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

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.

arXiv comment5 pages, 2 figures

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• Markovian and non-Markovian quantum measurements
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• Absolutely $k$-Incoherent Quantum States and Spectral Inequalities for Factor Width of a Matrix
• Resource Theory of Non-absolute Separability
• Physical realization of realignment criteria using structural physical approximation
• A bipartite separable ball and its applications
• Role of quantum state texture in probing resource theories and quantum phase transition
• Sufficient criteria for absolute separability in arbitrary dimensions via linear map inverses
• Is absolute separability determined by the partial transpose?
• On the extreme points of sets of absolulely separable and PPT states
• Estimation of multivariate traces of states given partial classical information
• Spectral characterizations of entanglement witnesses
• Structural physical approximation of partial transposition makes possible to distinguish SLOCC inequivalent classes of three-qubit system