The distribution of quantum fidelities

TL;DR

This paper derives formulas for the distribution, variance, and average of fidelities resulting from imperfect quantum operations on qubits and linear maps, aiding in understanding quantum process performance.

Contribution

It provides new analytical expressions for fidelity distributions and statistical measures for quantum operations on finite-dimensional systems.

Findings

Derived fidelity distribution formulas for quantum operations

Calculated variance and average fidelities for linear maps

Applicable to general qubit and finite-dimensional systems

Abstract

When applied to different input states, an imperfect quantum operation yields output states with varying fidelities, defined as the absolute square of their overlap with the desired states. We present an expression for the distribution of fidelities for a class of operations applied to a general qubit state, and we present general expressions for the variance and input-space averaged fidelities of arbitrary linear maps on finite dimensional Hilbert spaces.