Finding purifications with minimal entanglement

Abstract

Purification is a well-known tool to represent mixed quantum states as pure states on an enlarged Hilbert space. A purification of a given state is not unique and its spatial entanglement strongly depends on the particular choice. This entanglement is linked to how efficiently the purified state can be represented using matrix-product states (MPS). Here, the authors introduce an MPS-based method that allows the user to efficiently find the minimally entangled purification of a given mixed state and demonstrate that it can significantly reduce the entanglement in certain cases.