Extracting the internal nonlocality from the dilated Hermiticity
- URL: http://arxiv.org/abs/2009.06121v2
- Date: Wed, 7 Jul 2021 00:38:57 GMT
- Title: Extracting the internal nonlocality from the dilated Hermiticity
- Authors: Minyi Huang, Ray-Kuang Lee, Junde Wu
- Abstract summary: We consider the problem of how to extract the internal nonlocality in the Hermitian dilation.
Our results make a difference between the Hermitian dilation and other global Hamiltonians without internal nonlocality.
- Score: 3.222802562733787
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: To effectively realize a $\cal PT$-symmetric system, one can dilate a $\cal
PT$-symmetric Hamiltonian to some global Hermitian one and simulate its
evolution in the dilated Hermitian system. However, with only a global
Hermitian Hamiltonian, how do we know whether it is a dilation and is useful
for simulation? To answer this question, we consider the problem of how to
extract the internal nonlocality in the Hermitian dilation. We unveil that the
internal nonlocality brings nontrivial correlations between the subsystems. By
evaluating the correlations with local measurements in three different
pictures, the resulting different expectations of the Bell operator reveal the
distinction of the internal nonlocality. When the simulated $\cal PT$-symmetric
Hamiltonian approaches its exceptional point, such a distinction tends to be
most significant. Our results clearly make a difference between the Hermitian
dilation and other global Hamiltonians without internal nonlocality. They also
provide the figure of merit to test the reliability of the simulation, as well
as to verify a $\cal PT$-symmetric (sub)system.
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