Quantum filtering for systems driven by fermion fields

TL;DR

This paper develops a quantum filtering theory for systems driven by fermion fields using fermion quantum stochastic calculus, connecting it to classical filtering theory and advancing quantum control methods.

Contribution

It introduces a fermion filtering framework based on fermion quantum stochastic calculus, bridging quantum and classical filtering theories.

Findings

Fermion filtering theory formulated using fermion quantum stochastic calculus

Connections established between quantum fermion filtering and classical filtering theory

Potential applications in quantum control and measurement of fermionic systems

Abstract

Recent developments in quantum technology mean that is it now possible to manipulate systems and measure fermion fields (e.g. reservoirs of electrons) at the quantum level. This progress has motivated some recent work on filtering theory for quantum systems driven by fermion fields by Korotkov, Milburn and others. The purpose of this paper is to develop fermion filtering theory using the fermion quantum stochastic calculus. We explain that this approach has close connections to the classical filtering theory that is a fundamental part of the systems and control theory that has developed over the past 50 years.