Eternal life of entropy in non-Hermitian quantum systems

Abstract

We find a new effect for the behaviour of Von Neumann entropy. For this we derive the framework for describing Von Neumann entropy in non-Hermitian quantum systems and then apply it to a simple interacting P T symmetric bosonic system. We show that our model is well defined even in the P T broken regime with the introduction of a time-dependent metric and that it displays three distinct behaviours relating to the P T symmetry of the original time-independent Hamiltonian. When the symmetry is unbroken, the entropy undergoes rapid decay to zero (so-called "sudden death") with a subsequent revival. At the exceptional point it decays asymptotically to zero and when the symmetry is spontaneously broken it decays asymptotically to a finite constant value ("eternal life").

Controlling decoherence via PT-symmetric non-Hermitian open quantum systems

“…We show the decoherence characteristics of the spinsystem by studying the entanglement of a two-spin system where the initial state of the system is a maximally entangled state and one of the spin is interacting with the bath. Interestingly, we found that the entanglement in our system persists indefinitely in the entire PTsymmetric regime, unlike the results shown in [34,35], albeit in different settings, which only hold within the spontaneous PT -broken regime and on the exceptional points, respectively.…”

Entanglement of Pseudo-Hermitian Random States

“…The importance of the authors’ findings of Ref. [ 1 ] lies in the consequences it has to the question of time evolution of non-Hermitian Hamiltonians [ 2 , 3 ], or, more precisely, to the evolution of their associated density matrices. It shows that by introducing an appropriate time-dependent metric, the density matrix of a non-Hermitian Hamiltonian can be linked to one of a Hermitian one by a similarity transformation.…”

“…Therefore, both share the same von Neumamm entropy. From a practical point of view, Dyson’s formula is an equation of motion that connects the metric and the Hamiltonians that in principle, can be solved as shown in [ 1 ]. On the other hand, the identification in Ref.…”

“…On the other hand, the identification in Ref. [ 1 ] of a regime in which entanglement is preserved in the time evolution is an important result with potential application in quantum computation.…”

“…The non-Hermiticity addressed in Refs. [ 1 , 4 , 5 ] is that related to the PT -symmetry. It can be shown that a complex non-Hermitian Hamiltonian invariant under the combined parity ( P ) and time reversal ( T ) transformations have eigenvalues which are real or complex conjugate.…”