Universality of finite time disentanglement

TL;DR

This paper explores how common finite time disentanglement is in bipartite quantum systems, conjecturing it occurs broadly except under local unitary operations, and proves this for specific cases including unitaries and qubits.

Contribution

It proposes and proves a conjecture that finite time disentanglement is universal except for local unitary dynamics, with specific proofs for unitaries and unital maps in qubits.

Findings

FTD occurs for all dynamics except local unitaries.

Proved FTD conjecture for unitaries and unital qubit maps.

Identified conditions under which product and pure states are preserved.

Abstract

In this paper we investigate how common is the phenomenon of Finite Time Disentanglement (FTD) with respect to the set of quantum dynamics of bipartite quantum states with finite dimensional Hilbert spaces. Considering a quantum dynamics from a general sense, as just a continuous family of Completely Positive Trace Preserving maps (parametrized by the time variable) acting on the space of the bipartite systems, we conjecture that FTD happens for all dynamics but those when all maps of the family are induced by local unitary operations. We prove this conjecture valid for two important cases: i) when all maps are induced by unitaries; ii) for pairs of qubits, when all maps are unital. Moreover, we prove some general results about unitaries/CPTP maps preserving product/pure states