Direct method for measuring of purity, superfidelity, and subfidelity of photonic two-qubit mixed states

TL;DR

This paper introduces a direct experimental method to measure the fidelity, superfidelity, and subfidelity of two-qubit mixed states, enabling efficient assessment of quantum states without full tomography.

Contribution

The paper presents a novel direct measurement technique for fidelity bounds and purity of two-qubit states, reducing the complexity of quantum state characterization.

Findings

Method allows direct measurement of overlaps between two-qubit states.

Applicable to measure purity and linear entropy of two-qubit states.

Comparison of experimental strategies for optical implementations.

Abstract

The Uhlmann-Jozsa fidelity (or, equivalently, the Bures distance) is a basic concept of quantum communication and quantum information, which however is very difficult to measure efficiently without recourse to quantum tomography. Here we propose a direct experimental method to estimate the fidelity between two unknown two-qubit mixed states via the measurement of the upper and lower bounds of the fidelity, which are referred to as the superfidelity and subfidelity, respectively. Our method enables a direct measurement of the first- and second-order overlaps between two arbitrary two-qubit states. In particular, the method can be applied to measure the purity (or linear entropy) of a single two-qubit mixed state in a direct experiment. We also propose and critically compare several experimental strategies for measuring the sub- and superfidelities of polarization states of photons in various linear-optical setups.