Recovery of contextuality based on mirror-like state discrimination in PT- and anti-PT-symmetric systems
arxiv(2024)
摘要
In the past decades, researches on parity-time (PT) and anti-parity-time(APT)
systems have garnered unprecedented attention, showcasing their various
intriguing characteristics and promising potentiality in extending canonical
Hermitian quantum mechanics. However, despite significant endeavors devoted to
this new field of physics, non-Hermitian dynamics of contextuality still
remains an uncharted region, either in PT-symmetry or APT-symmetry systems.
Since contextuality has also been proven to be the core resource for quantum
state discrimination (QSD) tasks, here we systematically investigate the novel
performance of contextuality through QSD in both systems, taking
mirror-symmetric three-state minimum error discrimination (MED) and maximum
confidence discrimination (MCD) scenarios as two examples. The time evolution
of contextuality in two scenarios and eight regimes (four regimes for each
scenario) are comprehensively compared and analyzed, with the difference of
initial states also considered. In the symmetry-unbroken regimes, our
simulation shows periodic oscillations of contextuality for both MED and MCD
scenarios, the period of which is state-independent but related to
non-Hermiticity of the system. Both MED and MCD shows non-trivial recovery of
contextuality exceeding its initial value in PT system, which is only existent
for MCD in APT system. In the symmetry-broken regimes, the success
probabilities of both scenarios start from a prompt decay at first, ending up
with a stable value which is constantly 1/3. Non-triviality is found only for
MCD scenario in PT system, where the recovered contextuality exceeds its
initial value.
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