We study the time evolution of four distance measures in the presence of initial systemenvironment correlations. It is well-known that the trace distance between two quantum states of an open system may increase due to initial correlations which leads to a breakdown of the contractivity of the reduced dynamics. Here we compare and analyze, for two different models, the time evolution of the trace distance, the Bures metric, the Hellinger distance and the Jensen-Shannon divergence regarding an increase above their initial values, witnessing initial correlations. This work generalizes, deepens and corrects the study performed by Dajka et al. [Phys. Rev. A 84 032120 (2011)] and thereby reveals generic features of the considered distance measures with respect to the capability of detecting initial system-environment correlations.
Correlations between a system and its environment lead to errors in an open quantum system. Detecting those correlations would be valuable for avoiding and/or correcting those errors. Here we show that we can detect correlations by only measuring the system itself if we know the cause of the interaction between the two, for example in the case of a dipole-dipole interaction. We investigate the unitary $U$ which is associated with the exchange Hamiltonian and examine the ability to detect initial correlations between a system and its environment for various types of initial states. The states w…
Generic mesoscopic quantum systems that interact with their environment tend to display appreciable correlations with environment that often play an important role in the physical properties of the system. However, the experimental methods needed to characterize such systems either ignore the role of initial correlations or scale unfavourably with system dimensions. Here, we present a technique that is agnostic to system-environment correlations and can be potentially implemented experimentally. Under a specific set of constraints, we demonstrate the ability to detect and measure specific corr…
We propose the use of a tunneling electromechanical transducer to dynamically detect Casimir forces between two conducting surfaces. The maximum distance for which Casimir forces should be detectable with our method is around $1 μ$m, while the lower limit is given by the ability to approach the surfaces. This technique should permit to study gravitational forces on the same range of distances, as well as the vacuum friction provided that very low dissipation mechanical resonators are used.
In this paper, we investigate the optimal nonadditive quantum error-detecting codes with distance two. The the numerical simulation shows that, with n being can be 5, 6, 7, 8, 10 and 12, such the n-qubit quantum error-detecting codes with maximal number of codewords can be found. Therein, except the n=7 case, the n-vertex loop graphs help find the optimal quantum codes.
We develop a general strategy for the detection of nonclassical system-environment correlations in the initial states of an open quantum system. The method employs a dephasing map which operates locally on the open system and leads to an experimentally accessible witness for genuine quantum correlations, measuring the Hilbert-Schmidt distance between pairs of open system states. We further derive the expectation value of the witness for various random matrix ensembles modeling generic features of complex quantum systems. This expectation value is shown to be proportional to a measure for the q…
Detecting Initial System-Environment Correlations from a Single Observable
Sharjah Maritime Academy（沙迦海事学院）；Department of Physical Sciences, Olive-Harvey College, City Colleges of Chicago（芝加哥城市学院奥莉-哈维学院物理科学系）；QuSTEAM Initiative（QuSTEAM倡议）；Department of Physics, University of the Basque Country UPV/EHU（巴斯克大学UPV/EHU物理系）；EHU Quantum Center, University of the Basque Country UPV/EHU（巴斯克大学UPV/EHU量子中心）
We construct a general measure for detecting the quantum speedup in both closed and open systems. The speed measure is based on the changing rate of the position of quantum states on a manifold with appropriate monotone Riemannian metrics. Any increase in speed is a clear signature of dynamical speedup. To clarify the mechanisms for quantum speedup, we first introduce the concept of longitudinal and transverse types of speedup: the former stems from the time evolution process itself with fixed initial conditions, while the latter is a result of adjusting initial conditions. We then apply the p…
Detecting spacelike vacuum entanglement at all distances and promoting negativity to a necessary and sufficient entanglement measure in many-body regimes
The role of initial qubit-environment correlations on trace distance between two qubit states is studied in the framework of non--Markovian pure dephasing. The growth of mixedness of reduced state quantified by linear entropy is shown to be related to the degree of initial qubit--environment correlations.
Intriguing features of the distance between two arbitrary states of an open quantum system are identified that are induced by initial system-environment correlations. As an example, we analyze a qubit dephasingly coupled to a bosonic environment. Within tailored parameter regimes, initial correlations are shown to substantially increase a distance between two qubit states evolving to long-time limit states according to exact non-Markovian dynamics. It exemplifies the breakdown of the distance contractivity of the reduced dynamics.
The time evolution of the trace distance between two states of an open quantum system may increase due to initial system-environment correlations, thus exhibiting a breakdown of distance contractivity of the reduced dynamics. We analyze how the time evolution of the distance depends on the chosen distance measure. Here we elucidate the behavior of the trace distance, the Hilbert- Schmidt distance, the Bures distance, the Hellinger distance and the quantum Jensen-Shannon divergence for two system-environment setups, namely a qubit bi-linearly coupled to an infinite and a finite size environment…
We investigate the ability of correlation measures to witness non-Markovian open quantum system dynamics. It is shown that the mutual information and any entanglement measure between the system and an ancilla do not witness all non-Markovian dynamics. A correlation measure is introduced, and it is proven that, in an enlarged setting with two ancillary systems, this measure detects almost all non-Markovian dynamics, except possibly a zero-measure set of dynamics that is non-bijective in finite time-intervals. Our proof is constructive and provides different initial states detecting the non-Mark…
The trace distance between two states of an open quantum system quantifies their distinguishability, and for a fixed environmental state can increase above its initial value only in the presence of initial system-environment correlations. We provide for the first time experimental evidence of such a behavior. In our all-optical apparatus we exploit spontaneous parametric down conversion as a source of polarization entangled states, and a spatial light modulator to introduce in a general fashion correlations between the polarization and the momentum degrees of freedom, which act as environment.
Recently, the principle of \textit{passivity} has been used to set bounds on the evolution of a microscopic quantum system with a thermal initial state. In this work, we experimentally demonstrate the utility of two passivity based frameworks: global passivity and passivity deformation, for the detection of a "hidden" or unaccounted environment. We employ two trapped-ion qubits undergoing unitary evolution, which may optionally be coupled to an unobserved environment qubit. Evaluating the measurement data from the system qubits, we show that global passivity can verify the presence of a coupli…
We demonstrate that local application of a weak external field increases distinguishability between states with and without initial correlations. We consider the case where a two-level system linearly and adiabatically interacts with an infinite number of bosons. We evaluate the trace distance (or, equivalently, the Hilbert-Schmidt distance) between the quantum states which evolve from two kinds of initial states; the correlated Gibbs state and its uncorrelated marginal state. We find that the trace distance increases above its initial value for any and all parameter settings. This indicates t…
The paradigm of Schrödinger's cat illustrates how quantum states preclude the assignment of definite properties to a macroscopic object (realism). In this work we develop a method to investigate the indefiniteness of cat states using currently available cold atom technology. The method we propose uses the observation of a statistical distribution to demonstrate the macroscopic distinction between dead and alive states, and uses the determination of the interferometric sensitivity (Fisher information) to detect the indefiniteness of the cat's vital status. We show how combining the two observat…
A quantum channel is said to be a mixed-unitary channel if it can be expressed as a convex combination of unitary channels. We prove that, given the Choi representation of a quantum channel, it is NP-hard with respect to polynomial-time Turing reductions to determine whether or not that channel is a mixed-unitary channel. This hardness result holds even under the assumption that the channel is not within an inverse-polynomial distance (in the dimension of the space upon which it acts) of the boundary of the mixed-unitary channels.
Motivated by the close relationship between quantum error-correction, topological order, the holographic AdS/CFT duality, and tensor networks, we initiate the study of approximate quantum error-detecting codes in matrix product states (MPS). We first show that using open-boundary MPS to define boundary to bulk encoding maps yields at most constant distance error-detecting codes. These are degenerate ground spaces of gapped local Hamiltonians. To get around this no-go result, we consider excited states, i.e., we use the excitation ansatz to construct encoding maps: these yield error-detecting c…
Single-qubit sensing protocols can be used to measure qubit-bath coupling parameters. However, for sufficiently large coupling, the sensing protocol itself perturbs the bath, which is predicted to result in a characteristic response in the sensing measurements. Here, we observe this bath perturbation, also known as a quantum quench, by preparing the nuclear spin bath of a nitrogen-vacancy (NV) center in polarized initial states and performing phase-resolved spin echo measurements on the NV electron spin. These measurements reveal a time-dependent phase determined by the initial state of the ba…
Classical versus non-classical photon states for detecting vacuum non-linearity
Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿罗森多夫赫尔姆霍兹中心）；The Extreme Light Infrastructure ERIC, ELI Beamlines Facility（极端光基础设施欧洲研究联盟，ELI光束线设施）；Institut für Theoretische Physik, Technische Universität Dresden（德累斯顿工业大学理论物理研究所）
We study the dynamics of a one dimensional quantum spin chain evolving from unentangled or entangled initial state. At a given instant of time a quantum dynamical process (ex. measurement) is performed on a single spin at one end of the chain, decohering the system. Through the further unitary evolution, a signal propagates in the spin chain, which can be detected from a measurement on a different spin at later times. From the dynamical unitary evolution of the decohered state from the epoch time, it is possible to detect the occurrence of the dynamical process. The propagation of the signal f…
We predict a geometric quantum phase shift of a moving electric dipole in the presence of an external magnetic field at a distance. On the basis of the Lorentz-covariant field interaction approach, we show that a geometric phase appears under the condition that the dipole is moving in the field-free region, which is distinct from the topological He-McKellar-Wilkens phase generated by a direct overlap of the dipole and the field. We discuss the experimental feasibility of detecting this phase with atomic interferometry and argue that detection of this phase would result in a deeper understandin…
All computing devices, including quantum computers, must exhibit that for a given input, an output is produced in accordance with the program. The outputs generated by quantum computers that fulfill these requirements are not temporally correlated, however. In a quantum-computing device comprising solid-state qubits such as superconducting qubits, any operation to rest the qubits to their initial state faces a practical problem. We applied a statistical analysis to a collection of random numbers output from a 20-qubit superconducting-qubit cloud quantum computer using the simplest random numbe…
