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Quantum information scrambling describes the rapid spread of initially localized information across an entire quantum many-body system through entanglement generation. Once scrambled, the original local information becomes encoded globally, inaccessible from any single subsystem. In this work, we introduce a protocol that enables information scrambling into the past, allowing decoding even before the original information is generated. This protocol is achieved by simulating a closed timelike curve (a theoretical construct in which particles can traverse backward in time) using probabilistic methods. Remarkably, we find that stronger scrambling dynamics enhance the fidelity of the decoding process. We further present a quantum circuit design and experimentally implement our protocol on cloud-based Quantinuum and IBM quantum computers. Our approach illuminates a unique quantum task: retrieving information encoded in the future without altering the past., Comment: 12 pages, 6 figures, 3 tables

We investigate non-Markovian transport dynamics and signatures of the Kondo effect in a single impurity Anderson model. The model consists of a quantum dot (QD) with ultra-strong coupling to a left lead and weak coupling to a right lead acting as a detector. We calculate the waiting time distribution (WTD) of electrons tunneling into the detector using a combination of the hierarchical equations of motion approach (HEOM) and a dressed master equation. Oscillations emerge in the short-time WTD, becoming more pronounced with stronger left-lead coupling. Fourier analysis reveals a blue shift in the oscillation frequency as coupling increases, indicating enhanced system-bath hybridization. Crucially, comparison with a dressed master equation confirms that these oscillations are a direct consequence of non-Markovian system-bath correlations. We examine the Kondo effect's influence on these oscillations by varying the quantum dot's Coulomb repulsion. Increasing this interaction enhances the WTD oscillations, coinciding with the signatures of a strengthened Kondo resonance in the quantum dot's density of states. Our results demonstrate that WTD oscillations offer a valuable tool for probing non-Markovian system-bath interactions and the emergence of Kondo correlations within quantum dot systems., Comment: 14 pages, 12 figures

Exceptional points (EPs) are singularities in the spectra of non-Hermitian operators, where eigenvalues and eigenvectors coalesce. Recently, open quantum systems have been increasingly explored as EP testbeds due to their natural non-Hermitian nature. However, existing works mostly focus on the Markovian limit, leaving a gap in understanding EPs in the non-Markovian regime. In this work, we address this gap by proposing a theoretical framework based on two numerically exact descriptions of non-Markovian dynamics: the pseudomode mapping and the hierarchical equations of motion. The proposed framework enables conventional spectral analysis for EP identification, establishing direct links between EPs and dynamic manifestations in open systems, such as non-exponential decays and enhanced sensitivity to external perturbations. We unveil pure non-Markovian EPs that are unobservable in the Markovian limit. Remarkably, the EP aligns with the Markovian-to-non-Markovian transition, and the EP condition is adjustable by modifying environmental spectral properties. Moreover, we show that structured environments can elevate EP order, thereby enhancing the system's sensitivity. These findings lay a theoretical foundation and open new avenues for non-Markovian reservoir engineering and non-Hermitian physics., Comment: 10+5 pages, 2 figures

The Liouvillian skin effect and the non-Hermitian skin effect have both been used to explain the localization of eigenmodes near system boundaries, though the former is arguably more accurate in some regimes due to its incorporation of quantum jumps. However, these frameworks predominantly focus on weak Markovian interactions, neglecting the potentially crucial role of memory effects. To address this, we investigate, utilizing the powerful hierarchical equations of motion method, how a non-Markovian environment can modify the Liouvillian skin effect. We demonstrate that a non-Markovian environment can induce a ``thick skin effect", where the skin mode broadens and shifts into the bulk. {We further identify that the skin-mode quantum coherence can only be generated when the coupling contains counter-rotating terms}, leading to the coherence-delocalization and oscillatory relaxation with a characteristic linear scaling with system size. Remarkably, both the skin-mode and steady-state coherence exhibit resistance to decoherence from additional environmental noise. These findings highlight the profound impact of system-bath correlations on relaxation and localization, revealing unique phenomena beyond conventional Markovian approximations., Comment: 15 pages, 9 figures

A sender can prepare a quantum state for a remote receiver using preshared entangled pairs, only the sender's single-qubit measurement, and the receiver's simple correction informed by the sender. It provides resource-efficient advantages over quantum teleportation for quantum information. Here, we propose the most efficient approach to detect the remote state preparation (RSP) based on the quantum benefits powered by quantum coherence's static resources of the shared pairs and the dynamic resources both the RSP participants input. It requires only the receiver's minimum of one additional coherence creation operation to verify RSP. Experimentally, we implement the introduced RSP assessment using different photon pair states generated from a high-quality polarization Sagnac interferometer, confirming the necessary and sufficient role played by the static and dynamic quantum coherence resources and demonstrating efficient RSP verification. Our results provide a route to efficiently assess RSP in practical scenarios such as quantum information in quantum networks.

To unequivocally distinguish genuine quantumness from classicality, a widely adopted approach focuses on the negative values of a quasi-distribution representation as compelling evidence of nonclassicality. Prominent examples include the dynamical process nonclassicality characterized by the canonical Hamiltonian ensemble representation (CHER) and the nonclassicality of quantum states characterized by the Wigner function. However, to construct a multivariate joint quasi-distribution function with negative values from experimental data is typically highly cumbersome. Here we propose a computational approach utilizing a deep generative model, processing three marginals, to construct the bivariate joint quasi-distribution functions. We first apply our model to tackle the challenging problem of the CHERs, which lacks universal solutions, rendering the problem ground-truth (GT) deficient. To overcome the GT deficiency of the CHER problem, we design optimal synthetic datasets to train our model. While trained with synthetic data, the physics-informed optimization enables our model to capture the detrimental effect of the thermal fluctuations on nonclassicality, which cannot be obtained from any analytical solutions. This underscores the reliability of our approach. This approach also allows us to predict the Wigner functions subject to thermal noises. Our model predicts the Wigner functions with a prominent accuracy by processing three marginals of probability distributions. Our approach also provides a significant reduction of the experimental efforts of constructing the Wigner functions of quantum states, giving rise to an efficient alternative way to realize the quantum state tomography., Comment: 15 pages, 5 figures

To store quantum information, quantum memory plays a central intermediate ingredient in a network. The minimal criterion for a reliable quantum memory is the maintenance of the entangled state, which can be described by the non-entanglement-breaking (non-EB) channel. In this work, we show that all single-qubit quantum memory can be quantified without trusting input state generation. In other words, we provide a semi-device-independent approach to quantify all single-qubit quantum memory. More specifically, we apply the concept of the two-qubit quantum steering ellipsoids to a single-qubit quantum channel and define the channel ellipsoids. An ellipsoid can be constructed by visualizing finite output states within the Bloch sphere. Since the Choi-Jamio{\l}kowski state of a channel can all be reconstructed from geometric data of the channel ellipsoid, a reliable quantum memory can be detected. Finally, we visually quantify the single-qubit quantum memory by observing the volume of the channel ellipsoid., Comment: 9 pages, 5 figures

One of the remarkable aspects of quantum steering is its ability to violate local uncertainty complementarity relations. In this vein of study, various steering witnesses employing different uncertainty relations have been developed including Reid's criteria. Here, we introduce a novel complementarity relation between system's quantum and classical uncertainties corresponding to the distillable coherence and the von-Neumann entropy, respectively. We demonstrate a superior steering detection efficiency compared to an entropic uncertainty relation. Notably, our proposed steering witness can detect ``all pure entangled states," while the entropic uncertainty relation cannot. We also experimentally validate such a property through a photonic system. Furthermore, a deeper connection to the uncertainty principle is revealed by showcasing the functionality of our proposed complementarity as a quantifier of measurement incompatibility and quantum steerability under genuine incoherent operations. Our work establishes a clear quantitative and operational link between coherence and steering, which are significant resources of quantum technologies, and underscores our efforts in bridging the uncertainty principle with quantum coherence., Comment: 18 pages, 5 figures

Entanglement potentials are popular measures of the nonclassicality of single-mode optical fields. These potentials are defined by the amount of entanglement (measured by, e.g., the negativity or concurrence) of the two-mode field generated by mixing a given single-mode field with the vacuum on a balanced beam splitter. We generalize this concept to define the potentials for Bell nonlocality and quantum steering in specific measurement scenarios, in order to quantify single-mode nonclassicality in a more refined way. Thus, we can study the hierarchy of three types of potentials in close analogy to the well-known hierarchy of the corresponding two-mode quantum correlations. For clarity of our presentation, we focus on the analysis of the nonclassicality potentials for arbitrary vacuum-one-photon superpositions (VOPSs), corresponding to a photon-number qubit. We discuss experimentally feasible implementations for the generation of single-mode VOPS states, their mixing with the vacuum on a balanced beam splitter, and their two-mode Wigner-function reconstruction using homodyne tomography to determine the potentials. We analyze the effects of imperfections, including phase damping and unbalanced beam splitting on the quality of the reconstructed two-mode states and nonclassicality potentials. Although we focus on the analysis of VOPS states, single-mode potentials can also be applied to study the nonclassicality of qudits or continuous-variable systems., Comment: 18 pages, 8 figures

We propose novel charging protocols for quantum batteries based on quantum superpositions of trajectories. Specifically, we consider that a qubit (the battery) interacts with multiple cavities or a single cavity at various positions, where the cavities act as chargers. Further, we introduce a quantum control prepared in a quantum superposition state, allowing the battery to be simultaneously charged by multiple cavities or a single cavity with different entry positions. To assess the battery's performance, we evaluate the maximum extractable work, referred to as ergotropy. Our main result is that the proposed protocols can utilize quantum interference effects to speed up the charging process. For the protocol involving multiple cavities, we observe a substantial increase in ergotropy as the number of superposed trajectories increases. In the case of the single-cavity protocol, we show that two superposed trajectories (entry positions) are sufficient to achieve the upper limit of the ergotropy throughout the entire charging process. Furthermore, we propose circuit models for these charging protocols and conduct proof-of-principle demonstrations on IBMQ and IonQ quantum processors. The results validate our theoretical predictions, demonstrating a clear enhancement in ergotropy., Comment: 12 pages, 8 figures

Nanoscale Fano resonances, with applications from telecommunications to ultra-sensitive biosensing, have prompted extensive research. We demonstrate that a superconducting qubit, jointly coupled to microwave waveguides and an inter-digital transducer composite device, can exhibit acoustic Fano resonances. Our analytical framework, leveraging the Taylor series approximation, elucidates the origins of these quantum acoustic resonances with periodic Fano-like interference. By analyzing the analytical Fano parameter, we demonstrate that the Fano resonances and their corresponding Fano widths near the resonance frequency of a giant atom can be precisely controlled and manipulated by adjusting the time delay. Moreover, not just the near-resonant Fano profiles, but the entire periodic Fano resonance features can be precisely modulated from Lorentz, Fano to quasi-Lorentz shapes by tuning the coupling strength of the microwave waveguide. Our analytical framework offers insights into the control and manipulation of periodic Fano resonances in quantum acoustic waves, thereby presenting significant potential for applications such as quantum information processing, sensing, and communication., Comment: 13 pages, 5 figures

The hierarchical equations of motion (HEOM) approach can describe the reduced dynamics of a system simultaneously coupled to multiple bosonic and fermionic environments. The complexity of exactly describing the system-environment interaction with the HEOM method usually results in time-consuming calculations and a large memory cost. Here, we introduce an open-source software package called HierarchicalEOM.jl: a Julia framework integrating the HEOM approach. HierarchicalEOM.jl features a collection of methods to compute bosonic and fermionic spectra, stationary states, and the full dynamics in the extended space of all auxiliary density operators (ADOs). The required handling of the ADOs multi-indexes is achieved through a user-friendly interface. We exemplify the functionalities of the package by analyzing a single impurity Anderson model, and an ultra-strongly coupled charge-cavity system interacting with bosonic and fermionic reservoirs. HierarchicalEOM.jl achieves a significant speedup with respect to the corresponding method in the Quantum Toolbox in Python (QuTiP), upon which this package is founded., Comment: 20 pages, 7 figures, 4 tables

Many-body localization (MBL) can occur when strong disorders prevent an interacting system from thermalization. To study the dynamics of such systems, it is typically necessary to perform an ensemble average over many different disorder configurations. Previous works have utilized an algorithm in which different disorder profiles are mapped into a quantum ancilla. By preparing the ancilla in a quantum superposition state, quantum parallelism can be harnessed to obtain the ensemble average in a single computation run. In this work, we modify this algorithm by performing a measurement on the ancilla. This enables the determination of conditional dynamics not only by the ensemble average but also by the quantum interference effect. Using a phenomenological analysis based on local integrals of motion, we demonstrate that this protocol can lead to an enhancement of the dephasing effect and a boost in the entanglement growth for systems in the deep MBL phase. We also present numerical simulations of the random XXZ model where this enhancement is also present in a smaller disorder strength, beyond the deep MBL regime., Comment: 7 pages, 4 figures

The Kondo effect is one of the most studied examples of strongly correlated quantum many-body physics. Another type of strongly correlated physics that has only recently been explored in detail (and become experimentally accessible) is that of ultrastrong coupling between light and matter. Here, we study a system which we denote as "Kondo QED") that combines both phenomena, consisting of a two-impurity Anderson model ultra-strongly coupled to a single-mode cavity. While presented as an abstract model, it is relevant for a range of future hybrid cavity-QED systems. Using the hierarchical equations of motion approach we show that the ultrastrong coupling of cavity photons to the electronic states (impurity) noticeably suppresses the electronic Kondo resonance due to the destruction of many-body correlations of the Kondo cloud. We observe this transfer of correlations from the Kondo cloud to the cavity by computing the entropy and mutual information of the impurity-cavity subsystems. In addition, in the weak lead-coupling limit and at zero-bias, the model exhibits a ground-state photon accumulation effect originating entirely from counter-rotating terms in the impurity-cavity interaction. Interestingly, in the strong lead-coupling limit, this accumulation is ``Kondo-enhanced'' by new transition paths opening when increasing the hybridization to the leads. This suggests a new mechanism for the generation of real photons from virtual states. We further show that the suppression of the Kondo effect is stable under broadening of the cavity resonance as a consequence of the interaction to an external bosonic continuum. Our findings pave the way for the simultaneous control of both the Kondo QED effect and a photon accumulation effect using the ultrastrong coupling of light and matter., Comment: 23 pages, 11 figures, 2 tables

Superposition of trajectories, which modify quantum evolutions by superposing paths through interferometry, has been utilized to enhance various quantum communication tasks. However, little is known about its impact from the viewpoint of open quantum systems. Thus, we examine this subject from the perspective of system-environment interactions. We show that the superposition of multiple trajectories can result in quantum state freezing, suggesting a space-time dual to the quantum Zeno effect. Moreover, non-trivial Dicke-like super(sub)radiance can be triggered without utilizing multi-atom correlations., Comment: 12 pages and 4 figures

We develop a discrete fermion approach for modelling the strong interaction of an arbitrary system interacting with continuum electronic reservoirs. The approach is based on a pseudo-fermion decomposition of the continuum bath correlation functions, and is only limited by the accuracy of this decomposition. We show that to obtain this decomposition one can allow for imaginary pseudo-fermion parameters, and strong damping in individual pseudo-fermions, without introducing unwanted approximations. For a non-interacting single-resonant level, we benchmark our approach against an analytical solution and an exact hierachical-equations-of-motion approach. We also show that, for the interacting case, this simple method can capture the strongly correlated low-temperature physics of Kondo resonance., Comment: 15 pages, 4 figures

The interplay between thermal machines and quantum correlations is of great interest in both quantum thermodynamics and quantum information science. Recently, a quantum Szil\'ard engine has been proposed, showing that the quantum steerability between a Maxwell's demon and a work medium can be beneficial to a work extraction task. Nevertheless, this type of quantum-fueled machine is usually fragile in the presence of decoherence effects. We provide an example of the pure dephasing process, showing that the engine's quantumness can be degraded. Therefore, in this work, we tackle this question by introducing a second demon who can access a control system and make the work medium pass through two dephasing channels in a manner of quantum superposition. Furthermore, we provide a quantum circuit to simulate our proposed concept and test it on IBMQ and IonQ quantum computers., Comment: 10 pages, 7 figures, 2 tables

Quantum steering is an important correlation in quantum information theory. A recent work [Nat. Commun. 12, 2410 (2021)] showed that quantum steering is also useful for quantum metrology. Here, we extend the exploration of steering-enhanced quantum metrology from single noiseless phase shifts to superpositions of noisy phase shifts. As concrete examples, we consider a control system that manipulates a target system to pass through a superposition of either dephased or depolarized phase shifts channels. We show that using such superpositions of noisy phase shifts can suppress the effects of noise and improve metrology. Furthermore, we also implemented proof-of-principle experiments for a superposition of dephased phase shifts on the IBM Quantum Experience, demonstrating a clear improvement on metrology., Comment: 12 pages, 7 figures

Studies have shown that the Hilbert spaces of non-Hermitian systems require nontrivial metrics. Here, we demonstrate how evolution dimensions, in addition to time, can emerge naturally from a geometric formalism. Specifically, in this formalism, Hamiltonians can be interpreted as a Christoffel symbol-like operators, and the Schroedinger equation as a parallel transport in this formalism. We then derive the evolution equations for the states and metrics along the emergent dimensions and find that the curvature of the Hilbert space bundle for any given closed system is locally flat. Finally, we show that the fidelity susceptibilities and the Berry curvatures of states are related to these emergent parallel transports., Comment: 20 pages, 1 figure

Quantum steering is the central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another one via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables measurement assemblage (SEO), first proposed to connect the problem of steerability with measurement incompatibility. We provide an efficient method to compute the maximal extractable steerability via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples., Comment: 13 pages, 2 figures, comments welcome!

We present a canonical derivation of an influence superoperator which generates the reduced dynamics of a Fermionic quantum system linearly coupled to a Fermionic environment initially at thermal equilibrium. We use this formalism to derive a generalized-Lindblad master equation (in the Markovian limit) and a generalized version of the hierarchical equations of motion valid in arbitrary parity-symmetry conditions, important for the correct evaluation of system correlation functions and spectra., Comment: 33 pages, 2 figures

One-way quantum computing is a promising candidate for fault-tolerant quantum computing. Here, we propose new protocols to realize a deterministic one-way CNOT gate and one-way $X$-rotations on quantum-computing platforms. By applying a delayed-choice scheme, we overcome a limit of most currently available quantum computers, which are unable to implement further operations on measured qubits or operations conditioned on measurement results from other qubits. Moreover, we decrease the error rate of the one-way logic gates, compared to the original protocol using local operations and classical communication (LOCC). In addition, we apply our deterministic one-way CNOT gate in the Deutsch-Jozsa algorithm to show the feasibility of our proposal. We demonstrate all these one-way gates and algorithms by running experiments on the cloud quantum-computing platform IBM Quantum Experience.

Quantum channels breaking entanglement, incompatibility, or nonlocality are defined as such because they are not useful for entanglement-based, one-sided device-independent, or device-independent quantum information processing, respectively. Here, we show that such breaking channels are related to complementary tests of macrorealism i.e., temporal separability, channel unsteerability, temporal unsteerability, and the temporal Bell inequality. To demonstrate this we first define a steerability-breaking channel, which is conceptually similar to entanglement and nonlocality-breaking channels and prove that it is identical to an incompatibility-breaking channel. A hierarchy of quantum non-breaking channels is derived, akin to the existing hierarchy relations for temporal and spatial quantum correlations. We then introduce the concept of channels that break temporal correlations, explain how they are related to the standard breaking channels, and prove the following results: (1) A robustness-based measure for non-entanglement-breaking channels can be probed by temporal nonseparability. (2) A non-steerability-breaking channel can be quantified by channel steering. (3) Temporal steerability and non-macrorealism can be used for, respectively, distinguishing unital steerability-breaking channels and nonlocality-breaking channels for a maximally entangled state. Finally, a two-dimensional depolarizing channel is experimentally implemented as a proof-of-principle example to demonstrate the hierarchy relation of non-breaking channels using temporal quantum correlations, Comment: Comments welcome

The Leggett-Garg inequality (LGI) distinguishes nonmacrorealistic channels from macrorealistic ones by constraining the experimental outcomes of the underlying system. In this work, we propose a class of channels which, initially, cannot violate the LGI (in the form of the temporal Bell inequality) but can violate it after the application of stochastic pre- and post- operations (SPPOs). As a proof-of-principle experiment, we demonstrate the stochastic pre- and post- operations in an amplitude-damping channel with photonic qubits. We denote the above phenomenon as hidden nonmacrorealistic channels. We also discuss the relationship between this hidden nonmacrorealistic channels (in terms of the temporal Clauser-Horne-Shimony-Holt (CHSH) inequality) and the strongly nonlocality-breaking channel, which breaks the hidden spatial CHSH nonlocality for arbitrary states. In general, if the channel satisfies hidden nonmacrorealism, it is not a strongly CHSH nonlocality-breaking channel., Comment: Comments welcome

Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation of a Bell inequality. In this work, we provide the direct link between Bell nonlocality and the quantification of measurement incompatibility. This includes quantifiers for both incompatible and genuine-multipartite incompatible measurements. Our method straightforwardly generalizes to include constraints on the system's dimension (semi-device-independent approach) and on projective measurements, providing improved bounds on incompatibility quantifiers, and to include the prepare-and-measure scenario., Comment: 15 pages, 4 figures. Comments welcome! v2: Accepted version

Quantum state transfer (QST) provides a method to send arbitrary quantum states from one system to another. Such a concept is crucial for transmitting quantum information into the quantum memory, quantum processor, and quantum network. The standard benchmark of QST is the average fidelity between the prepared and received states. In this work, we provide a new benchmark which reveals the non-classicality of QST based on spatio-temporal steering (STS). More specifically, we show that the local-hidden-state (LHS) model in STS can be viewed as the classical strategy of state transfer. Therefore, we can quantify the non-classicality of QST process by measuring the spatio-temporal steerability. We then apply the spatio-temporal steerability measurement technique to benchmark quantum devices including the IBM quantum experience and QuTech quantum inspire under QST tasks. The experimental results show that the spatio-temporal steerability decreases as the circuit depth increases, and the reduction agrees with the noise model, which refers to the accumulation of errors during the QST process. Moreover, we provide a quantity to estimate the signaling effect which could result from gate errors or intrinsic non-Markovian effect of the devices., Comment: 13 pages, 5 figures, 2 tables