Entanglement dynamics in a non-Markovian environment: An exactly solvable model

Abstract

We study the non-Markovian effects on the dynamics of entanglement in an exactly-solvable model that involves two independent oscillators each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time-correlations, we see non-monotonic evolution of the uncertainties in observables. Further, we extend this exact solution to the two-particle problem and find the dynamics of entanglement in a subspace. We find the phenomena of 'sudden death' and 'rebirth' of entanglement. Interestingly, all memory effects enter via the functional form of the energy and hence the time of death and rebirth is controlled by the amount of noisy energy added into each oscillator. If this energy increases above (decreases below) a threshold, we obtain sudden death (rebirth) of entanglement.

Distributed correlations and information flows within a hybrid multipartite quantum-classical system

“…The utilization of quantum correlations, like entanglement, nonlocality, and discord, is in fact jeopardized by the detrimental effects of the environment surrounding the quantum system [6][7][8][9][10][11][12] so that finding strategies to preserve them has become a main requirement. Non-Markovian noise, originating from structured environments or from strong couplings [4][5][6]13], has been shown to enable dynamical revivals of quantum correlations independently of the quantum [8,[14][15][16][17] or classical [18][19][20][21][22][23][24][25][26][27][28][29][30][31] nature of the environment, allowing an extension of their exploitation time. It is therefore of basic interest to understand the origin of these revival phenomenons.…”

Dynamics of noisy quantum systems in the Heisenberg picture: Application to the stability of fractional charge

“…Even for a fully quadratic system, the noise-averaged effective theory is interacting (see, e.g, Refs. [6,21,22]). For simplicity, hereafter, we focus on the case with only one such quadratic fluctuating term…”

Rabi oscillations, decoherence, and disentanglement in a qubit–spin-bath system

“…As mentioned earlier, the non-Markovian behavior caused by the spin environment may result in novel dynamics of the pairwise entanglement of two qubits each coupled to their own spin bath, as observed in a locally interacting qubitspin-bath system [33]. ESD and subsequent revivals have also been observed to occur in two qubits when they are coupled to classical interacting spin baths [53] and external fields [54], the latter of which has been demonstrated experimentally [55], and to stochastic noise sources [56]. Furthermore, understanding the relation between decoherence and disentanglement is believed to be of importance both for the foundations of quantum mechanics and practical applications in quantum information science [50,[57][58][59][60].…”