Decoherence and entanglement evolution of two qubits coupled through Heisenberg interactions to a spin bath in thermal equilibrium

Abstract

The decoherence and entanglement dynamics of two interacting qubits coupled through Heisenberg XY interactions to a spin bath in thermal equilibrium are studied. The exact form of the reduced density matrix is derived for finite and infinite numbers of environmental spins. It is shown that decoherence can be minimized at low bath temperatures and strong coupling between the qubits. Some initial product states evolve into entangled ones, initially entangled states lose completely or partially their entanglement. The relation between the fidelity and the concurrence is also investigated.

A nontrivial bosonic representation of large spin systems at high temperatures

“…Let us begin by proving some results about the behaviour of the spin operators Ŝα / [8][9][10][11][12]. By the multinomial theorem we have that…”

Aspects of the decoherence in high-spin environments: Breakdown of the mean-field approximation

“…where the decoherence time τ D can be determined via the second-order master equation, describing the evolution of the open system (see, e.g., [16]). Explicitly, we find that…”

“…Needless to say that these features depend on the physical nature of the degrees of freedom characterizing its constituents. Therefore, it is no surprise that most of the investigations have dealt with developing various techniques that enable the elimination of the spin or the bosonic degrees of freedom of the environment [6][7][8][9][10][11][12][13][14][15][16][17], which allows one to focus on the evolution of the central system. The mathematical tools needed for such calculations vary depending on whether the environment is of spin or bosonic nature.…”

Decay rates and decoherence of an interstitial two-level spin impurity in a ferromagnetic lattice

“…It has been widely used in many contexts and it is of great usefulness to test the validity of the numerical techniques used to solve complicated problems. Depending on whether the degrees of freedom are of bosonic or of spin nature, many techniques have been proposed in order to fulfill this task [6][7][8][9][10][11][12][13][14][15][16][17]. It should be emphasized that the two key points that make some models so interesting reside in the possibility to integrate out the bosonic degrees of freedom through the introduction of a spectral density (usually of Lorentzian form), and in the use of the so-called Born approximations and Markovian.…”