Search

The method of horizontal scaled factorial moments as outlined by Bialas and Peschanski was used to conduct intermittency analysis for $pp$ collisions at $\sqrt{s}=$ 0.9, 7 and 8 TeV from the CMS experiment. The data was obtained and processed from the CERN Open Data Portal. It was found from 1D analysis that the intermittency strength decreases with increasing energy, indicating that the signature of the $\alpha$-model of random cascading that the former is based on seems to be weakening. Intermittency was stronger in 2D, but did not reveal any clear trend with increasing collision energy.

Multifractal analysis was performed on $pp$ collision data at $\sqrt{s}=$ 0.9, 7 and 8 TeV from the CMS experiment at CERN. The data was obtained and processed from the CERN Open Data Portal. Vertical analysis was used to compute the generalised dimensions $D_q$ and the multifractal spectra $f(\alpha)$ of the data, which reveals the level of complexity of its pseudorapidity distribution. It was found that the $f(\alpha)$ curves widen with increasing collision energy, signalling an increase in branching complexity.

A Chou-Yang type multiplicity distribution comprising a total multiplicity component and a binomial asymmetry component is used to describe charged hadron multiplicity data at $\sqrt{s}=$ 0.9, 7 and 8 TeV from the CMS experiment at CERN. The data was obtained and processed from the CERN Open Data Portal. For the total multiplicity component, it was found that a convex sum of a Negative Binomial Distribution and a Furry-Yule Distribution is able to describe the shoulder-like structure characteristic of KNO scaling violation well. The mean cluster size produced from collisions was also found to increase with collision energy. A prediction is given for $pp$ collisions at $\sqrt{s}=$ 14 TeV.

The intermittency-type fluctuations as outlined by Bialas and Peschanski in the 1980s is analysed in $pp$ collisions at $\sqrt{s}=$ 0.9, 7 and 8 TeV from the CMS collaboration at CERN. Our preliminary analysis shows that the intermittency exponents in the bin-averaged scaled factorial moments decrease in magnitude with increasing collision energy at the TeV scale, which suggests that the cascading nature of multiparticle production described by the $\alpha$-model is weakening. We outline possible areas planned for future studies.

Oscillations in modified combinants ($C_j$s) have been of interest to multiparticle production mechanisms since the 1990s. Recently, there has been a discussion on how these oscillations can be reproduced by compounding a binomial distribution with a negative binomial distribution. In this work, we explore a stochastic branching model based on a simple interaction term $\lambda\overline{\psi}\phi\psi$ for partons and propose a hadronization scheme to arrive at the final multiplicity distribution. We study the effects that compounding our model with a binomial distribution has on $C_j$s and explore its physical implications. We find that there is a significant difference in the oscillations in $C_j$s between high energy $pp$ and $p\bar{p}$ scattering that our model can reproduce.

Giovannini's parton branching equation is integrated numerically using the 4th-order Runge-Kutta method. Using a simple hadronisation model, a charged-hadron multiplicity distribution is obtained. This model is then fitted to various experimental data up to the TeV scale to study how the Giovannini parameters vary with collision energy and type. The model is able to describe hadronic collisions up to the TeV scale and reveals the emergence of gluonic activity as the centre-of-mass energy increases. A prediction is made for $\sqrt{s}$ = 14 TeV., Comment: 11 pages, 14 figures, 8 tables

It has been shown recently that additional information can be obtained from charged particle multiplicity distribution by investigating their modified combinants $C_j$, which exhibit periodic oscillatory behaviour. The modified combinants obtained from experimental data can be expressed in a recurrent form involving the probability of obtaining $N$ charged particles $P(N)$, scaled by the void probability $P(0)$. The effects of various experimental observables such as $|\eta|$, $p_T$ and centre-of-mass collision energy $\sqrt{s}$ on the oscillatory behaviour of $C_j$ will be discussed., Comment: 5 pages, 2 figures. Proceedings for the SSEAN 2019 Meeting

We propose a scheme for entanglement distribution among different single atoms trapped in separated cavities. In our scheme, by reflecting an input coherent optical pulse from a cavity with a single trapped atom, a controlled phase-shift gate between the atom and the coherent optical pulse is achieved. Based on this gate and homodyne detection, we construct an $n$-qubit parity gate and show its use for distribution of a large class of entangled states in one shot, including the GHZ state $\left\vert GHZ_{n}\right\rangle $, W state $\left\vert W_{n}\right\rangle $, Dicke state $\left\vert D_{n,k}\right\rangle $ and certain sums of Dicke states $% \left\vert G_{n,k}\right\rangle $. We also show such distribution could be performed with high success probability and high fidelity even in the presence of channel loss., Comment: 8 pages, 6 figures

A new approach to the classical limit of Grover's algorithm is discussed by assuming a very rapid dephasing of a system between consecutive Grover's unitary operations, which drives pure quantum states to decohered mixed states. One can identify a specific element among $N$ unsorted elements by a probability of the order of unity after $k\sim N$ steps of classical amplification, which is realized by a combination of Grover's unitary operation and rapid dephasing, in contrast to $k\sim \pi \sqrt{N}/4$ steps in quantum mechanical amplification. The initial two-state system with enormously unbalanced existence probabilities, which is realized by a chosen specific state and a superposition of all the rest of states among $N$ unsorted states, is crucial in the present analysis of classical amplification. This analysis illustrates Grover's algorithm in extremely noisy circumstances. A similar increase from $k\sim \sqrt{N}$ to $k\sim N$ steps due to the loss of quantum coherence takes place in the {\em analog} model of Farhi and Gutmann where the entanglement does not play an obvious role. This supports a view that entanglement is crucial in quantum computation to describe quantum states by a set of qubits, but the actual speedup of the quantum computation is based on quantum coherence., Comment: 15 pages. Substantially modified with an additional author and the change of the title. This version is going to be published in Mod. Phys. Lett. A

Genuine multipartite entanglement has been found in some spin chain systems. However, genuine multipartite nonlocality, which is much rarer than genuine multipartite entanglement, has never been found in any spin chain system. Here we present genuine multipartite nonlocality in a spin chain system. After introducing the definition of genuine multipartite nonlocality and a multipartite Bell-type inequality, we construct a group of joint measurements for the inequality in a one-dimensional ferromagnetic $N$-qubit chain with nearest-neighbor XXZ interaction, and many violations to the inequality have been found. The violations do indicate that genuine multipartite nonlocality exists in this ferromagnetic spin-1/2 chain system. Last but not least, we also calculate genuine multipartite entanglement concurrence in the same spin chain to demonstrate the difference and relationship between genuine multipartite nonlocality and genuine multipartite entanglement., Comment: 7 pages, 5 figures

In this work, the absorption spectrum of a two-level ion in a linear Paul trap is investigated, the ion is supposed to be driven by two orthogonal laser beams, the one along the axial of the trap acts as the control light beam, the other as probe beam. When the frequency of the control laser is tuned to the first red sideband of the ionic transition, the coupling between the internal states of the ion and vibrational mode turns out to be a Jaynes-Cummings (JC) Hamiltonian, which together with the coupling between the probe beam and the two-level ion constructs a {\Lambda}-type three-level structure. In this case the transparency window may appear in the absorption spectrum of the probe light, which is induced by the ionic vibration and is very similar to the cavity induced transparency [1996 Opt. Commun. 126 230-235]. On the other hand, when the frequency of the control laser is tuned to the first blue sideband of the ionic transition, the two-level ion and vibrational mode are governed by an anti-Jaynes-Cummings (anti-JC) Hamiltonian, the total system including the probe beam forms a V -type threelevel structure. And the Autler-Townes splitting in the absorption spectrum is found., Comment: 6 pages, 3 figures, accepted for publication by Laser Physics Letters

We propose a hierarchy of Bell-type inequalities for arbitrary $n$-partite systems that identify the different degrees of nonlocality ranging from standard to genuine multipartite nonlocality. After introducing the definition of nonsignaling $m$-locality, we show that the observed joint probabilities in any nonsignaling $m$-local realistic models should satisfy the $(m-1)$-th Bell-type inequality. When $m=2$ the corresponding inequality reduces to the one shown in [Phys. Rev. Lett. 112, 140404 (2014)] whose violation indicates genuine multipartite nonlocality, and when $m=n$ the corresponding inequality is just Hardy's inequality whose violation indicates standard multipartite nonlocality. Furthermore, several examples are provided to demonstrate their hierarchy of multipartite nonlocality., Comment: 6 pages

A conceptually simpler proof of the separability criterion for two-qubit systems, which is referred to as "Hefei inequality" in literature, is presented. This inequality gives a necessary and sufficient separability criterion for any mixed two-qubit system unlike the Bell-CHSH inequality that cannot test the mixed-states such as the Werner state when regarded as a separability criterion. The original derivation of this inequality emphasized the uncertainty relation of complementary observables, but we show that the uncertainty relation does not play any role in the actual derivation and the Peres-Hodrodecki condition is solely responsible for the inequality. Our derivation, which contains technically novel aspects such as an analogy to the Dirac equation, sheds light on this inequality and on the fundamental issue to what extent the uncertainty relation can provide a test of entanglement. This separability criterion is illustrated for an exact treatment of the Werner state., Comment: 7 pages. The presentation up-dated and made more precise

The practically useful criteria of separable states $\rho=\sum_{k}w_{k}\rho_{k}$ in $d=2\times2$ are discussed. The equality $G({\bf a},{\bf b})= 4[\langle \psi|P({\bf a})\otimes P({\bf b})|\psi\rangle-\langle \psi|P({\bf a})\otimes{\bf 1}|\psi\rangle\langle \psi|{\bf 1}\otimes P({\bf b})|\psi\rangle]=0$ for any two projection operators $P({\bf a})$ and $P({\bf b})$ provides a necessary and sufficient separability criterion in the case of a separable pure state $\rho=|\psi\rangle\langle\psi|$. We propose the separability criteria of mixed states, which are given by ${\rm Tr}\rho\{{\bf a}\cdot {\bf \sigma}\otimes {\bf b}\cdot {\bf \sigma}\}=(1/3)C\cos\varphi$ for two spin $1/2$ systems and $4{\rm Tr}\rho \{P({\bf a})\otimes P({\bf b})\}=1+(1/2)C\cos2\varphi$ for two photon systems, respectively, after taking a geometrical angular average of ${\bf a}$ and ${\bf b}$ with fixed $\cos\varphi={\bf a}\cdot{\bf b}$. Here $-1\leq C\leq 1$, and the difference in the numerical coefficients $1/2$ and $1/3$ arises from the different rotational properties of the spinor and the transverse photon. If one instead takes an average over the states in the $d=2$ Hilbert space, the criterion for two photon systems is replaced by $4{\rm Tr}\rho \{P({\bf a})\otimes P({\bf b})\}=1+(1/3)C\cos2\varphi$. Those separability criteria are shown to be very efficient using the existing experimental data of Aspect et al. in 1981 and Sakai et al. in 2006. When the Werner state is applied to two photon systems, it is shown that the Hilbert space average can judge its inseparability but not the geometrical angular average., Comment: 14 pages, 3 figures

The existence of minimal length scale has motivated the proposal of generalized uncertainty principle, which provides a potential routine to probe quantum gravitational effects in low-energy quantum mechanics experiment. Hitherto, the tabletop experiment of testing deviations from ordinary quantum mechanics are mostly based on microscopic objects. However, the feasibility of these studies are challenged by the recent study of spacetime quantization for composite macroscopic body. In this paper, we propose a scheme to probe quantum gravity effects by revealing the deviations from predictions of Heisenberg uncertainty principle. Our scheme focus on manipulating the interaction sequences between external laser fields and a single trapped ion to seek evidence of spacetime quantization, therefore reduce the complicity induced by large bodies to some extent. The relevant study for microscopic particles is crucial considering the lack of satisfactory theories regarding basic properties for multi-particles in the framework of quantum gravity. Meanwhile, we are managed to set a new upper limit for deformation parameter.

Bound entanglement, being entangled yet not distillable, is essential to our understandings of the relations between nonlocality and entanglement besides its applications in certain quantum information tasks. Recently, bound entangled states that violate a Bell inequality have been constructed for a two-qutrit system, disproving a conjecture by Peres that bound entanglement is local. Here we shall construct such kind of nonlocal bound entangled states for all finite dimensions larger than two, making possible their experimental demonstrations on most general systems. We propose a Bell inequality, based on a Hardy-type argument for nonlocality, and a steering inequality to identify their nonlocality. We also provide a family of entanglement witnesses to detect their entanglement beyond the Bell inequality and the steering inequality., Comment: 9 Pages, 2 Tables + 3 Figures

Being able to implement effective entanglement distribution in noisy environments is a key step towards practical quantum communication, and long-term efforts have been made on the development of it. Recently, it has been found that the null-result weak measurement (NRWM) can be used to enhance probabilistically the entanglement of a single copy of amplitude-damped entangled state. This paper investigates remote distributions of bipartite and multipartite entangled states in the amplitudedamping environment by combining NRWMs and entanglement distillation protocols (EDPs). We show that the NRWM has no positive effect on the distribution of bipartite maximally entangled states and multipartite Greenberger-Horne-Zeilinger states, although it is able to increase the amount of entanglement of each source state (noisy entangled state) of EDPs with a certain probability. However, we find that the NRWM would contribute to remote distributions of multipartite W states. We demonstrate that the NRWM can not only reduce the fidelity thresholds for distillability of decohered W states, but also raise the distillation efficiencies of W states. Our results suggest a new idea for quantifying the ability of a local filtering operation in protecting entanglement from decoherence., Comment: 15 pages, 9 figures. Minor revision has been made

We present observable lower bounds for several bipartite entanglement measures including entanglement of formation, geometric measure of entanglement, concurrence, convex-roof extended negativity, and G-concurrence. The lower bounds facilitate estimates of these entanglement measures for arbitrary finite-dimensional bipartite states. Moreover, these lower bounds can be calculated analytically from the expectation value of a single observable. Based on our results, we use several real experimental measurement data to get lower bounds of entanglement measures for these experimentally realized states. In addition, we also study the relations between entanglement measures., Comment: 10 pages, 4 figures

We propose a hybrid quantum architecture for engineering a photonicMott insulator-superfluid phase transition in a two-dimensional (2D) square lattice of a superconducting transmission line resonator (TLR) coupled to a single nitrogen-vacancy (NV) center encircled by a persistent current qubit. The localization-delocalization transition results from the interplay between the on-site repulsion and the nonlocal tunneling. The phase boundary in the case of photon hopping with real-valued and complex-valued amplitudes can be obtained using the mean-field approach. Also, the quantum jump technique is employed to describe the phase diagram when the dissipative effects are considered. The unique feature of our architecture is the good tunability of effective on-site repulsion and photon-hopping rate, and the local statistical property of TLRs which can be analyzed readily using presentmicrowave techniques. Our work opens new perspectives in quantum simulation of condensed-matter and many-body physics using a hybrid spin circuit-QED system. The experimental challenges are realizable using currently available technologies.

By incorporating the asymmetry of local protocols, i.e., some party has to start with a nontrivial measurement, into an operational method of detecting the local indistinguishability proposed by Horodecki {\it et al.} [Phys.Rev.Lett. 90 047902 (2003)], we derive a computable criterion to efficiently detect the local indistinguishability of maximally entangled states. Locally indistinguishable sets of $d$ maximally entangled states in a $d\otimes d$ system are systematically constructed for all $d\ge 4$ as an application. Furthermore, by exploiting the fact that local protocols are necessarily separable, we explicitly construct small sets of $k$ locally indistinguishable maximally entangled states with the ratio $k/d$ approaching 3/4. In particular, in a $d\otimes d$ system with even $d\ge 6$, there always exist $d-1$ maximally entangled states that are locally indistinguishable by separable measurements., Comment: 6 pages, 1 table

We establish a quantitative relation between Hardy's paradox and the breaking of uncertainty principle in the sense of measurement-disturbance relations in the conditional measurement of non-commuting operators. The analysis of the inconsistency of local realism with entanglement by Hardy is simplified if this breaking of measurement-disturbance relations is taken into account, and a much simplified experimental test of local realism is illustrated in the framework of Hardy's thought experiment. The essence of Hardy's model is identified as a combination of two conditional measurements, which give rise to definite eigenvalues to two non-commuting operators simultaneously in hidden-variables models. Better understanding of the intimate interplay of entanglement and measurement-disturbance is crucial in the current discussions of Hardy's paradox using the idea of weak measurement, which is based on a general analysis of measurement-disturbance relations., Comment: 6 pages. PRA (in press)

A kind of paradoxical effects has been demonstrated that the pigeonhole principle, i.e., if three pigeons are put in two pigeonholes then at least two pigeons must stay in the same hole, fails in certain quantum mechanical scenario. Here we shall show how to associate a proof of Kochen-Specker theorem with a quantum pigeonhole effect and vise versa, e.g., from state-independent proofs of Kochen-Specker theorem some kind of state-independent quantum pigeonhole effects can be demonstrated. In particular, a state-independent version of the quantum Cheshire cat, which can be rendered as a kind of quantum pigeonhole effect about the trouble of putting two pigeons in two or more pigeonholes, arises from Peres-Mermin's magic square proof of contextuality., Comment: The last example is replaced by GHZ paradoxes from qudit graphs

Controlling the decoherence induced by the interaction of quantum system with its environment is a fundamental challenge in quantum technology. Utilizing Floquet theory, we explore the constructive role of temporal periodic driving in suppressing decoherence of a spin-1/2 particle coupled to a spin bath. It is revealed that, accompanying the formation of a Floquet bound state in the quasienergy spectrum of the whole system including the system and its environment, the dissipation of the spin system can be inhibited and the system tends to coherently synchronize with the driving. It can be seen as an analog to the decoherence suppression induced by the structured environment in spatially periodic photonic crystal setting. Comparing with other decoherence control schemes, our protocol is robust against the fluctuation of control parameters and easy to realize in practice. It suggests a promising perspective of periodic driving in decoherence control., Comment: 8 pages, 5 figures

Tunneling experiment is a key technique for detecting Majorana fermion in solid state systems. We use Keldysh non-equilibrium Green function method to study multi-lead tunneling in superconducting nanowire with Rashba and Dresselhaus spin-orbit couplings. A zero-bias \textit{dc} conductance peak appears in our setup which signifies the existence of Majorana fermion and is in accordance with previous experimental results on InSb nanowire. Interestingly, due to the exotic property of Majorana fermion, there exists a hole transmission channel which makes the currents asymmetric at the left and right leads. The \textit{ac} current response mediated by Majorana fermion is also studied here. To discuss the impacts of Coulomb interaction and disorder on the transport property of Majorana nanowire, we use the renormalization group method to study the phase diagram of the wire. It is found that there is a topological phase transition under the interplay of superconductivity and disorder. We find that the Majorana transport is preserved in the superconducting-dominated topological phase and destroyed in the disorder-dominated non-topological insulator phase.

In this work, the dynamics of the deformed one-dimensional harmonic oscillator with minimal length uncertainty is examined and the analytical solutions for time evolution of position and momentum operators are presented in which the rough approximation that neglects the higher order terms in BakerHausdor lemma is avoided. Based on these analytical solutions the uncertainties for position and momentum operators are calculated in a coherent state, and an unexpected squeezing effect in both coordinate and momentum directions is found in comparison with ordinary harmonic oscillator. Obviously such a squeezing effect is induced by the minimal length uncertainty (gravitational effects). Our results are applied to the electrons trapped in strong magnetic fields to examine the degree of the existing squeezing effect in a real system, which shows the squeezing degree induced by minimal length uncertainty is very small., Comment: 9 pages, 3 figures

Fragile quantum features such as entanglement are employed to improve the precision of parameter estimation and as a consequence the quantum gain becomes vulnerable to noise. As an established tool to subdue noise, quantum error correction is unfortunately overprotective because the quantum enhancement can still be achieved even if the states are irrecoverably affected, provided that the quantum Fisher information, which sets the ultimate limit to the precision of metrological schemes, is preserved and attained. Here, we develop a theory of robust metrological schemes that preserve the quantum Fisher information instead of the quantum states themselves against noise. After deriving a minimal set of testable conditions on this kind of robustness, we construct a family of $2t+1$ qubits metrological schemes being immune to $t$-qubit errors after the signal sensing. In comparison at least five qubits are required for correcting arbitrary 1-qubit errors in standard quantum error correction., Comment: 12 pages, 4 figures

Heisenberg's uncertainty relations for measurement quantify how well we can jointly measure two complementary observables and have attracted much experimental and theoretical attention recently. Here we provide an exact tradeoff between the worst-case errors in measuring jointly two observables of a qubit, i.e., all the allowed and forbidden pairs of errors, especially asymmetric ones, are exactly pinpointed. For each pair of optimal errors we provide an optimal joint measurement that is realizable without introducing any ancilla and entanglement. Possible experimental implementations are discussed and Toronto experiment [Rozema et al., Phys. Rev. Lett. 109, 100404 (2012)] can be readily adapted to an optimal joint measurement of two orthogonal observables., Comment: 4 pages, 2 figures

We extend the recent result of bipartite Bell singlet [Carr and Saffman, Phys. Rev. Lett. {\bf111}, (2013)] to a stationary three-dimensional entanglement between two-individual neutral Rydberg atoms. This proposal makes full use of the coherent dynamics provided by Rydberg mediated interaction and the dissipative factor originating from the spontaneous emission of Rydberg state. The numerical simulation of the master equation reveals that both the target state negativity ${\cal N}(\hat\rho_{\infty})$ and fidelity ${\cal F}(\hat\rho_{\infty})$ can exceed 99.90%. Furthermore, a steady three-atom singlet state $|S_3\rangle$ is also achievable based on the same mechanism., Comment: 7 pages, 4 figures

In comparison with entanglement and Bell nonlocality, Einstein-Podolsky-Rosen steering is a newly emerged research topic and in its incipient stage. Although Einstein-Podolsky-Rosen steering has been explored via violations of steering inequalities both theoretically and experimentally, the known inequalities in the literatures are far from well-developed. As a result, it is not yet possible to observe Einstein-Podolsky-Rosen steering for some steerable mixed states. Recently, a simple approach was presented to identify Einstein-Podolsky-Rosen steering based on all-versus-nothing argument, offering a strong condition to witness the steerability of a family of two-qubit (pure or mixed) entangled states. In this work, we show that the all-versus-nothing proof of Einstein-Podolsky-Rosen steering can be tested by measuring the projective probabilities. Through the bound of probabilities imposed by local-hidden-state model, the proposed test shows that steering can be detected by the all-versus-nothing argument experimentally even in the presence of imprecision and errors. Our test can be implemented in many physical systems and we discuss the possible realizations of our scheme with non-Abelian anyons and trapped ions., Comment: 8 pages, 3 figures. Accepted by Scientific Reports

We develop a general and consistent model of neutrino oscillation based on the quantum field theoretical description of the neutrino production and detection processes. Emphasis is placed on the locality of the interactions of these processes, where on top of the usual application of the four fermion local Hamiltonian, we assume that weak interactions switched on only when the wave functions of the particles involved are overlapping and switched off upon their separation. A key assumption in our treatment is that the wave packet sizes of the particles, in particular, the neutrino producing source particles and the neutrino absorbing detector particles, are taken to be negligible compared with their mean free path in their respective medium. With this assumption, and taking into considerations of the finite time of neutrino production, neutrino wave packets with well-defined edges are generated. This fact, together with the locality of weak interactions, enable us to relate the propagation time to the propagation distance, thus doing away with the ad hoc time averaging procedure normally employing in derivations of neutrino oscillation formula. No assumptions on the particular forms of particle wave functions; for example, Gaussians, need to be made. A good feature of our approach is that the neutrino oscillation formula is automatically normalised if the in-going states of the production and detection processes are normalised. We also show that causality and unitarity cannot both be satisfied in virtual neutrino models., Comment: 32 pages, 10 figures

We re-examine d=4 hidden-variables-models for a system of two spin-$1/2$ particles in view of the concrete model of Hardy, who analyzed the criterion of entanglement without referring to inequality. The basis of our analysis is the linearity of the probability measure related to the Born probability interpretation, which excludes non-contextual hidden-variables models in $d\geq 3$. To be specific, we note the inconsistency of the non-contextual hidden-variables model in $d=4$ with the linearity of the quantum mechanical probability measure in the sense $\langle\psi|{\bf a}\cdot {\bf \sigma}\otimes{\bf b}\cdot {\bf \sigma}|\psi\rangle+\langle\psi|{\bf a}\cdot {\bf \sigma}\otimes{\bf b}^{\prime}\cdot {\bf \sigma}|\psi\rangle=\langle\psi|{\bf a}\cdot {\bf \sigma}\otimes ({\bf b}+{\bf b}^{\prime})\cdot {\bf \sigma}|\psi\rangle$ for non-collinear ${\bf b}$ and ${\bf b}^{\prime}$. It is then shown that Hardy's model in $d=4$ does not lead to a unique mathematical expression in the demonstration of the discrepancy of local realism (hidden-variables model) with entanglement and thus his proof is incomplete. We identify the origin of this non-uniqueness with the non-uniqueness of translating quantum mechanical expressions into expressions in hidden-variables models, which results from the failure of the above linearity of the probability measure. In contrast, if the linearity of the probability measure is strictly imposed, which is tantamount to asking that the non-contextual hidden-variables model in $d=4$ gives the CHSH inequality $|\langle B\rangle|\leq 2$ uniquely, it is shown that the hidden-variables model can describe only separable quantum mechanical states; this conclusion is in perfect agreement with the so-called Gisin's theorem which states that $|\langle B\rangle|\leq 2$ implies separable states., Comment: 15 pages. To appear in Int. J. Mod. Phys. A

Whereas complementarity manifests itself via two incompatible observables, quantum contextuality can only be revealed via the joint measurements among at least three observables. By incorporating unsharp measurements and joint measurements into a realistic model, we reestablish an inequality due to Liang, Spekkens, and Wiseman rigorously based on the assumption of noncontextuality alone. Its violation therefore unambiguously pinpoints the quantum contextuality of a two-level system. The maximal violation is attained by three triplewise jointly measurable observables that are pairwise jointly measured in an incompatible way. We also present the necessary and sufficient condition of triplewise joint measurability of three unbiased observables of a qubit., Comment: 8 pages and 2 figures, Comments are welcome

We present a proposal for generation of a robust tripartite Greenberger-Horne-Zeilinger state among three-individual neutral Rydberg atoms. By modulating the relation between two-photon detuning and Rydberg interaction strength $U_{ij}(r)$, an effective Raman coupling is obtained between the hyperfine ground states $|F=2,M=2\rangle$ of three $^{87}$Rb atoms and the Rydberg states $|rrr\rangle$ via the third-order perturbation theory. This method is also capable of implementing a three-qubit controlled-phase gate with each qubit encoded into the hyperfine ground states $|F=1,M=1\rangle$ and $|F=2,M=2\rangle$. As an extension, we generalize our scheme to the case of multipartite GHZ state and quantum gate in virtue of high-order perturbation theory., Comment: 6 pages, 5 figures

Entanglement is studied in the framework of Dyson's S-matrix theory in relativistic quantum field theory, which leads to a natural definition of entangled states of a particle-antiparticle pair and the spin operator from a Noether current. As an explicit example, the decay of a massive pseudo-scalar particle into a pair of electron and positron is analyzed. Two spin operators are extracted from the Noether current. The Wigner spin operator characterizes spin states at the rest frame of each fermion and, although not measurable in the laboratory, gives rise to a straightforward generalization of low energy analysis of entanglement to the ultra-relativistic domain. In contrast, if one adopts a (modified) Dirac spin operator, the entanglement measured by spin correlation becomes maximal near the threshold of the decay, while the entanglement is replaced by the classical correlation for the ultra-relativistic electron-positron pair by analogy to the case of neutrinos, for which a hidden-variables-type description is possible. Chiral symmetry differentiates the spin angular momentum and the magnetic moment. The use of weak interaction that can measure helicity is suggested in the analysis of entanglement at high energies instead of a Stern-Gerlach apparatus which is useless for the electron. A difference between the electron spin at high energies and the photon linear polarization is also noted. The Standard Model can describe all the observable properties of leptons., Comment: 17 pages. Substantially modified and extended. The title has been changed. To appear in PRD

We present a dissipative protocol to engineer two $^{87}Rb$ atoms into a form of three-dimensional entangled state via spontaneous emission. The combination of coupling between ground states via microwave fields and dissipation induced by spontaneous emission make the current scheme deterministic and a stationary entangled state can always be achieved without state initialization. Moreover, this scheme can be straightforwardly generalized to preparation of an $N$-dimensional entangled state in principle., Comment: 5 pages, 5 figures

Topological feature has become an intensively studied subject in many fields of physics. As a witness of topological phase, the edge states are topologically protected and may be helpful in quantum information processing. In this paper, we define a measure to quantify the dynamical localization of system and simulate the localization in the 1D Aubry-Andr\'{e} model. We find an interesting connection between the edge states and the dynamical localization of the system, this connection may be used as a signature of edge state and topological phase., Comment: 5 pages, 6 figures

In statistical mechanics, any quantum system in equilibrium with its weakly coupled reservoir is described by a canonical state at the same temperature as the reservoir. Here, by studying the equilibration dynamics of a harmonic oscillator interacting with a reservoir, we evaluate microscopically the condition under which the equilibration to a canonical state is valid. It is revealed that the non-Markovian effect and the availability of a stationary state of the total system play a profound role in the equilibration. In the Markovian limit, the conventional canonical state can be recovered. In the non-Markovian regime, when the stationary state is absent, the system equilibrates to a generalized canonical state at an effective temperature; whenever the stationary state is present, the equilibrium state of the system cannot be described by any canonical state anymore. Our finding of the physical condition on such noncanonical equilibration might have significant impact on statistical physics. A physical scheme based on circuit QED is proposed to test our results.

Studying out-of-equilibrium physics in quantum systems under quantum quench is of vast experimental and theoretical interests. Using periodic quantum quenches, we present an experimentally accessible scheme to simulate the quantum Zeno and anti-Zeno effects in an open quantum system of a single superconducting qubit interacting with an array of transmission line resonators. The scheme is based on the following two observations: Firstly, compared with conventional systems, the short-time non-exponential decay in our superconducting circuit system is readily observed; and secondly, a quench-off process mimics an ideal projective measurement when its time duration is sufficiently long. Our results show the active role of quantum quench in quantum simulation and control., Comment: 5 pages, 3 figures

We present a new approach for implementing a $\sqrt{\rm swap}$ gate between two spatially far apart sites connected by a large-size coupled cavity array as quantum bus. The duration is only related to the parity of cavity number but independent of a specific number of cavity, thus it is possible to process quantum information in an arbitrary long distance in principle without time varied. Referring to the recent experimental progresses on coupled-cavity array, we also make an assessment of the scalability and take the cavity number $N$ = 5 as an example to illustrate the robustness of our proposal via quantum process tomography., Comment: 5 pages, 4 figures

Heisenberg's uncertainty principle is quantified by error-disturbance tradeoff relations, which have been tested experimentally in various scenarios. Here we shall report improved new versions of various error-disturbance tradeoff relations by decomposing the measurement errors into two different components, namely, operator bias and fuzziness. Our improved uncertainty relations reveal the tradeoffs between these two components of errors, and imply various conditionally valid error-tradeoff relations for the unbiased and projective measurements. We also design a quantum circuit to measure the two components of the error and disturbance.

We present two efficient methods for implementing the Fredkin gate with atoms separately trapped in an array of three high-$Q$ coupled cavities. The first proposal is based on the resonant dynamics, which leads to a fast resonant interaction in a certain subspace while leaving others unchanged, and the second one utilizes a dispersive interaction such that the effective long-distance dipole-dipole interaction between two distributed target qubits is achieved by virtually excited process. Both schemes can achieve the standard form of the Fredkin gate in a single step without any subsequent single-qubit operation. The effects of decoherence on the performance of the gate are also analyzed in virtue of master equation, and the strictly numerical simulation reveals that the average fidelity of the quantum gate is high., Comment: title changed

Quantum correlation provides a promising measure beyond entanglement. Here, we propose a necessary and sufficient condition for nonzero quantum correlation in continuous variable systems, which is simple and easy to perform in terms of a marker $Q_r$. In order to get this condition, we introduce continuous-variable local orthogonal bases of the operator space, which are generalized from the orthogonal basis sets in local operator space for discrete variables. Based on this, we obtain the marker $Q_r$ for all bipartite continuous variable states, and provide several examples including two-mode Gaussian and non-Gaussian states. Our result may provide a candidate for quantum correlation measures, and can be measured by designed quantum circuits., Comment: 17 pages, 2 figures

Entanglement detection and estimation are fundamental in quantum information science. Compared with discrete-variable states, for which lots of efficient entanglement detection criteria and lower bounds of entanglement measures have been proposed, the continuous-variable entanglement is much less understood. Here we shall present a family of entanglement witnesses based on continuous-variable local orthogonal observables (CVLOOs) to detect and estimate entanglement of Gaussian and non-Gaussian states, especially for bound entangled states. By choosing an optimal set of CVLOOs our entanglement witness is equivalent to the realignment criterion and can be used to detect bound entanglement of a class of 2+2 mode Gaussian states. Via our entanglement witness, lower bounds of two typical entanglement measures for arbitrary two-mode continuous-variable states are obtained., Comment: 11 pages, 1 figure

Protecting quantum correlation from decoherence is one of the crucial issues in quantum information processing. It has been commonly recognized that any initial quantum correlation of a composite system diminishes asymptotically or abruptly to zero under local Markovian decoherence. Here we show that, contrary to this recognition, a noticeable Gaussian quantum discord of a continuous-variable bipartite system can be frozen in the steady state in the non-Markovian dynamics if each of the subsystems forms a localized mode with its local reservoir. The condition for this frozen quantum discord can be reached by appropriately engineering the structure of the reservoirs. The possible realization of our results in a coupled cavity array system formed by a photonic crystal is proposed., Comment: 6 pages, 5 figures

Nonlocal correlations as revealed by the violations to Bell inequalities are incompatible with local models without any nonlocal correlations. However some tripartite entangled states, e.g., symmetric pure states, exhibit a stronger nonlocality even incompatible with hybrid local/nonlocal models allowing nonlocal correlations between any two parties. Here we propose a three-particle Hardy-type test without inequality, as illustrated by a gedanken experiment, that is failed by all non-signaling local models while is passed by all tripartite entangled asymmetric pure states. Our result implies that every tripartite entangled state, regardless of the dimensions of the underlying Hilbert spaces, passes a Hardy-type test and therefore is genuine tripartite nonlocal. Maximal success probability and a generalization to multipartite cases of our test are also presented.

We examine the topological properties of a spin-singlet superconductor with Rashba and Dresselhaus (110) spin-orbit couplings. We demonstrate that there are several topological invariants in the Bogoliubov-de Gennes (BdG) Hamiltonian by symmetry analysis. We use the Pfaffian invariant $\mathcal{P}$ for the particle-hole symmetry to demonstrate all the possible phase diagrams of the BdG Hamiltonian. We find that the edge spectrum is either Dirac cone or flat band which supports the emergence of the Majorana fermion in this system. For the Majorana flat bands, a higher symmetric BdG Hamiltonian is needed to make them topologically stable. The Pfaffian invariant $\mathcal{P}(k_{y})$ and the winding number $\mathcal{W}(k_{y})$ are used in determining the location of the Majorana flat bands.