Random positive operator valued measures
arXiv:1902.04751 · doi:10.1063/1.5131028
Abstract
We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting eigenvalue distributions with the help of free probability theory. Similarly, we obtain the large system limit for several quantities of interest in quantum information theory, such as the sharpness, the noise content, and the probability range. Finally, we study different compatibility criteria, and we compare them for generic POVMs.
33 pages. v3: small modifications
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- Theory of versatile fidelity estimation with confidence
- Order preserving maps on quantum measurements
- Comparison of estimation limits for quantum two-parameter estimation
- The compatibility dimension of quantum measurements
- Morphophoric POVMs, generalised qplexes, and 2-designs
- Completeness Stability of Quantum Measurements
- Creation of quantum coherence with general measurement processes