Determining eigenvalues of a density matrix with minimal information in a single experimental setting

TL;DR

This paper introduces a minimal, single-measurement method to determine all eigenvalues of an unknown density matrix, enabling efficient characterization of quantum states without full state reconstruction.

Contribution

A novel approach to extract all eigenvalues of a density matrix using only one observable measurement in a single experimental setup.

Findings

Eigenvalues can be determined with minimal parameters.

Method is applicable in linear optical and superconducting systems.

No full quantum state tomography needed.

Abstract

Eigenvalues of a density matrix characterize well the quantum state's properties, such as coherence and entanglement. We propose a simple method to determine all the eigenvalues of an unknown density matrix of a finite-dimensional system in a single experimental setting. Without fully reconstructing a quantum state, eigenvalues are determined with the minimal number of parameters obtained by a measurement of a single observable. Moreover, its implementation is illustrated in linear optical and superconducting systems.