Fermionic quantum operations: a computational framework I. Basic invariance properties

TL;DR

This paper investigates the fundamental invariance properties of fermionic quantum (FQ) operations for two-element systems, analyzing how these properties are represented in their formal power series expansions.

Contribution

It introduces a formal framework linking invariance properties of FQ operations to their power series representations, laying groundwork for understanding their behavior.

Findings

Invariance properties are reflected in the structure of power series expansions.

Provides a formal approach to analyze FQ operations for n=2.

Sets the stage for further exploration of FQ conform-operations for n=3.

Abstract

The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case $n=2$, and FQ conform-operations in the case $n=3$. In this first part we study how the basic invariance properties of FQ operations ($n=2$) are reflected in their formal power series expansions.