Average entanglement dynamics in open two-qubit systems with continuous monitoring

Abstract

We present a comprehensive implementation of the quantum trajectory theory for the description of the entanglement dynamics in a Markovian open quantum system made of two qubits. We introduce the average concurrence to characterize the entanglement in the system and derive a deterministic evolution equation for it that depends on the ways information is read from the environment. This builded in flexibility of the method is used to address two actual issues in quantum information: entanglement protection and entanglement estimation. We identify general physical situations in which an entanglement protection protocol based on local monitoring of the environment can be implemented. Additionally, we methodically find unravelings of the system dynamics providing analytical tight bounds for the unmonitored entanglement in the system at all times. We conclude by showing the independence of the method on the choice of entanglement measure.

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

“…Remarkably, we are able to construct explicitly a measurement on a realistic quantum environment that realizes an environment-assisted entanglement protection scenario, generalizing earlier considerations on Markov open quantum systems [22,46,47].…”

“…Exact results on entanglement evolution in multipartite open systems with non-Markovian dynamics are scarce [9], making it difficult to asses how tight our bound really is. Yet, for the case of two qubits with only one of them coupled to a dephasing channel, the exact entanglement dynamics is given in [22] for Markovian and in [44] for non-Markovian dynamics, our bound exactly reproduces this entanglement evolution. Indeed, our bound is also exact for any N -partite open system, where only one subsystem of dimension two is exposed to an arbitrary dephasing channel [37].…”

“…Changing these parameters allows control over the noise correlations driving the stochastic dynamics, which can be used to optimize the trajectories e.g. for entanglement detection [21,22]. Moreover, in the Markov case, a physical interpretation for the stochastic states can be given in terms of continuous monitoring of the environment of the open system [23].Recently, there have been similar efforts in the non-Markovian regime.…”

“…Ref. [22,44]). For comparison we show the bound obtained for x ξ=0 (T ) (red dashed line), corresponding to the bound using the standard NMQSD (η = 0).…”

Atom-field entanglement in cavity QED: Nonlinearity and saturation

“…For weak fields the unraveling is irrelevant, as the system is well approximated by a pure state for many lifetimes, as the jump rate P (t)dt = γ σ z (t) + 1/2 dt and σ z (t) ≈ −1 for weak fields, so jump events are relatively rare. It has been shown that while entanglement is different for different unravelings, for a given unraveling all measures of entanglement show similar behavior as system parameters are changed [16].…”