On the qubits dynamics in random matrix environment

Abstract

We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment. We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso-and even nanosize. We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition. We then workout an analog of BornMarkov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord. We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits. In particular, we find the vanishing of the entanglement at finite moments and its subsequent revivals (entanglement sudden death and entanglement sudden birth). Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.

The Dynamics of Quantum Correlations of Two Qubits in a Common Environment Modeled by Large Random Matrices

“…

This paper is a continuation of our previous paper [8], in which we have studied the dynamics of quantum correlations of two qubits embedded each into its own disordered multiconnected environment. We modeled the environment by random matrices of large size allowing for a possibility to describe meso-and even nanoenvironments.

…”

“…The approximation does not imply in general the Markovian evolution in our model but allows for sufficiently detailed analysis both analytical and numerical of the evolution of several widely used quantifiers of quantum correlation, mainly entanglement. We find a number of new patterns of qubits dynamics comparing with the case of independent environments studied in [8] and displaying the role of dynamical (indirect, via the environment) correlations in the enhancing and diversification of qubit evolution. Our results, (announced in [9]), can be viewed as a manifestation of the universality of certain properties of the decoherent qubit evolution which have been found previously in various exact and approximate versions of two-qubit models with macroscopic bosonic environment.…”

“…In view of this the models of dynamics of qubits, the basic entities of quantum information science, embedded in an environment comprise an active branch of quantum information theory and adjacent fields, see [4,11,25,33,40] for reviews. In particular, there exists a certain amount of models, where the qubits-environment Hamiltonians include random matrices of large size, see our paper [8] for the comparative analysis of these models. It is worth mentioning that random matrices have been widely using to describe complex quantum systems of large but not necessary macroscopic size, see e.g., [3,18,32] for results and references.…”

“…It is worth mentioning that random matrices have been widely using to describe complex quantum systems of large but not necessary macroscopic size, see e.g., [3,18,32] for results and references. In particular, in our recent work [8] we analyzed the evolution of two qubits interacting with (i) either a two-component environment with dynamically independent components each interacting with its "own" qubit, (ii) or a one-component environment interacting with one of two qubits while the second qubit is free (so called ancilla).…”

“…In this paper we will present our results on a physically different and, we believe, quite interesting model of two qubits interacting with a common environment also modeled by random matrices. In this case we have to work out the corresponding dynamics anew by using an extension of random matrix techniques of our earlier works [22,8,9,32]. As a result, we are able to study a variety of interesting time evolutions both new and found in other models of environment for the widely used quantifiers of quantum correlations (the concurrence, the negativity, the quantum discord and the von Neumann entropy).…”