Finding purifications with minimal entanglement

TL;DR

This paper presents an MPS-based method to find purifications of quantum states with minimal entanglement, improving efficiency in representing mixed states especially at low temperatures and after quenches.

Contribution

The authors introduce an iterative MPS approach to minimize entanglement in purifications, enabling more efficient representations of quantum states.

Findings

Entanglement can be significantly reduced in thermofield double purifications at low temperatures.

The method can slow down entanglement growth after a quench from infinite temperature.

Minimally entangled purifications enhance the efficiency of quantum state representations.

Abstract

Purification is a tool that allows to represent mixed quantum states as pure states on enlarged Hilbert spaces. A purification of a given state is not unique and its entanglement strongly depends on the particular choice made. Moreover, in one-dimensional systems, the amount of entanglement is linked to how efficiently the purified state can be represented using matrix-product states (MPS). We introduce an MPS based method that allows to find the minimally entangled representation by iteratively minimizing the second Renyi entropy. First, we consider the thermofield double purification and show that its entanglement can be strongly reduced especially at low temperatures. Second, we show that a slowdown of the entanglement growth following a quench of an infinite temperature state is possible.