Parametrization and Optimization of Gaussian Non-Markovian Unravelings for Open Quantum Dynamics

Abstract

We derive a family of Gaussian non-Markovian stochastic Schrödinger equations for the dynamics of open quantum systems. The different unravelings correspond to different choices of squeezed coherent states, reflecting different measurement schemes on the environment. Consequently, we are able to give a single shot measurement interpretation for the stochastic states and microscopic expressions for the noise correlations of the Gaussian process. By construction, the reduced dynamics of the open system does not depend on the squeezing parameters. They determine the non-Hermitian Gaussian correlation, a wide range of which are compatible with the Markov limit. We demonstrate the versatility of our results for quantum information tasks in the non-Markovian regime. In particular, by optimizing the squeezing parameters, we can tailor unravelings for improving entanglement bounds or for environment-assisted entanglement protection.

Non-Markovian Quantum Dynamics in a Squeezed Reservoir

“…The non-Markovian open system dynamics of this model can be described with non-Markovian quantum state diffusion (NMQSD) [22,24,28]. NMQSD is a stochastic unraveling of reduced open system dynamics in terms of a Gaussian colored noise process z(t) with statistics E[z(t)z * (s)] = α(t, s) and E[z(t)] = E[z(t)z(s)] = 0.…”

“…In this article, we investigate open quantum system dynamics in a non-stationary reservoir consisting of oscillators prepared in two-mode squeezed states (broad band squeezed reservoir) [18]. We derive an exact description of the reduced state dynamics using non-Markovian quantum state diffusion (NMQSD) [22][23][24]. Then, using NMQSD as a starting point, we derive a Hierarchy of Equations of Motion [25] (HEOM) for the density matrix of the open system based on the Hierarchy of stochastic Pure States (HOPS) [26].…”

Memory Effects in Quantum Dynamics Modelled by Quantum Renewal Processes

“…If the operators can be obtained by the action of CPTP maps applied on the very same initial state , each can be associated to a different trajectory, whose occurrence probability is indeed given by the corresponding . There exist two main types of decompositions directly linked to a trajectory picture of the dynamics: time-continuous, as exemplified by quantum state diffusion [ 75 , 76 , 77 ], and so called jump unravelings [ 78 , 79 ]. As recalled above, also quantum renewal processes have direct decomposition in terms of trajectories, which are defined at the level of the density operators; see, in particular, Equation ( 12 ).…”

Memory effects in quantum dynamics modelled by quantum renewal processes

“…If the operators can be obtained by the action of CPTP maps Λ i t applied on the very same initial state ρ(0), each ρ i (t) can be associated to a different trajectory, whose occurrence probability is indeed given by the corresponding p i (t). There exist two main types of decompositions directly linked to a trajectory picture of the dynamics: time-continuous, as exemplary quantum state diffusion [76][77][78], and so called jump unravelings [79,80]. As recalled above, also quantum renewal processes have a direct decomposition in terms of trajectories, which are defined at the level of the density operators, see in particular Eq.…”