The Entanglement Timescale

TL;DR

This paper derives a general timescale for entanglement development between two quantum subsystems, linking it to their correlated uncertainty, and extends the concept to mixed states, broadening its applicability.

Contribution

It introduces a universal entanglement timescale formula applicable to arbitrary Hamiltonians and initial states, generalizing decoherence timescales to mixed states.

Findings

Entanglement timescale inversely proportional to correlated uncertainty

Applicable to pure and mixed initial states

Generalizes decoherence timescale concept

Abstract

We derive the timescale for two initially pure subsystems to become entangled with each other through an arbitrary Hamiltonian that couples them. The entanglement timescale is inversely proportional to the "correlated uncertainty" between the two subsystems, a quantity which we will define and analyze in this paper. Our result is still applicable when one of the subsystems started in an arbitrarily mixed state, thus it generalizes the well-known "decoherence timescale" while coupled to a thermal state.