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arXiv:1209.3461 · Physical Review A

Entanglement and discord: Accelerated observations of local and global modes

Jason Doukas, Eric G. Brown, Andrzej Dragan, Robert B. Mann

Published Jan 10, 2013• 63 citations
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Abstract

We investigate the amount of entanglement and quantum discord extractable from a two-mode squeezed state as considered from the viewpoint of two observers, Alice (inertial) and Rob (accelerated). We find that using localized modes produces qualitatively different correlation properties for large accelerations than do Unruh modes. Specifically, the entanglement undergoes a sudden death as a function of acceleration, and the discord asymptotes to zero in the limit of infinite acceleration. We conclude that the previous Unruh mode analyses do not determine the acceleration-dependent entanglement and discord degradation of a given quantum state.

DOI
10.1103/physreva.87.012306

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We investigate the amount of entanglement and quantum discord extractable from a two-mode squeezed state as considered from the viewpoint of two observers, Alice (inertial) and Rob (accelerated). We find that using localized modes produces qualitatively different correlation properties for large accelerations than do Unruh modes. Specifically, the entanglement undergoes a sudden death as a function of acceleration, and the discord asymptotes to zero in the limit of infinite acceleration. We conclude that the previous Unruh mode analyses do not determine the acceleration-dependent entanglement and discord degradation of a given quantum state.
We calculate the quantum discord between two free modes of a scalar field, which start in a maximally entangled state and then undergo a relative constant acceleration. In a regime where there is no distillable entanglement due to the Unruh effect, we show that there is a finite amount of quantum discord, which is a measure of purely quantum correlations in a state over and above quantum entanglement. Even in the limit of infinite acceleration of the observer detecting one of the modes, we provide evidence for a nonzero amount of purely quantum correlations. We discuss our result in the context of secure quantum communications involving eavesdroppers in noninertial frames.
We investigate the redistribution of continuous-variable Gaussian quantum discord under the Unruh effect for both one and two uniformly accelerated observers. The discord shared between the inertial mode and the accessible accelerated mode, as well as that between the two accessible accelerated modes, decays monotonically with acceleration and vanishes in the limit a→∞a\to\inftya→∞, while the Unruh effect generates discord in all causally disconnected Rindler mode pairs. The initial quantum correlation is therefore redistributed across Rindler partitions rather than destroyed. We further characterize how the squeezing parameter sss and field frequency ωωω control the discord in different mode-pair classes. For causally connected pairs, sss and ωωω exert comparable, interchangeable effects; for cross-region pairs, the squeezing parameter dominates; and for intra-observer cross-region pairs, the field frequency is more influential. In the two-observer case, the AIIA_{II}AII​-BIIB_{II}BII​ pair exhibits non-monotonic behavior with a peak whose position shifts to larger aaa as ωωω increases, and both parameters contribute only weakly except near an optimal ωs\fracω{s}sω​ ratio.
We review a recently introduced unified approach to the analytical quantification of correlations in Gaussian states of bosonic scalar fields by means of Renyi-2 entropy. This allows us to obtain handy formulae for classical, quantum, total correlations, as well as bipartite and multipartite entanglement. We apply our techniques to the study of correlations between two modes of a scalar field as described by observers in different states of motion. When one or both observers are in uniform acceleration, the quantum and classical correlations are degraded differently by the Unruh effect, depending on which mode is detected. Residual quantum correlations, in the form of quantum discord without entanglement, may survive in the limit of an infinitely accelerated observer Rob, provided they are revealed in a measurement performed by the inertial Alice.
A uniformly accelerated observer perceives the Minkowski vacuum as a thermal bath, so acceleration acts as a noise channel on correlations shared with an inertial partner. For a Dirac field in the standard treatment, the resulting map is a one-sided amplitude-damping channel, and entanglement and quantum discord survive at infinite acceleration. We introduce a symmetric Unruh-like map in which the vacuum and the one-particle state both exchange amplitude with the inaccessible Rindler region; for a Bell state it yields a bit-flip channel whose flip probability is the Fermi-Dirac occupation at the Unruh temperature. Using negativity, mutual information, and all six pairwise quantum discords, we find that the entanglement and discord between the inertial observer and the accessible mode vanish together at infinite acceleration, leaving only one bit of classical correlation. These results show that the fate of quantum correlations in noninertial frames depends on the structure of the Minkowski-Rindler map.
We revisit the ``field entanglement in noninertial frames'' scenario extensively studied in previous literature and demonstrate that the geometric discord, a proposed measure of generalized quantum correlations, decays to zero in the infinite acceleration limit. This is in contrast with previous research showing that the acceleration-induced degradation of quantum discord was not strong enough to extinguish discord in this limit. We argue that our finding has two opposing but noncontradicting implications. On the one hand, the usable quantum correlations in the large acceleration regime appear severely limited for any protocols making use of geometric discord as a figure of merit. On the other hand, our result indicates, in corroboration with other recent work, that the geometric discord is not a faithful measure of quantum correlations, especially in the case of continuous-variable systems, due to the existence of states which have finite quantum discord but are nevertheless infinitesimally close (in the Hilbert-Schmidt norm) to a zero-discord state.
We present a localized solution to the problem of entanglement degradation in noninertial frames. A two-mode squeezed state is considered from the viewpoint of two observers, Alice (inertial) and Rob (accelerated), each observing a single localized mode of the field. We study the state of these modes to determine how much entanglement the observers can extract from the initial state. The dominant source of degradation is an inevitable mode mismatch between the mode of the squeezed state Rob is given and the mode he is able to observe from his accelerated frame. Leakage of the initial mode through Rob's horizon places a limit on his ability to fully measure the state, leading to an inevitable degradation of entanglement that even in principle cannot be fully retrieved by any measurement device.