2. detection of the light being scattered from the object and 3. a detector with spatial resolution. These indispensable ingredients in typical imaging scenarios may limit their applicability in the imaging of biological or other sensitive specimens due to unavailable photon-starved detection capabilities and inevitable damage induced by interaction. Here, we propose and experimentally realize a quantum imaging protocol that alleviates all three requirements. By embedding a single-photon Michelson interferometer into a nonlinear interferometer based on induced coherence and harnessing single-pixel imaging technique, we demonstrate interaction-free, single-pixel quantum imaging of a structured object with undetected photons. Thereby, we push the capability of quantum imaging to the extreme point in which no interaction is required between object and photons and the detection requirement is greatly reduced. Our work paves the path for applications in characterizing delicate samples with single-pixel imaging at silicon-detectable wavelengths.

The cover-time problem, i.e., time to visit every site in a system, is one of the key issues of random walks with wide applications in natural, social, and engineered systems. Addressing the full distribution of cover times for random walk on complex structures has been a long-standing challenge and has attracted persistent efforts. Yet, the known results are essentially limited to homogeneous systems, where different sites are on an equal footing and have identical or close mean first-passage times, such as random walks on a torus. In contrast, realistic random walks are prevailingly heterogeneous with diversified mean first-passage times. Does a universal distribution still exist? Here, by considering the most general situations, we uncover a generalized rescaling relation for the cover time, exploiting the diversified mean first-passage times that have not been accounted for before. This allows us to concretely establish a universal distribution of the rescaled cover times for heterogeneous random walks, which turns out to be the Gumbel universality class that is ubiquitous for a large family of extreme value statistics. Our analysis is based on the transfer matrix framework, which is generic that besides heterogeneity, it is also robust against biased protocols, directed links, and self-connecting loops. The finding is corroborated with extensive numerical simulations of diverse heterogeneous non-compact random walks on both model and realistic topological structures. Our new technical ingredient may be exploited for other extreme value or ergodicity problems with nonidentical distributions., Comment: 12 pages, 6 figures

When solving the Einstein's equations for an isolated system of masses, V. Fock introduces harmonic reference frame and obtains an unambiguous solution. Further, he concludes that there exists a harmonic reference frame which is determined uniquely apart from a Lorentz transformation if suitable supplementary conditions are imposed. It is known that wave equations keep the same form under Lorentz transformations. Thus, we speculate that Fock's special harmonic reference frames may have provided us a clue to derive the Einstein's equations in some special class of non-inertial reference frames. Following this clue, generalized Einstein's equations in some special non-inertial reference frames are derived based on the theory of vacuum mechanics. If the field is weak and the reference frame is quasi-inertial, these generalized Einstein's equations reduce to Einstein's equations. Thus, this theory may also explain all the experiments which support the theory of general relativity. There exist some differences between this theory and the theory of general relativity., Comment: 14 pages, 0 figures, LATEX2e. arXiv admin note: text overlap with arXiv:1806.07724

Lord Kelvin believed that the electromagnetic aether must also generate gravity. Presently, we have no methods to determine the density of the electromagnetic aether, or we say the $\Omega(1)$ substratum. Thus, we also suppose that vacuum is filled with another kind of continuously distributed substance, which may be called the $\Omega(2)$ substratum. Based on a theorem of V. Fock on the mass tensor of a fluid, the contravariant energy-momentum tensors of the $\Omega(1)$ and $\Omega(2)$ substrata are established. Quasi-static solutions of the gravitational field equations in vacuum are obtained. Based on an assumption, relationships between the contravariant energy-momentum tensors of the $\Omega(1)$ and $\Omega(2)$ substrata and the contravariant metric tensor are obtained. Thus, the cosmological constant is calculated theoretically. The $\Omega(1)$ and $\Omega(2)$ substrata may be a possible candidate of the dark energy. According to the theory of vacuum mechanics, only those energy-momentum tensors of discrete or continuously distributed sinks in the $\Omega(0)$ substratum are permitted to act as the source terms in the generalized Einstein's equations. Thus, the zero-point energy of electromagnetic fields is not qualified for a source term in the generalized Einstein's equations. Some people believed that all kinds of energies should act as source terms in the Einstein's equations. It may be this unwarranted belief that leads to the cosmological constant problem. The mass density of the $\Omega(1)$ and $\Omega(2)$ substrata is equivalent to that of around $3$ protons contained in a box with a volume of $1$ cubic metre., Comment: 12 pages, 0 figures,Version 4.0 of REVTeX

In this work, we study the $D\bar{D}$, $DD$, $D\bar{D}_s$, $DD_s$, $D_s\bar{D}_s$ and $D_sD_s$ tetraquark molecular states with the $J^{PC}=0^{++}$ via the QCD sum rules. The prediction $M_{D_s\bar {D}_s} = 3.98\pm0.10\, \rm{GeV}$ is in very good agreement with the experimental value $M_{X(3960)} = 3956 \pm 5\pm 10 \,\rm{MeV}$ from the LHCb collaboration and supports assigning the $X(3960)$ as the $D_s^+D_s^-$ molecular state with the $J^{PC}=0^{++}$. We take account of our previous works on the four-quark states consisting of two color-neutral clusters, and acquire the mass spectrum of the ground state hidden-charm and doubly-charm tetraquark molecular states., Comment: 9 pages, 8 figures

Quantum network facilitates the secure transmission of information between different users. Establishing communication links among multiple users in a scalable and efficient way is important for realizing a large-scale quantum network. Here we develop an energy-time entanglement-based dense wavelength division multiplexed network based on an integrated silicon nitride micro-ring resonator, which offers a wide frequency span (covering at least the entire C-band) and narrow bandwidth modes (~ 650MHz). Six pairs of photons are selected to form a fully and simultaneously connected four-user quantum network. The observed quantum interference visibilities are well above the classical limits among all users. Each pair of users perform the BBM92 protocol for quantum key distribution. Our results pave the way for realizing large-scale quantum networks with integrated photonic architecture.

A recent result from Fermilab suggests that the measured W-boson mass deviates from the prediction of the Standard Model (SM) with a significance of $>7\sigma$, and there may exist new physics beyond the SM. It is proposed that the inert two Higgs doublet model (i2HDM) can well explain the new W-boson mass. Meanwhile, the lightest neutral scalar $S$ in the i2HDM can be stable and play the role of dark matter with a preferred dark matter mass of $\sim 54-74$ GeV. It is also found that part of the parameter space of this model can explain both the Galactic center GeV gamma-ray excess detected by $Fermi$-LAT and the GeV antiproton excess detected by AMS-02 through a $SS\rightarrow WW^*$ annihilation. In this paper, we aim to test the possible common i2HDM origin of the three anomaly/excesses using the $Fermi$-LAT observations of Milky Way dwarf spheroidal (dSph) galaxies. We perform single and stacking analyses on 19 dSphs that have J-factor measurements. We find that our upper limits are below the favored parameters and seems to be able to exclude the possibility of a common origin of the three anomaly/excesses. However, because the J-factor measurements include relatively large uncertainties, which come from the measurements of stellar kinematics, whether this model could be reliably excluded needs to be further confirmed by future observations., Comment: 10 pages, 4 figures, updated to match the accepted version

Wave-particle duality and entanglement are two fundamental characteristics of quantum mechanics. All previous works on experimental investigations in wave{particle properties of single photons (or single particles in general) show that a well-defined interferometer setting determines a well-defined property of single photons. Here we take a conceptual step forward and control the wave-particle property of single photons with quantum entanglement. By doing so, we experimentally test the complementarity principle in a scenario, in which the setting of the interferometer is not defined at any instance of the experiment, not even in principle. To achieve this goal, we send the photon of interest (S) into a quantum Mach-Zehnder interferometer (MZI), in which the output beam splitter of the MZI is controlled by the quantum state of the second photon (C), who is entangled with a third photon (A). Therefore, the individual quantum state of photon C is undefined, which implements the undefined settings of the MZI for photon S. This is realized by using three cascaded phase-stable interferometers for three photons. There is typically no well-defined setting of the MZI, and thus the very formulation of the wave-particle properties becomes internally inconsistent.

The interference of quanta lies at the heart of quantum physics. The multipartite generalization of single-quanta interference creates entanglement, the coherent superposition of states shared by several quanta. Entanglement allows non-local correlations between many quanta and hence is a key resource for quantum information technology. Entanglement is typically considered to be essential for creating non-local correlations, manifested by multipartite interference. Here, we show that this is not the case and demonstrate multiphoton non-local quantum interference without entanglement of any intrinsic properties of the photons. We harness the superposition of the physical origin of a four-photon product state, which leads to constructive and destructive interference of the photons' mere existence. With the intrinsic indistinguishability in the generation process of photons, we realize four-photon frustrated quantum interference. We furthermore establish non-local control of multipartite quantum interference, in which we tune the phase of one undetected photon and observe the interference of the other three photons. Our work paves the way for fundamental studies of non-locality and potential applications in quantum technologies.

We introduce a generalization of tridendriform algebras, where each of the three products are replaced by a family of products indexed by a set $\Omega$. We study the needed structure on $\Omega$ for free $\Omega$-tridendriform algebras to be built on Schr{\"o}der trees (as it is the case in the classical case), with convenient decorations on their leaves. We obtain in this way extended triassociative semigroups. We describe commutative $\Omega$-tridendriform algebras in terms of typed words. We also study links with generalizations of Rota-Baxter algebras and describe the Koszul duals of the corresponding operads.

We introduce a generalization of parametrized Rota-Baxter algebras, which includes family and matching Rota-Baxter algebras. We study the structure needed on the set $\Omega$ of parameters in order to obtain that free Rota-Baxter algebras are described in terms of typed and angularly decorated planar rooted trees: we obtain the notion of $\lambda$-extended diassociative semigroup, which includes sets (for matching Rota-Baxter algebras) and semigroups (for family Rota-Baxter algebras), and many other examples. We also describe free commutative $\Omega$-Rota-Baxter algebras generated by a commutative algebra A in terms of typed words.

In the present work, we construct the color-singlet-color-singlet type four-quark currents to investigate the $D_s\bar{D}_{s1}$ and $D_s^*\bar{D}_{s0}^*$ tetraquark molecular states with the $J^{PC}=1^{--}$ and $1^{-+}$ via the QCD sum rules, and obtain satisfactory results. We can search for the $D_s\bar{D}_{s1}$ and $D_s^*\bar{D}_{s0}^*$ tetraquark molecular states with the $J^{PC}=1^{--}$ and $1^{-+}$ at the BESIII and Belle II in the future., Comment: 11 pages, 4 figures

In this paper we investigate some properties of equilibrium points in n-dimensional linear control systems with saturated state feedback. We provide an index formula for equilibrium points and discuss its relation to boundaries of attraction basins in feedback systems with single input. In addition, we also touch upon convexity of attraction basin.

We employ quantum state and process tomography with time-bin qubits to benchmark a city-wide metropolitan quantum communication system. Over this network, we implement real-time feedback control systems for stabilizing the phase of the time-bin qubits, and obtain a 99.3% quantum process fidelity to the ideal channel, indicating the high quality of the whole quantum communication system. This allows us to implement field trial of high performance quantum key distribution using coherent one way protocol with average quantum bit error rate and visibility of 0.25% and 99.2% during 12 hours over 61 km. Our results pave the way for the high-performance quantum network with metropolitan fibers., Comment: 6 pages, 4 figures

In this paper, we introduce the Hom-algebra setting of the notions of matching Rota-Baxter algebras, matching (tri)dendriform algebras and matching (pre)Lie algebras. Moreover, we study the properties and relationships between categories of these matching Hom-algebraic structures., Comment: 20pages

Integrated photonics provides a route both to miniaturize quantum key distribution (QKD) devices and to enhance their performance. A key element for achieving discrete-variable QKD is a single-photon detector. It is highly desirable to integrate detectors onto a photonic chip to enable the realization of practical and scalable quantum networks. We realize an integrated heterogeneous superconducting-silicon-photonic chip. Harnessing the unique high-speed feature of our optical waveguide-integrated superconducting detector, we perform the first optimal Bell-state measurement (BSM) of time-bin encoded qubits generated from two independent lasers. The optimal BSM enables an increased key rate of measurement-device-independent QKD, which is immune to all attacks against the detection system, and hence provides the basis for a QKD network with untrusted relays. Together with the time-multiplexed technique, we have enhanced the sifted key rate by almost one order of magnitude. With a 125 MHz clock rate, we obtain a secure key rate of 6.166 kbps over 24.0 dB loss, which is comparable to the state-of-the-art MDI-QKD experimental results with GHz clock rate. Combined with integrated QKD transmitters, a scalable, chip-based and cost-effective QKD network should become realizable in the near future., Comment: Major updates: 1. Realize optimal Bell-state measurement for time-bin qubits; 2. With a 125 MHz clock rate, the generated secure key rate is comparable to the state-of-the-art MDI-QKD experimental results with GHz clock rate

Quantum walks (QW) are of crucial importance in the development of quantum information processing algorithms. Recently, several quantum algorithms have been proposed to implement network analysis, in particular to rank the centrality of nodes in networks represented by graphs. Employing QW in centrality ranking is advantageous comparing to certain widely used classical algorithms (e.g. PageRank) because QW approach can lift the vertex rank degeneracy in certain graphs. However, it is challenging to implement a directed graph via QW, since it corresponds to a non-Hermitian Hamiltonian and thus cannot be accomplished by conventional QW. Here we report the realizations of centrality rankings of both a three-vertex and four-vertex directed graphs with parity-time (PT) symmetric quantum walks. To achieve this, we use high-dimensional photonic quantum states, optical circuitries consisting of multiple concatenated interferometers and dimension dependent loss. Importantly, we demonstrate the advantage of QW approach experimentally by breaking the vertex rank degeneracy in a four-vertex graph. Our work shows that PT-symmetric quantum walks may be useful for realizing advanced algorithm in a quantum network.

Surface plasmon polaritons (SPPs) are collective excitations of free electrons propagating along a metal-dielectric interface. Although some basic quantum properties of SPPs, such as the preservation of entanglement, the wave-particle duality of a single plasmon, the quantum interference of two plasmons, and the verification of entanglement generation, have been shown, more advanced quantum information protocols have yet to be demonstrated with SPPs. Here, we experimentally realize quantum state teleportation between single photons and SPPs. To achieve this, we use polarization-entangled photon pairs, coherent photon-plasmon-photon conversion on a metallic subwavelength hole array, complete Bell-state measurements and an active feed-forward technique. The results of both quantum state and quantum process tomography confirm the quantum nature of the SPP mediated teleportation. An average state fidelity of 0.889$\pm$0.004 and a process fidelity of 0.820$\pm$0.005, which are well above the classical limit, are achieved. Our work shows that SPPs may be useful for realizing complex quantum protocols in a photonic-plasmonic hybrid quantum network., Comment: 10+14 pages, 4+10 figures

Frequency non-degenerate entangled photon pairs have been employed in quantum communication, imaging, and sensing. To characterize quantum entangled state with long-wavelength (infrared, IR or even terahertz, THz) photon, one needs to either develop the single-photon detectors at the corresponding wavelengths or use novel tomography technique, which does not rely on single-photon detections, such as stimulated emission tomography (SET). We use standard quantum state tomography and SET to measure the density matrix of entangled photon pairs, with one photon at 1550 nm and the other one at 810 nm, and obtain highly consistent results, showing the reliability of SET. Our work paves the way for efficient measurement of entangled photons with highly dissimilar frequencies, even to the frequencies where single-photon detections are not available., Comment: 7 pages, 3 figures

Entanglement is a counterintuitive feature of quantum physics that is at the heart of quantum technology. High-dimensional quantum states offer unique advantages in various quantum information tasks. Integrated photonic chips have recently emerged as a leading platform for the generation, manipulation and detection of entangled photons. Here, we report a silicon photonic chip that uses novel interferometric resonance-enhanced photon-pair sources, spectral demultiplexers and high-dimensional reconfigurable circuitries to generate, manipulate and analyse path-entangled three-dimensional qutrit states. By minimizing on-chip electrical and thermal cross-talk, we obtain high-quality quantum interference with visibilities above 96.5% and a maximumly entangled qutrit state with a fidelity of 95.5%. We further explore the fundamental properties of entangled qutrits to test quantum nonlocality and contextuality, and to implement quantum simulations of graphs and high-precision optical phase measurements. Our work paves the path for the development of multiphoton high-dimensional quantum technologies., Comment: 36 pages, 14 figures

Wave-particle duality epitomizes the counterintuitive character of quantum physics. A striking illustration is the quantum delay-choice experiment, which is based on Wheeler's classic delayed-choice gedanken experiment, but with the addition of a quantum-controlled device enabling wave-to-particle transitions. Here we realize a quantum delayed-choice experiment in which we control the wave and the particle states of photons and in particular the phase between them, thus directly establishing the created quantum nature of the wave-particle. We generate three-photon entangled states and inject one photon into a Mach--Zehnder interferometer embedded in a 187-m-long two-photon Hong-Ou-Mandel interferometer. The third photon is sent 141m away from the interferometers and remotely prepares a two-photon quantum gate according to independent active choices under Einstein locality conditions. We have realized transitions between wave and particle states in both classical and quantum scenarios, and therefore tests of the complementarity principle that go fundamentally beyond earlier implementations., Comment: 15 pages, 15 figures

With the development of big data and artificial intelligence, the technology of urban computing becomes more mature and widely used. In urban computing, using GPS-based trajectory data to discover urban dense areas, extract similar urban trajectories, predict urban traffic, and solve traffic congestion problems are all important issues. This paper presents a GPS-based trajectory pattern mining system called TPM. Firstly, the TPM can mine urban dense areas via clustering the spatial-temporal data, and automatically generate trajectories after the timing trajectory identification. Mainly, we propose a method for trajectory similarity matching, and similar trajectories can be extracted via the trajectory similarity matching in this system. The TPM can be applied to the trajectory system equipped with the GPS device, such as the vehicle trajectory, the bicycle trajectory, the electronic bracelet trajectory, etc., to provide services for traffic navigation and journey recommendation. Meantime, the system can provide support in the decision for urban resource allocation, urban functional region identification, traffic congestion and so on.

Nonlocal self-similarity and group sparsity have been widely utilized in image compressive sensing (CS). However, when the sampling rate is low, the internal prior information of degraded images may be not enough for accurate restoration, resulting in loss of image edges and details. In this paper, we propose a joint group and residual sparse coding method for CS image recovery (JGRSC-CS). In the proposed JGRSC-CS, patch group is treated as the basic unit of sparse coding and two dictionaries (namely internal and external dictionaries) are applied to exploit the sparse representation of each group simultaneously. The internal self-adaptive dictionary is used to remove artifacts, and an external Gaussian Mixture Model (GMM) dictionary, learned from clean training images, is used to enhance details and texture. To make the proposed method effective and robust, the split Bregman method is adopted to reconstruct the whole image. Experimental results manifest the proposed JGRSC-CS algorithm outperforms existing state-of-the-art methods in both peak signal to noise ratio (PSNR) and visual quality., Comment: 27 pages, 7 figures

For flows, the singular cycles connecting saddle periodic orbit and saddle equilibrium can poten- tially result in the so-called singular horseshoe, which means the existence of a non-uniformly hyperbolic chaotic invariant set. However, it is very hard to find a specific dynamical system that exhibits such singular cycles in general. In this paper, the existence of the singular cycles involved in saddle periodic orbits is studied by two types of piecewise affine systems: one is the piecewise affine system having an admissible saddle point with only real eigenvalues and an admissible saddle periodic orbit, and the other is the piecewise affine system having an admissible saddle- focus and an admissible saddle periodic orbit. Precisely, several kinds of sufficient conditions are obtained for the existence of only one heteroclinic cycle or only two heteroclinic cycles in the two types of piecewise affine systems, respectively. In addition, some examples are presented to illustrate the results., Comment: 21 pages,5 figures

Background: We sought to determine if ripple oscillations (80-120Hz), detected in intracranial EEG (iEEG) recordings of epilepsy patients, correlate with an enhancement or disruption of verbal episodic memory encoding. Methods: We defined ripple and spike events in depth iEEG recordings during list learning in 107 patients with focal epilepsy. We used logistic regression models (LRMs) to investigate the relationship between the occurrence of ripple and spike events during word presentation and the odds of successful word recall following a distractor epoch, and included the seizure onset zone (SOZ) as a covariate in the LRMs. Results: We detected events during 58,312 word presentation trials from 7,630 unique electrode sites. The probability of ripple on spike (RonS) events was increased in the seizure onset zone (SOZ, p<0.04). In the left temporal neocortex RonS events during word presentation corresponded with a decrease in the odds ratio (OR) of successful recall, however this effect only met significance in the SOZ (OR of word recall 0.71, 95% CI: 0.59-0.85, n=158 events, adaptive Hochberg p<0.01). Ripple on oscillation events (RonO) that occurred in the left temporal neocortex non-SOZ also correlated with decreased odds of successful recall (OR 0.52, 95% CI: 0.34-0.80, n=140, adaptive Hochberg , p<0.01). Spikes and RonS that occurred during word presentation in the left middle temporal gyrus during word presentation correlated with the most significant decrease in the odds of successful recall, irrespective of the location of the SOZ (adaptive Hochberg, p<0.01). Conclusion: Ripples and spikes generated in left temporal neocortex are associated with impaired verbal episodic memory encoding.

J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial coordinate systems, we construct a tensorial potential which satisfies the wave equations. Inspired by the equations of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, generalized Einstein's equations in inertial systems are derived based on some assumptions. These equations reduce to Einstein's equations in case of weak field in harmonic coordinate systems., Comment: 13 pages, 1 figure, Version 4.0 of REVTeX

In this paper, a random clique network model to mimic the large clustering coefficient and the modular structure that exist in many real complex networks, such as social networks, artificial networks, and protein interaction networks, is introduced by combining the random selection rule of the Erd\"os and R\'enyi (ER) model and the concept of cliques. We find that random clique networks having a small average degree differ from the ER network in that they have a large clustering coefficient and a power law clustering spectrum, while networks having a high average degree have similar properties as the ER model. In addition, we find that the relation between the clustering coefficient and the average degree shows a non-monotonic behavior and that the degree distributions can be fit by multiple Poisson curves; we explain the origin of such novel behaviors and degree distributions., Comment: 7 pages,10 figures

The design, fabrication, and detailed calibration of essential building blocks towards fully integrated linear-optics quantum computation are discussed. Photonic devices are made from silicon nitride rib waveguides, where measurements on ring resonators show small propagation losses. Directional couplers are designed to be insensitive to fabrication variations. Their offset and coupling lengths are measured, as well as the phase difference between the transmitted and reflected light. With careful calibrations, the insertion loss of the directional couplers is found to be small. Finally, an integrated controlled-NOT circuit is characterized by measuring the transmission through different combinations of inputs and outputs. The gate fidelity for the CNOT operation with this circuit is estimated to be 99.81% after post selection. This high fidelity is due to our robust design, good fabrication reproducibility, and extensive characterizations.

Quantum information processing holds great promise for communicating and computing data efficiently. However, scaling current photonic implementation approaches to larger system size remains an outstanding challenge for realizing disruptive quantum technology. Two main ingredients of quantum information processors are quantum interference and single-photon detectors. Here we develop a hybrid superconducting-photonic circuit system to show how these elements can be combined in a scalable fashion on a silicon chip. We demonstrate the suitability of this approach for integrated quantum optics by interfering and detecting photon pairs directly on the chip with waveguide-coupled single-photon detectors. Using a directional coupler implemented with silicon nitride nanophotonic waveguides, we observe 97% interference visibility when measuring photon statistics with two monolithically integrated superconducting single photon detectors. The photonic circuit and detector fabrication processes are compatible with standard semiconductor thin-film technology, making it possible to implement more complex and larger scale quantum photonic circuits on silicon chips., Comment: 11 pages, 8 figures

A complete set of primitive orthogonal idempotents plays an important role in the representation theory of an associative algebra. In this paper, we construct a complete set of primitive orthogonal idempotents for any finite Brandt semigroup algebra., Comment: 10 pages

We revisit the famous Nos\'e-Hoover system in this paper and show the existence of some averagely conservative regions which are filled with an infinite sequence of nested tori. Depending on initial conditions, some invariant tori are of trefoil knot type, while the others are of trivial knot type. Moreover, we present a variety of interlinked invariant tori whose initial conditions are chosen from different averagely conservative regions and give all the interlinking numbers of those interlinked tori, showing that this quadratic system possesses so rich dynamic properties., Comment: 8 pages,8 figures

The wave-particle duality dates back to Einstein's explanation of the photoelectric effect through quanta of light and de Broglie's hypothesis of matter waves. Quantum mechanics uses an abstract description for the behavior of physical systems such as photons, electrons, or atoms. Whether quantum predictions for single systems in an interferometric experiment allow an intuitive understanding in terms of the particle or wave picture, depends on the specific configuration which is being used. In principle, this leaves open the possibility that quantum systems always either behave definitely as a particle or definitely as a wave in every experimental run by a priori adapting to the specific experimental situation. This is precisely what is tried to be excluded by delayed-choice experiments, in which the observer chooses to reveal the particle or wave character -- or even a continuous transformation between the two -- of a quantum system at a late stage of the experiment. We review the history of delayed-choice gedanken experiments, which can be traced back to the early days of quantum mechanics. Then we discuss their experimental realizations, in particular Wheeler's delayed choice in interferometric setups as well as delayed-choice quantum erasure and entanglement swapping. The latter is particularly interesting, because it elevates the wave-particle duality of a single quantum system to an entanglement-separability duality of multiple systems.

Although interference is a classical-wave phenomenon, the superposition principle, which underlies interference of individual particles, is at the heart of quantum physics. An interaction-free measurements (IFM) harnesses the wave-particle duality of single photons to sense the presence of an object via the modification of the interference pattern, which can be accomplished even if the photon and the object haven't interacted with each other. By using the quantum Zeno effect, the efficiency of an IFM can be made arbitrarily close to unity. Here we report an on-chip realization of the IFM based on silicon photonics. We exploit the inherent advantages of the lithographically written waveguides: excellent interferometric phase stability and mode matching, and obtain multipath interference with visibility above 98%. We achieved a normalized IFM efficiency up to 68.2%, which exceeds the 50% limit of the original IFM proposal., Comment: 4.5 pages + supplemental material