Exact and local compression of quantum bipartite states

TL;DR

This paper presents a method for exactly compressing bipartite quantum states locally, providing formulas and bounds for minimal dimensions, with applications to quantum channel compression.

Contribution

It introduces a closed-form expression for minimal local compression dimensions and applies it to quantum channel output reduction.

Findings

Derived a closed-form formula for minimal local compression dimensions.

Provided numerically tractable bounds on the Schmidt rank.

Applied the method to analyze quantum channel output compression.

Abstract

We study exact local compression of a quantum bipartite state; that is, applying local quantum operations to reduce the dimensions of the Hilbert spaces while perfectly preserving the correlation. We provide a closed-form expression for the minimal achievable dimensions, formulated as a minimization of the Schmidt rank of a particular pure state constructed from the given state. Numerically tractable upper and lower bounds on this rank are also obtained. As an application, we consider the exact compression of quantum channels. This method enables the analysis of a post-processing step that reduces the output dimensions while retaining the information contained in the original channel's output.