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Chinese Physics Letters

Dynamics of Fermionic Geometric Discord beyond Single-Mode Approximations

Muhammad Asif Ramzan

Published Jun 1, 2013• 3 citations
Publisher

Abstract

Geometric quantum discord of fermionic systems in the relativistic regime, that is, beyond the single-mode approximation, is investigated. It is shown that geometric quantum discord for the fermionic systems in non-inertial frames converges at an infinite acceleration limit, which means that the fermionic systems become independent of the choice of Unruh modes (q R ) beyond single-mode approximation. The discord may vanish or be retained depending upon the level of mixedness of the fermionic system. The dynamics of geometric discord are investigated under amplitude damping, depolarizing, phase damping and flipping channels. The vanishing behavior of discord is seen for a higher level of decoherence in the infinite acceleration limit. The depolarizing channel dominantly affects the fermionic geometric discord as compared to the amplitude and phase damping channels. This implies that the depolarizing channel has most destructive influence on the discord of the fermionic systems. However, the flipping channels have a symmetrical effect on the discord. Moreover, the discord heavily depends on the mixedness parameter of the quantum state of the fermionic systems in accelerated frames beyond single-mode approximation.

DOI
10.1088/0256-307x/30/6/060307

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Geometric quantum discord of fermionic systems in the relativistic regime, that is, beyond the single-mode approximation, is investigated. It is shown that geometric quantum discord for the fermionic systems in non-inertial frames converges at an infinite acceleration limit, which means that the fermionic systems become independent of the choice of Unruh modes (q R ) beyond single-mode approximation. The discord may vanish or be retained depending upon the level of mixedness of the fermionic system. The dynamics of geometric discord are investigated under amplitude damping, depolarizing, phase damping and flipping channels. The vanishing behavior of discord is seen for a higher level of decoherence in the infinite acceleration limit. The depolarizing channel dominantly affects the fermionic geometric discord as compared to the amplitude and phase damping channels. This implies that the depolarizing channel has most destructive influence on the discord of the fermionic systems. However, the flipping channels have a symmetrical effect on the discord. Moreover, the discord heavily depends on the mixedness parameter of the quantum state of the fermionic systems in accelerated frames beyond single-mode approximation.
In this article, we investigate the geometric discord of quantum states of fermionic system in accelerated frame. It is shown by the method beyond the single-mode approximation, depending on the region considered, that the geometric discord for the entangled quantum states of fermionic system in accelerated frame can vanish or be retained at the infinite acceleration limit: it does not disappear when the quantum state of the particle(Alice)-particle(Bob in region I) case or the particle(Alice)-antiparticle(Bob in region II) is considered and it disappears when the particle(Alice)-antiparticle(Bob in region I) case or the particle(Alice)-particle(Bob in region II) one is considered.
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.
Abstract Using the single-mode approximation we study the quantum correlations of a free Dirac field on the Werner state in the noninertial frame. We present analytical quantum discord D and its geometric measurement D G . We notice that the quantum discord still exists for the system ρ ARI even in the acceleration limit. We also calculate the entanglement of formation (EOF) and the geometric measure of entanglement ( E G ) to compare the behaviors of the entanglement with the quantum discord. The entanglement is nonzero for the fidelity of the Werner state with a Bell state F > 0.5, while the quantum discord is equal to zero only for F = 0.25. We also observe that the quantum discord is more robust to the change of acceleration than the entanglement, which is more sensitive to the acceleration.
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.
The level surfaces of geometric discord for a class of two-qubit non-X states are investigated when the Bloch vectors are in arbitrary directions. The level surfaces of constant geometric discord are formed by three intersecting open tubes along three orthogonal directions. When Bloch vectors increase, the tubes along one or two directions shrink towards the center and may either totally disappear or the open tubes may become closed tubes when the Bloch vectors reach a critical value. In the generalized amplitude damping channel, the evolution of geometric discord shows double sudden changes when the parameter γ increases. In the phase damping channel, the freezing phenomenon of geometric discord also exists.
We focus our attention on two-qubit mixed states as initial states, and apply the geometric measure of quantum discord to investigate quantum discord properties in the background of a Schwarzschild black hole under phase damping, phase flip and bit flip channels, respectively. Several analytical complementary relationships based on quantum discords for bipartite subsystems are proposed. For the three channel noises, the behaviors of discords are similar, the accessible discords always degrade as the Hawking acceleration rising, but sudden death never occurs, while the inaccessible discords increase from zero monotonically. Interestingly, in the case of the bit flip channel and phase flip channel, the discords perform symmetrically with the decay probability rising.