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Physical Review A

Creation of quantum steering by interaction with a common bath

Zhe Sun, Xiaoqiang Xu, Бо Лю

Published May 7, 2018• 10 citations
Publisher

Abstract

By applying the hierarchy equation method, we computationally study the creation of quantum steering in a two-qubit system interacting with a common bosonic bath. The calculation does not adopt conventional approximate approaches, such as the Born, Markov, rotating-wave, and other perturbative approximations. Three kinds of quantum steering, i.e., Einstein-Podolsky-Rosen steering (EPRS), temporal steering (TS), and spatiotemporal steering (STS), are considered. Since the initial state of the two qubits is chosen as a product state, there does not exist EPRS at the beginning. During the evolution, we find that STS as well as EPRS are generated at the same time. An inversion relationship between STS and TS is revealed. By varying the system-bath coupling strength from weak to ultrastrong regimes, we find the nonmonotonic dependence of STS, TS, and EPRS on the coupling strength. It is interesting to study the dynamics of the three kinds of quantum steering by using an exactly numerical method, which is not considered in previous researches.

DOI
10.1103/physreva.97.052309

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Publisher's Note: Quantification of Einstein-Podolsky-Rosen steering for two-qubit states [Phys. Rev. A 93 , 020103(R) (2016)]

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By applying the hierarchy equation method, we computationally study the creation of quantum steering in a two-qubit system interacting with a common bosonic bath. The calculation does not adopt conventional approximate approaches, such as the Born, Markov, rotating-wave, and other perturbative approximations. Three kinds of quantum steering, i.e., Einstein-Podolsky-Rosen steering (EPRS), temporal steering (TS), and spatiotemporal steering (STS), are considered. Since the initial state of the two qubits is chosen as a product state, there does not exist EPRS at the beginning. During the evolution, we find that STS as well as EPRS are generated at the same time. An inversion relationship between STS and TS is revealed. By varying the system-bath coupling strength from weak to ultrastrong regimes, we find the nonmonotonic dependence of STS, TS, and EPRS on the coupling strength. It is interesting to study the dynamics of the three kinds of quantum steering by using an exactly numerical method, which is not considered in previous researches.
We experimentally simulate a quantum channel in a linear optical setup, which is modeled by a two-level system (i.e., qubit) interacting with a bosonic bath. Unlike the traditional works, we treat the system–bath interaction without applying the Born approximation, the Markov approximation, or the rotating-wave approximation (RWA). To the best of our knowledge, this is the first experimental simulation of a quantum channel without any of the approximations mentioned above by using linear optical devices. This non-RWA channel provides a more accurate picture of the quantum open-system dynamics. It not only reveals the effect of the counterrotating terms but also enables us to consider arbitrarily strong coupling regimes. With the proposed channel, we further experimentally investigate the dynamics of the quantum temporal steering (TS), i.e., a temporal analog of Einstein–Podolsky–Rosen steering. The experimental and theoretical results are in good agreement and show that the counterrotating terms significantly influence the TS dynamics. The TS in non-RWA and RWA channels presents different dynamics. However, we emphasize that the results without RWA are closer to realistic situations and thus more reliable. Due to the close relationship between TS and the security of the quantum cryptographic protocols, our findings are expected to have useful applications in secure quantum communications. This work also inspires future interest in studying other quantum coherence properties in the non-RWA channels.
Characterizing the dynamics of open systems usually starts with a perturbative theory and involves various approximations, such as the Born, Markov and rotating-wave approximation (RWA). However, the approximation approaches could introduce more or less incompleteness in describing the bath behaviors. Here, we consider a quantum channel, which is modeled by a qubit (a two-level system) interacting with a bosonic bath. Unlike the traditional works, we experimentally simulate the system-bath interaction without applying the Born, Markov, and rotating-wave approximations. To our knowledge, this is the first experimental simulation of the quantum channels without any approximations mentioned above, by using linear optical devices. The results are quite useful and interesting, which not only reveal the effect of the counter-rotating terms but also present a more accurate picture of the quantum channel dynamics. Besides, we experimentally investigate the dynamics of the quantum temporal steering (TS), i.e., a temporal analogue of Einstein-Podolsky-Rosen steering. The experimental and theoretical results are in good agreement and show that the counter-rotating terms significantly influence the TS dynamics. When one monogamously associates TS with the security of the cryptographic protocols (e.g., BB84), our experimental tests reveal that the channels based on RWA will provide exaggerated security durations, while they are actually insecure in non-RWA channel cases. This implies that doing RWA may result in a risk for the security of quantum key distribution. Our findings are expected to have useful applications in secure quantum communications and future interesting TS studies.
By using the Born Markovian master equation, we study the relationship among the Einstein-Podolsky-Rosen (EPR) steering, Bell nonlocality, and quantum entanglement of entangled coherent states (ECSs) under decoherence. We illustrate the dynamical behavior of the three types of correlations for various optical field strength regimes. In general, we find that correlation measurements begin at their maximum and decline over time. We find that quantum steering and nonlocality behave similarly in terms of photon number during dynamics. Furthermore, we discover that ECSs with steerability can violate the Bell inequality, and that not every ECS with Bell nonlocality is steerable. In the current work, without the memory stored in the environment, some of the initial states with maximal values of quantum steering, Bell nonlocality, and entanglement can provide a delayed loss of that value during temporal evolution, which is of interest to the current study.
Dynamics of the quantum entanglement and quantum discord of two qubits in two independent baths and a common bath with the Lorentzian spectrum are studied exactly in the numerical sense within the hierarchy approach. The effects of the counter-rotating-wave terms from the system–bath coherence on these quantum correlations are systematically discussed and comparisons with previous ones under the rotating-wave approximation are also performed. For two independent baths, beyond the weak system–bath coupling, the counter-rotating-wave terms essentially change evolutions of both the entanglement and quantum discord. With increase of the coupling, revival of the entanglement after a period of complete disentanglement is suppressed dramatically and finally disappears, and the quantum discord becomes smaller monotonically. For the common bath, the entanglement is also suppressed by the counter-rotating-wave terms, but the quantum discord shows quite different behaviors if initiated from spin-correlated states. In the non-Markovian regime, the quantum discord is almost not influenced by the counter-rotating-wave terms and is generally finite in the long-time evolution at arbitrary coupling while in the Markovian regime, it is significantly enhanced with the strong coupling.
Einstein–Podolsky–Rosen (EPR) steering is an example of nontrivial quantum nonlocality and characteristic in the non-classical world. The directivity (or asymmetry) is a fascinating trait of EPR steering, and it is different from other quantum nonlocalities. Here, we consider the strategy in which two atoms compose a two-qubit X state, and the two atoms are owned by Alice and Bob, respectively. The atom of Alice suffers from a reservoir, and the atom of Bob couples with a bit flip channel. The influences of auxiliary qubits on EPR steering and its directions are revealed by means of the entropy uncertainty relation. The results indicate that EPR steering declines with growing time t when adding fewer auxiliary qubits. The EPR steering behaves as damped oscillation when introducing more auxiliary qubits in the strong coupling regime. In the weak coupling regime, the EPR steering monotonously decreases as t increases when coupling auxiliary qubits. The increases in auxiliary qubits are responsible for the fact that the steerability from Alice to Bob (or from Bob to Alice) can be more effectively revealed. Notably, the introductions of more auxiliary qubits can change the situation that steerability from Alice to Bob is certain to a situation in which steerability from Bob to Alice is certain.
In the last few years, several criteria to identify Einstein-Podolsky-Rosen steering have been proposed and experimentally implemented. On the operational side, however, the evaluation of the steerability degree of a given state has shown to be a difficult task and only a few results are known. In this work, we propose a measure of steering that is based on the maximal violation of well-established steering inequalities. Applying this approach to two-qubit states, we managed to derive simple closed formulas for steering in the two- and three-measurement scenarios. We also provide closed formulas for quantifiers of Bell nonlocality in the respective scenarios. Finally, we show that our measures of steering verify the entanglement-steering-nonlocality hierarchy and reproduce results reported so far.