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

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 Schrödinger 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.

Mixing-induced quantum non-Markovianity and information flow

“…However, mixing of quantum dynamical maps leads to new time evolutions, whose Markovianity properties can be related in a quite counter-intuitive way to the Markovianity of the original maps [18][19][20][21][22][23]. In particular one can consider random mixtures of unitary evolutions showing up memory effects, so that objections have been raised about the validity of the interpretation of non-Markovianity in terms of information flow [24,25]. On the contrary, here we demonstrate that the procedure of mixing dynamical maps can be understood in a natural way which is fully consistent with the existing theoretical characterization of quantum non-Markovianity.…”

Role of non-Markovianity and backflow of information in the speed of quantum evolution

“…We finally consider an example of multiply decohering dynamics, that is, a qubit undergoing a Pauli channel [38,[56][57][58]. This evolution can be described by the following time-local master equation:…”

IBM Q Experience as a versatile experimental testbed for simulating open quantum systems

“…In this paper, we demonstrate that a careful circuit decomposition allows us to experimentally implement a vast number of fundamental open quantum systems models for one and two qubits. Not only are we able to generate different classes of open quantum dynamics, namely, unital (e.g pure dephasing dynamical maps), non-unital (e.g., amplitude damping dynamical maps), phase covariant, and non-phase covariant (Pauli dynamical maps), but also we can explore the Markovian to non-Markovian crossover, including the recently discovered examples of essential [16] and eternal [54,55] non-Markovianity. We implement a recently proposed non-Markovianity witness [56] and we use our simulator to prove the nonmonotonic behaviour of quantum channel capacity [15] and extractable work [31], with implications to quantum communication and quantum thermodynamics.…”