Fermionic Quasi-free States and Maps in Information Theory

TL;DR

This paper develops a foundational framework for quantum information theory of fermionic systems, focusing on entropy measures, quasi-free states, and affine maps, with explicit characterizations and calculations.

Contribution

It introduces a comprehensive toolbox for analyzing quasi-free fermionic states and maps, including entropy measures and their computation via one-particle functions.

Findings

Characterization of quasi-free affine maps on fermionic states

Explicit formulas for entropy and relative entropy in quasi-free systems

Analysis of Choi matrices and Jamiolkowski states for certain maps

Abstract

This paper and the results therein are geared towards building a basic toolbox for calculations in quantum information theory of quasi-free fermionic systems. Various entropy and relative entropy measures are discussed and the calculation of these reduced to evaluating functions on the one-particle component of quasi-free states. The set of quasi-free affine maps on the state space is determined and fully characterized in terms of operations on one-particle subspaces. For a subclass of trace preserving completely positive maps and for their duals, Choi matrices and Jamiolkowski states are discussed.