Reduced dynamics in quasi-Hermitian systems

Abstract

Evolutions under non-Hermitian Hamiltonians with unbroken $\mathcal{P}\mathcal{T}$ symmetry can be considered unitary under appropriate choices of inner products, facilitated by the so-called metric operator. While it is understood that the choice of the metric operator has no bearing on the description of the system, in this work, we show that this choice does dictate the entanglement structure of the system. We show that the partial trace of the Hermitized density matrix gives the correct representation of the reduced subsystem, and based on such operations, we elucidate the metric dependency of the reduced dynamics and consequently the observable dependence of the subsystem decomposition. We use a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum walk as a toy model to study this metric dependency, where we use the internal (coin state) as the subsystem of interest and study the coin-position entanglement and non-Markovianity of the coin dynamics.

8+2 pages, 3 figures, 1 table; published version. Title changed from "Reduced dynamics of a PT-symmetric evolution"

References in corpus (19)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Non-Markovian dynamics in open quantum systems
• Universal computation by quantum walk
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• 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
• Topological Transition in a Non-Hermitian Quantum Walk
• Quantum tensor product structures are observable-induced
• Virtual Quantum Subsystems
• Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction
• Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries
• Local PT symmetry violates the no-signaling principle
• Non-Hermitian Hamiltonians and no-go theorems in quantum information
• Explicit definition of $\mathcal{P}\mathcal{T}$ symmetry for non-unitary quantum walks with gain and loss
• Consistency of PT-symmetric quantum mechanics
• Multiparameter estimation perspective on non-Hermitian singularity-enhanced sensing
• Non-Hermitian quantum walks and non-Markovianity: the coin-position interaction