Complete Conditions for Entanglement Transfer

Abstract

We investigate the conditions to entangle two qubits interacting with local environments driven by a continuous-variable correlated field. We find the conditions to transfer the entanglement from the driving field to the qubits both in dynamical and steady-state cases. We see how the quantum correlations initially present in the driving field play a critical role in the entanglement-transfer process. The system we treat is general enough to be adapted to different physical setups.

Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment

“…With the expression of J r , we can derive the master equation for the reduced density matrix (26). This is shown in Appendix A.…”

“…Of interest is a comparison with the model that consists of 2HO each in its own heat bath. In our model, the coupling to a common heat bath can give rise to several new features, of particular interest here is the generation of entanglement between the two Brownian particles due to the back-action of the heat bath on the system [24,25,26,27]. Let us first rewrite the total Hamiltonian in terms of a set of new variables X, x, P, p defined as…”

Characterization of the entanglement of two squeezed states

“…We have also checked that, for τ ≤ 10, the transferred entanglement corresponding to other choices of s and other rescaled interaction times is always smaller than the value achieved at τ = 8 with s = 1.1. The considerations of experimental observability of the entangling power discussed in [17,18,25] are valid in the context of the present work. Given the similarity between entangled coherent states and the class of ESV's, it is not difficult to think about applications of ESS's in QIP schemes such as those described in [26].…”

“…Alternatively (and somehow more operatively) we can also check for the capability of the state at hand to induce entanglement, by means of just bi-local interactions, into an initially separable state of two non-interacting qubits. This has been formalized by the so-called entangling power test, which has been applied in order to get some physical insight into some problems of quantum state characterization and has demonstrated to be powerful under many points of view [17,18,25]. A full description of the protocol is certainly not the main focus of this work and we refer to the available literature for a detailed analysis of the entangling power test.…”

“…Each interaction is local to a qubit-mode subsystem. In the spirit of [17,18,25], here we assume a resonant Jaynes-Cummings coupling of equal strength g for each local interaction. The state of the two CV modes is then traced out in order to get the reduced (mixed) density matrix for the qubits.…”