Shannon theory for quantum systems and beyond: information compression for fermions

TL;DR

This paper develops a theoretical framework for compressing fermionic quantum information, highlighting the importance of preserving correlations due to superselection rules and establishing a fermionic source coding theorem based on entanglement fidelity.

Contribution

It introduces a fermionic version of the quantum source coding theorem and demonstrates that entanglement fidelity is a superior reliability measure for fermionic systems.

Findings

Entanglement fidelity effectively assesses correlation preservation in fermionic compression.

A fermionic source coding theorem analogous to the quantum case is established.

Von Neumann entropy remains the minimal rate for reliable fermionic compression.

Abstract

We address the task of compression of fermionic quantum information. Due to the parity superselection rule, differently from the case of encoding of quantum information in qubit states, part of the information carried by fermionic systems is encoded in their delocalised correlations. As a consequence, reliability of a compression protocol must be assessed in a way that necessarily accounts also for the preservation of correlations. This implies that input/output fidelity is not a satisfactory figure of merit for fermionic compression schemes. We then discuss various aspects regarding the assessment of reliability of an encoding scheme, and show that entanglement fidelity in the fermionic case is capable of evaluating the preservation of correlations, thus revealing itself strictly stronger than input/output fidelity, unlike the qubit case. We then introduce a fermionic version of the source coding theorem showing that, as in the quantum case, the von Neumann entropy is the minimal rate for which a fermionic compression scheme exists, that is reliable according to the entanglement fidelity criterion.