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arXiv:1510.07556

Steerability of Quantum Coherence in Accelerated Frame

Mondal, Debasis, Chiranjib Mukhopadhyay

Published Oct 26, 2015• 7 citations
arXivHTMLPDF

Abstract

The interplay between steering and quantum coherence is studied in a scenario, where two atoms move through an external massless scalar field. We show that just like entanglement, the steering induced coherence of the equilibrium state may increase or decrease with acceleration depending on the initial condition of the state. We also investigate the condition for coherence steerability - as opposed to simple state steerability. Interestingly, we find that the quantum coherence of the equilibrium state cannot be steered, even when the steering induced coherence is non-zero. We argue that under any condition, gravity prohibits the coherence steering of the equilibrium state.

DOI
10.48550/arxiv.1510.07556

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The interplay between steering and quantum coherence is studied in a scenario, where two atoms move through an external massless scalar field. We show that just like entanglement, the steering induced coherence of the equilibrium state may increase or decrease with acceleration depending on the initial condition of the state. We also investigate the condition for coherence steerability - as opposed to simple state steerability. Interestingly, we find that the quantum coherence of the equilibrium state cannot be steered, even when the steering induced coherence is non-zero. We argue that under any condition, gravity prohibits the coherence steering of the equilibrium state.
In this paper, the bidirectional steering between two accelerated partners sharing initially different classes of entangled states is discussed. Due to the decoherence, the steerability and its degree decrease either as the acceleration increases or the partners share initially a small amount of quantum correlations. The possibility of increasing the steerability is investigated by applying the filtering process. Our results show that by increasing the filtering strength, one can improve the upper bounds of the steerability and the range of acceleration at which the steerability is possible. Steering large coherent states is much better than steering less coherent ones.
We investigate the behavior of quantum steering for a pair of quantum qubits described by the Heisenberg model with external magnetic field and in equilibrium with a reservoir at temperature T . Generally, the steerable weight, which is used to identify the steerability, is suppressed by thermal fluctuations. When the magnetic field is vanishing, the steerable weight behaves like the quantum entanglement. When the magnetic field is not zero, the steerable weight is dramatically different from the other quantities used to identify the quantum correlations between the two spins, i.e. , the concurrence, quantum discord and coherence. In the strong magnetic field limit, all of the other quantities we studied are vanishing for the Ising model, while steerable weight tends to one. This demonstrates that the strong transverse magnetic field is helpful to preserve the quantum steerability of the Ising model.
Quantum steering is a perplexing feature at the heart of quantum mechanics that provides profound implications in understanding the nature of physical reality. On the other hand, the effect of relativistic features on quantum systems is vital in understanding the underlying foundations of physics. In this work, we study the effects of Unruh acceleration on the quantum steering of a two-qubit system. In particular, we consider the so-called quantum steering ellipsoid and the maximally-steered coherence in a non-inertial frame and find closed-form analytic expressions for the role of the Unruh acceleration in these quantities. Analyzing the conditions for the steerability of the system, we develop a geometric description for the effect of Unruh acceleration on the quantum steering of a two-qubit system.
In this work, there are two parties, Alice on Earth and Bob on the satellite, which initially share an entangled state, and some open problems, which emerge during quantum steering that Alice remotely steers Bob, are investigated. Our analytical results indicate that all entangled pure states and maximally entangled evolution states (EESs) are steerable, and not every entangled evolution state is steerable and some steerable states are only locally correlated. Besides, quantum steering from Alice to Bob experiences a "sudden death" with increasing decoherence strength. However, shortly after that, quantum steering experiences a recovery with the increase of decoherence strength in bit flip (BF) and phase flip (PF) channels. Interestingly, while they initially share an entangled pure state, all EESs are steerable and obey Bell nonlocality in PF and phase damping channels. In BF channels, all steerable states can violate Bell-CHSH inequality, but some EESs are unable to be employed to realize steering. However, when they initially share an entangled mixed state, the outcome is different from that of the pure state. Furthermore, the steerability of entangled mixed states is weaker than that of entangled pure states. Thereby, decoherence can induce the degradation of quantum steering, and the steerability of state is associated with the interaction between quantum systems and reservoirs.
Occupying a position between entanglement and Bell nonlocality, Einstein-Podolsky-Rosen (EPR) steering has attracted increasing attention in recent years. Many criteria have been proposed and experimentally implemented to characterize EPR-steering. Nevertheless, only a few results are available to quantify steerability using analytical results. In this work, we propose a method for quantifying the steerability in two-qubit quantum states in the two-setting EPR-steering scenario, using the connection between joint measurability and steerability. We derive an analytical formula for the steerability of a class of X-states. The sufficient and necessary conditions for two-setting EPR-steering are presented. Based on these results, a class of asymmetric states, namely, one-way steerable states, are obtained.