Dynamics and Recovery of Genuine Multipartite Einstein–Podolsky–Rosen Steering and Genuine Multipartite Nonlocality for a Dissipative Dirac System via the Unruh Effect
Abstract The dynamics behaviors of genuine multipartite Einstein–Podolsky–Rosen steering (GMS) and genuine multipartite nonlocality (GMN) are investigated herein, and how the lost GMS and GMN under a mixed decoherence system can be recovered is explored. Explicitly, the decoherence system can be modeled by that a tripartite Werner‐type state suffers from the non‐Markovian regimes and one subsystem of the tripartite is under a non‐inertial frame. The conditions for steerable and nonlocal states can be obtained with respect to the tripartite Werner‐type state established initially. GMS and GMN are very fragile and vulnerable under the influence of the collective decoherence. GMS and GMN will vanish with growing intensity of the Unruh effect and the non‐Markovian reservoir. Besides, all achievable GMN's states are steerable, while not every steerable state (GMS's state) can achieve nonlocality. This means that the steering–nonlocality hierarchy is still tenable and GMN's states are a strict subset of the GMS's states in such a scenario. Subsequently, an available methodology to recover the damaged GMS and GMN is proposed. It turns out that the lost GMS and GMN can be effectively restored, and the ability of GMS and GMN to suppress the collective decoherence can be enhanced.
Abstract The dynamics behaviors of genuine multipartite Einstein–Podolsky–Rosen steering (GMS) and genuine multipartite nonlocality (GMN) are investigated herein, and how the lost GMS and GMN under a mixed decoherence system can be recovered is explored. Explicitly, the decoherence system can be modeled by that a tripartite Werner‐type state suffers from the non‐Markovian regimes and one subsystem of the tripartite is under a non‐inertial frame. The conditions for steerable and nonlocal states can be obtained with respect to the tripartite Werner‐type state established initially. GMS and GMN are very fragile and vulnerable under the influence of the collective decoherence. GMS and GMN will vanish with growing intensity of the Unruh effect and the non‐Markovian reservoir. Besides, all achievable GMN's states are steerable, while not every steerable state (GMS's state) can achieve nonlocality. This means that the steering–nonlocality hierarchy is still tenable and GMN's states are a strict subset of the GMS's states in such a scenario. Subsequently, an available methodology to recover the damaged GMS and GMN is proposed. It turns out that the lost GMS and GMN can be effectively restored, and the ability of GMS and GMN to suppress the collective decoherence can be enhanced.
Einstein–Podolsky–Rosen steering is a peculiar quantum nonlocal correlation and has unique physical characteristics and a wide application prospect. Even more importantly, multipartite steerable states have more vital applications in the future quantum information field. Thus, in this work, we explored the dynamics characteristics of both genuine multipartite steering (GMS) and genuine multipartite entanglement (GME) and the relations of both under an open tripartite system. Specifically, the tripartite decoherence system may be modeled by the three parties of a tripartite state that undergo the noisy channels. The conditions for genuine entangled and steerable states can be acquired for the initial tripartite state. The results showed that decoherence noises can degrade the genuine multipartite entanglement and genuine multipartite steering and even induce its death. Explicitly, GME and GMS disappear with the increase in the decoherence strength under the phase damping channel. However, GME and GMS rapidly decay to death with the increase in the channel-noise factor and then come back to life soon after in the bit flip channel. Additionally, the results indicate that GMS is born of GME, but GME does not imply GMS, which means that the set of genuine multipartite steerable states is a strict subset of the set of genuine multipartite entangled states. These conclusions may be useful for discussing the relationship of quantum nonlocal correlations (GME and GMS) in the decoherence systems.
Abstract We investigate the behavior of (1 → 2) and (2 → 1) genuine tripartite EPR steering in generalized GHZ (GGHZ) states when observers undergo relativistic acceleration, and extend the analysis to network quantum steering in linear networks composed of two Bell states. Within the free Dirac field framework, our results demonstrate that both types of genuine tripartite steering and network steering exhibit monotonic degradation with increasing acceleration. In the single-accelerator scenario, all steering types persist even at infinite acceleration, while physically inaccessible (2 → 1) genuine steering emerges at high accelerations. Strikingly contrasting behavior is observed when two observers accelerate, where sudden death of steering occurs in all cases. Furthermore, we study the dynamical evolution of both genuine tripartite steering and network quantum steering in noninertial frames when one accelerated qubit undergoes decoherence. We reveal a hierarchy of sensitivity for both steering types to different decoherence noises in noninertial frames, and find that genuine tripartite steering and network quantum steering are more sensitive to quantum decoherence effects than to the Unruh effect.
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.
Abstract In this letter, the dynamic behavior of Einstein–Podolsky–Rosen (EPR) steering and the redistribution of EPR steering under a relativistic framework are investigated. Specifically, we explore the scenario that particle A held by Alice is in a flat space–time and another particle B held by Bob entangled with A is in a non-inertial framework. The results show that EPR steering from Alice to Bob is dramatically destroyed by the Unruh effect caused by the acceleration of Bob. Besides, EPR steering possess asymmetry, and EPR steering asymmetry increases with growing intensity of the Unruh effect, implying that the Unruh effect can bring about EPR steering asymmetry. Furthermore, the reduced physically accessible EPR steering from Alice to Bob is distributed to the physically inaccessible EPR steering (from Alice to anti-Bob or from Bob to anti-Bob). Notably, unlike entanglement and quantum discord, only one of the EPR steering from Alice to anti-Bob and Bob to anti-Bob experiences a sudden birth with increase in the acceleration parameter, which means that they cannot simultaneously survive. That is, the monogamous relationship of EPR steering is still tenable in such a scenario. Consequently, we believe that EPR steering could also serve as an important information resource within long-distance quantum secure communication under the relativistic framework.
Asymmetric Einstein–Podolsky–Rosen (EPR) steering means the ability of one party to nonlocally “steer” the state in the other side through local measurements. The asymmetric property of EPR steering provides adequate security in one-sided device-independent secure quantum communication protocols. In this paper, we theoretically investigate the asymmetric EPR steering schemes between two subsystems of multipartite entangled states by an asymmetric modulation method. Two schemes, including tripartite entangled state to bipartite steering and quadripartite entangled state to tripartite steering, are investigated. By reconstructing the covariance matrix of continuous variable multipartite Gaussian states, we quantify the steerability of manipulating two different subsystems and demonstrate the EPR steering parameter versus various types of states’ parameters. Our work provides a reference for asymmetric quantum information processing and enriches resources for secure quantum networks.
Quantum nonlocality manifests in multipartite systems through entanglement, Bell's nonlocality, and Einstein-Podolsky-Rosen (EPR) steering. While Peres's positive-partial-transpose criterion provides a simple and powerful test for entanglement, a comparably elegant spectral criterion for detecting EPR steering remains an open challenge. In this work, we systematically explore whether a Peres-type criterion can be established for EPR steering in the two-qubit system. Focusing on rank-2 (including rank-1) states and the two-qubit Werner state, we analyze the eigenvalues of their partially transposed density matrices and construct a significant steering criterion based on symmetric combinations of these eigenvalues. We prove that this criterion serves as a necessary and sufficient condition for steerability for the Werner state, all two-qubit pure states, all two-qubit rank-2 states. Furthermore, we validate the criterion for higher-rank states (rank-3 and rank-4) and show that the results align with known steering inequalities. Our findings suggest a more unified framework for detecting quantum nonlocality via partial transposition and open avenues for further theoretical and numerical investigations into steering detection.