Internal nonlocality in generally dilated Hermiticity

• URL: http://arxiv.org/abs/2111.05270v3
• Date: Fri, 17 Jun 2022 12:33:49 GMT
• Title: Internal nonlocality in generally dilated Hermiticity
• Authors: Minyi Huang and Ray-Kuang Lee
• Abstract summary: A global Hermitian Hamiltonian can be generated through the dilation from a small Hilbert space. Our results provide a device-independent test on the reliability of the simulation in the global Hermiticity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: According to von Neumann, the global Hamiltonian of whole universe must be Hermitian in order to keep the eigenvalues real and to construct a self-consistent quantum theory. In addition to the open system approach by introducing environmental degrees of freedom to a small system, a global Hermitian Hamiltonian can also be generated through the dilation from a small Hilbert space. For example, a local non-Hermitian $\cal PT$-symmetric system can be simulated with a global Hermitian one by the Naimark dilation. When shared by Alice and Bob, the internal nonlocality in such dilated Hermitian systems is revealed recently, but only with a two-fold structure. In this paper, we extend such a discussion to the generalized case when the two-fold structure breaks. The internal nonlocality is discussed with different correlation pictures and the corresponding correlation bounds. Our results provide a device-independent test on the reliability of the simulation in the global Hermiticity.

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