Internal nonlocality in generally dilated Hermiticity

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 $\mathcal{P}\mathcal{T}$-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.

arXiv comment12 pages, close to the published version

References in corpus (16)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Bell nonlocality
• Non-Hermitian Physics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermitian Representation of Quantum Mechanics
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Detection-Loophole-Free Test of Quantum Nonlocality, and Applications
• Observation of parity-time symmetry breaking in a single spin system
• Information Retrieval and Criticality in Parity-Time-Symmetric Systems
• The Naimark dilated PT-symmetric brachistochrone
• Local PT symmetry violates the no-signaling principle
• Simulating broken $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian systems by weak measurement
• Embedding, simulation and consistency of $\mathcal{P}\mathcal{T}$ -symmetric quantum Theory
• Extracting the internal nonlocality from the dilated Hermiticity