Any Quantum Many-Body State under Local Dissipation will be Disentangled in Finite Time

TL;DR

This paper proves that all quantum many-body states subjected to local dissipation become fully separable in finite time, regardless of system size, under certain conditions like a finite damping gap and full-rank steady state.

Contribution

It establishes a universal finite-time disentanglement result for quantum many-body states under local dissipation, combining measurement-based state reconstruction and quantum channel convergence.

Findings

Disentanglement occurs in finite time under local dissipation.

The result holds regardless of system size.

Conditions include finite damping gap and full-rank steady state.

Abstract

We prove that any quantum many-spin state under genetic local dissipation will be fully separable after a finite time independent of the system size. Such a sudden death of many-body entanglement occurs universally provided that there is a finite damping gap and the unique steady-state density matrix is of full rank. This result is rigorously derived by combining a state-reconstruction identity based on random measurements and the convergence bound for quantum channels. Related works and possible generalizations are also discussed.