Homodyne extimation of quantum states purity by exploiting covariant uncertainty relation

TL;DR

This paper demonstrates an experimental method to estimate the purity of quantum states using homodyne detection and tomographic data, linking uncertainty relations to state purity in quantum information.

Contribution

It introduces a practical approach to determine quantum state purity from homodyne measurements, enhancing real-time quantum information processing capabilities.

Findings

Purity can be inferred from homodyne tomograms using uncertainty relations.

Thermal states serve as a paradigm for mixed quantum states.

Homodyne detection acts as an effective purity-meter in quantum protocols.

Abstract

We experimentally verify uncertainty relations for mixed states in the tomographic representation by measuring the radiation field tomograms, i.e. homodyne distributions. Thermal states of single-mode radiation field are discussed in details as paradigm of mixed quantum state. By considering the connection between generalised uncertainty relations and optical tomograms is seen that the purity of the states can be retrieved by statistical analysis of the homodyne data. The purity parameter assumes a relevant role in quantum information where the effective fidelities of protocols depend critically on the purity of the information carrier states. In this contest the homodyne detector becomes an easy to handle purity-meter for the state on-line with a running quantum information protocol.