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The European Physical Journal C

Quantum discord of mixed states under noisy channels in the curved spacetime

Yuxuan Xiong, Zhiling Pi, Tinggui Zhang, Xiaofen Huang

Published Mar 29, 2026• 5 citations
Publisher

Abstract

Abstract 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.

DOI
10.1140/epjc/s10052-026-15563-w

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Abstract 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.
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.
We focus our attention on tripartite mixed states as initial states, and apply coherence concurrence to investigate quantum coherence properties in the background of a Schwarzschild black hole under phase damping, phase flip and bit flip channels, respectively. Several analytic complementary relationships based on coherence concurrence for tripartite subsystems are proposed. In the case of the bit flip channel, the behavior of the coherence concurrence is similar to the one of the phase damping channel, the accessible coherence concurrence always degrades as the Hawking acceleration rising, but sudden death never occurs, while the inaccessible coherence increases from zero monotonically. Interestingly, the coherence concurrence is decreasing at first and then increasing as the decay probability rising under phase flip channel. Unlike the case of tripartite pure states, the coherence concurrence of mixed state with X shape is equal to l1l_1l1​ -norm of coherence.
We focus our attention on tripartite mixed states as initial states, and apply coherence concurrence to investigate quantum coherence properties in the background of a Schwarzschild black hole under phase damping, phase flip and bit flip channels, respectively. Several analytic complementary relationships based on coherence concurrence for tripartite subsystems are proposed. In the case of the bit flip channel, the behavior of the coherence concurrence is similar to the one of the phase damping channel, the accessible coherence concurrence always degrades as the Hawking acceleration rising, but sudden death never occurs, while the inaccessible coherence increases from zero monotonically. Interestingly, the coherence concurrence is decreasing at first and then increasing as the decay probability rising under phase flip channel. Unlike the case of tripartite pure states, the coherence concurrence of mixed state with X shape is equal to l 1 -norm of coherence.
We investigate the geometric quantum discord of bipartite Werner states influenced by Hawking radiation in the quantum atmosphere of a Schwarzschild black hole. We find that the geometric quantum discord in the physically accessible region exhibits a nonmonotonic behavior: it first decreases and then increases as the normalized radial distance increases, while the discord in the physically inaccessible region shows the exact opposite trend. A pronounced extremum of geometric quantum discord occurs precisely at the position corresponding to the peak intensity of Hawking radiation. Furthermore, we find that the Hartle Hawking constant and the event horizon radius exert opposite effects on the strength of quantum correlation redistribution: a larger Hartle Hawking constant enhances the redistribution effect, whereas a larger event horizon radius suppresses it.
We study the symmetry properties in the dynamics of quantum correlations for two-qubit systems in one-sided noisy channels, with respect to a switch in the location of noise from one qubit to the other. We consider four different channel types, namely depolarizing, amplitude damping, bit-flip, and bit-phase-flip channel, and identify the classes of initial states leading to symmetric decay of entanglement, non-locality and discord. Our results show that the symmetric decay of quantum correlations is not directly linked to the presence or absence of symmetry in the initial state, while it does depend on the type of correlation considered as well as on the type of noise. We prove that asymmetric decay can be used to infer, in certain cases, characteristic properties of the channel. We also show that the location of noise may lead to dramatic changes in the persistence of phenomena such as entanglement sudden death and time-invariant discord.
To characterize the effect of Hawking radiation induced by the quantum atmosphere beyond the event horizon on entanglement, we employ concurrence as the entanglement measure for a bipartite mixed state and investigate its evolution with Hawking temperature. We find that the physically accessible concurrence decreases as the Hawking acceleration increases, whereas the physically inaccessible concurrence exhibits the opposite behavior, increasing monotonically from zero. We further establish several trade-off relations on concurrence, revealing its distribution between physically accessible and inaccessible regions. Additionally, we study the dynamics of concurrence under three types of channel noise. The results indicate that the evolution of concurrence depends on the specific noise channel: unlike the phase damping channel, sudden death of concurrence occurs in both phase flip and bit flip channels, the concurrence exhibits a certain symmetry with respect to the noise parameter during its evolution under bit flip channel noise.