Internal nonlocality in generally dilated Hermiticity

TL;DR

This paper explores the internal nonlocality in globally dilated Hermitian systems, extending previous two-fold structure results to more general cases, and provides a device-independent test for simulation reliability.

Contribution

It generalizes the study of internal nonlocality in dilated Hermitian systems beyond the two-fold structure, analyzing correlation bounds and offering a new test for simulation accuracy.

Findings

Internal nonlocality persists in generalized dilated Hermitian systems.

Correlation bounds can serve as device-independent tests.

Extended the understanding of nonlocality in quantum dilations.

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.