Entanglement Evolution via Quantum Resonances

TL;DR

This paper develops a resonance-based framework to analyze the dynamics of entanglement in two qubits interacting with thermal reservoirs, showing entanglement decay in finite time under thermalization.

Contribution

It introduces a resonance representation of the reduced dynamics for all times, allowing explicit bounds on entanglement decay times based on resonance data.

Findings

Entanglement dies out in finite time during thermalization.

The dynamics within energy subspaces are Markovian and decoupled.

Explicit bounds on entanglement survival times are derived.

Abstract

We consider two qubits interacting with local and collective thermal reservoirs. Each spin-reservoir interaction consists of an energy exchange and an energy conserving channel. We prove a resonance representation of the reduced dynamics of the spins, valid for all times t>=0, with errors (small interaction) estimated rigorously, uniformly in time. Subspaces associated to non-interacting energy differences evolve independently, partitioning the reduced density matrix into dynamically decoupled clusters of jointly evolving matrix elements. Within each subspace the dynamics is markovian with a generator determined entirely by the resonance data of the full Hamiltonian. Based on the resonance representation we examine the evolution of entanglement (concurrence). We show that, whenever thermalization takes place, entanglement of any initial state dies out in a finite time and will not return. For a concrete class of initially entangled spin states we find explicit bounds on entanglement survival and death times in terms of the initial state and the resonance data.