Physically realizable entanglement by local continuous measurements

Abstract

Quantum systems prepared in pure states evolve into mixtures under environmental action. Physically realizable ensembles are the pure state decompositions of those mixtures that can be generated in time through continuous measurements of the environment. Here, we define physically realizable entanglement as the average entanglement over realizable ensembles. We optimize the measurement strategy to maximize and minimize this quantity through local observations on the independent environments that cause two qubits to disentangle in time. We then compare it with the entanglement bounds for the unmonitored system. For some relevant noise sources the maximum realizable entanglement coincides with the upper bound, establishing the scheme as an alternative to locally protect entanglement. However, for local strategies, the lower bound of the unmonitored system is not reached. Decoherence is the process in which the exchange of information between a quantum system and an external environment continuously downgrades quantum properties of the former [1]. This dynamics turns initially pure entangled states into mixed less entangled ones, destroying the capacity of the system for quantum applications. In this picture, the description of the properties of the system in time results from ignoring the information that leaks into the environment and only considering the general statistical characteristics of the reservoir. If, however, one is able to recover some of this information by, for example, continuously observing changes into the environment, the time evolution of the system undergoes a different dynamics which is conditioned on the results of these observations. Such conditional evolutions are usually referred to as quantum trajectories [1] because if the system is initially prepared in a pure state, the sequence of measurements performed on the environment determines a respective sequence of other pure states for the system. Each trajectory corresponds to one realization of the experiment and the open system evolution is recovered when averaging over all possible trajectories. Such trajectories have already been observed both in massive particles and light [2].There are infinitely many different ways to observe a physical environment, also referred to as unravellings. Each one of them defines a different set of experimentally realizable trajectories. However, even though at any given time the incoherent sum over all possible trajectories reproduces the quantum state of the unmonitored system, that does not mean that all its pure state decompositions are available, since not all ensembles can be achieved through this continuous monitoring process [3]. The fact that one can reconstruct the state allows one to recover the average value of any observable in time by averaging over the trajectories. However, when it comes to obtaining the entanglement of the system, the restrictions imposed by the unraveled time evolution may be too strong [4].In this paper, we investigate equivalent local measurement strategies over the i...

Recovering entanglement by local operations

“…The example of the two qubits affected by low-frequency noise highlights that when a bipartite quantum system is affected by classical non-Markovian noise, the induced nonMarkovian dynamics of the bipartite system does not justify by itself the occurrence of entanglement 3 The physical decomposition of the AB system interacting with another quantum system in general is not unique, see Appendix A.2. The decomposition we choose may be physically realizable in cavity QED systems, moreover one can numerically check that it gives the largest amount of average entanglement [28]. 4 It is worth to notice that Eq.…”

“…The measurement of the environment E removes the arbitrariness of the ρ Q decomposition, the system Q being physically described [9,10,28,33,43] by the ensemble (A.20). Once the classical information about the outcomes k is known, the average entanglement E av (A k ) can be obtained by means of local operations.…”

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

“…Unravelings of the system are now parameterized by the left upper part of u only. The equation of motion (22) for the average concurrence reduces to…”

“…As a consequence, also the entanglement in the system vary according to how the environment is being monitored, and its time evolution can then be systematically characterized in an efficient way [18,19]. Numerical and analytical explorations of this proposal allowed for the description of the dynamics of entanglement [18][19][20][21] and entanglement of assistance [22] in various experimentally relevant situations, and preluded the formulation of new protocols for entanglement protection [23] and quantum computation [24], as well as its extension for the study of general quantum correlations [25]. Here we present a rigorous implementation of the quantum trajectory theory for the systematic study of the dynamics of entanglement in open quantum systems of two-qubits, and lay with clarity the groundwork for its extension to quantum systems of arbitrary size.…”

Dynamics of genuine multipartite correlations in open quantum systems

“…This gives hope for a dynamical characterization of correlations when the dynamics themselves naturally give rise to a decomposition of the quantum state into an ensemble of pure states. For bipartite entanglement this has been exploited to define an average entanglement for open Markovian systems with an evolution described by a Lindblad master equation [7], and much work has been done in recent years to investigate this entanglement measure in various experimentally relevant situations [8][9][10][11][12]. We present an analogous definition for genuine multipartite correlations and show how it can be used to study the dynamical evolution of correlations in open multipartite quantum systems.…”