Entanglement of pseudo-Hermitian random states

Abstract

In a recent paper (arXiv:1905.07348v1), Dyson scheme to deal with density matrix of non-Hermitian Hamiltonians has been used to investigate the entanglement of states of a PT-symmetric bosonic system. They found that von Neumann entropy can show a different behavior in the broken and unbroken regime. We show that their results can be recast in terms of an abstract model of pseudo-Hermitian random matrices. It is found however that, although the formalism is practically the same, the entanglement is not of Fock states but of Bell states.

arXiv comment15 pages, 2 figures

References in corpus (26)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• PT-Symmetric Quantum Mechanics
• Sudden Death of Entanglement
• 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
• Sudden Death of Entanglement of Two Jaynes-Cummings Atoms
• Statistical distribution of quantum entanglement for a random bipartite state
• Time-dependent version of cryptohermitian quantum theory
• Unitary quantum evolution for time-dependent quasi-Hermitian systems with non-observable Hamiltonians
• Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator
• Phase Transitions in the Distribution of Bipartite Entanglement of a Random Pure State
• The non-Hermitian Swanson model with a time-dependent metric
• Random pure states: quantifying bipartite entanglement beyond the linear statistics
• Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State
• Mending the broken PT-regime via an explicit time-dependent Dyson map
• Eternal life of entropy in non-Hermitian quantum systems
• Solvable two dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime
• Pseudo-Hermitian random matrix theory
• Dynamics of finite dimensional non-hermitian systems with indefinite metric
• Generalized Weyl-Heisenberg algebra, qudit systems and entanglement measure of symmetric states via spin coherent states
• Optimal Spin Squeezed Steady State induced by the dynamics of non-hermtian hamiltonians
• Statistical properties of eigenvalues of an ensemble of pseudo-Hermitian Gaussian matrices
• Distribution of Schmidt-like eigenvalues for Gaussian Ensembles of the Random Matrix Theory