Better bounds on optimal measurement and entanglement recovery, with applications to uncertainty and monogamy relations
arXiv:1707.01114 · doi:10.1103/PhysRevA.96.042328
Abstract
We extend the recent bounds of Sason and Verdú relating Rényi entropy and Bayesian hypothesis testing [arXiv:1701.01974] to the quantum domain and show that they have a number of different applications. First, we obtain a sharper bound relating the optimal probability of correctly distinguishing elements of an ensemble of states to that of the pretty good measurement, and an analogous bound for optimal and pretty good entanglement recovery. Second, we obtain bounds relating optimal guessing and entanglement recovery to the fidelity of the state with a product state, which then leads to tight tripartite uncertainty and monogamy relations.
arXiv comment5 pages
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