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.
Highlights
A realistic modelling of many quantum phenomena inevitably needs to take into account the interaction of our system of interest with environmental degrees of freedom
In some cases of interest, the open system dynamics may be written in terms of a time-local master equation involving time-dependent functions as prefactors with otherwise GKSL form
Either there is no dynamical environment at all, the dynamics can be realised by a classical Markov process or, when embedded in a larger Hilbert space, there is no dynamics of the environmental state
Summary
With σα|±α〉 = ±|±α〉, Eq (9) leaves the populations 〈+α|ρ(t)|+α〉 and 〈−α|ρ(t)|−α〉 constant, the coherences 〈+α|ρ(t)|−α〉, 〈−α|ρ(t)|+α〉, decay with a factor e−2t. Since this CPT map is unital, the dynamics is of random unitary or random external field type[49,50,51,52,53]. A physical realisation of Eq (9) for pure initial states is obtained from a fluctuating field ξ(t) driving the unitary Schrödinger dynamics: i∂t ψ(t) = ξ(t)σα ψ(t). If ξ(t) represents Gaussian real white noise with 〈〈ξ(t)〉〉ξ = 0 and 〈〈ξ(t)ξ(s)〉〉ξ = δ(t − s), the noise-averaged state ρ(t) = 〈〈|ψ(t)〉〈ψ(t)|〉〉ξ is a solution of (9) (see Supplementary Information).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
