Eternal non-Markovianity: from random unitary to Markov chain realisations

TL;DR

This paper demonstrates how eternal non-Markovian quantum dynamics, characterized by negative decay rates, can be realized through simple stochastic processes, Markov mixtures, and quantum measurements, providing practical laboratory implementations.

Contribution

It introduces a new understanding of eternal non-Markovianity as arising from stochastic and Markovian dynamics, with explicit laboratory and measurement-based realizations.

Findings

ENM dynamics can be realized via stochastic Schrödinger equations.

A quantum trajectory approach based on unitary transformations and measurements is developed.

Extended Hilbert space representations with no ancilla dynamics are constructed.

Abstract

The theoretical description of quantum dynamics in an intriguing way does not necessarily imply the underlying dynamics is indeed intriguing. Here we show how a known very interesting master equation with an always negative decay rate [eternal non-Markovianity (ENM)] arises from simple stochastic Schr\"odinger dynamics (random unitary dynamics). Equivalently, it may be seen as arising from a mixture of Markov (semi-group) open system dynamics. Both these approaches lead to a more general family of CPT maps, characterized by a point within a parameter triangle. Our results show how ENM quantum dynamics can be realised easily in the laboratory. Moreover, we find a quantum time-continuously measured (quantum trajectory) realisation of the dynamics of the ENM master equation based on unitary transformations and projective measurements in an extended Hilbert space, guided by a classical Markov process. Furthermore, a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) representation of the dynamics in an extended Hilbert space can be found, with a remarkable property: there is no dynamics in the ancilla state. Finally, analogous constructions for two qubits extend these results from non-CP-divisible to non-P-divisible dynamics.