Better bounds on optimal measurement and entanglement recovery, with applications to uncertainty and monogamy relations

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.

5 pages

References in corpus (5)

• Optimal Cloning and Singlet Monogamy
• State Discrimination with Post-Measurement Information
• Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds
• Pretty good measures in quantum information theory
• Design of Optimal Dynamic Analyzers: Mathematical Aspects of Wave Pattern Recognition

Cited by in corpus (2)

• Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels
• On relating one-way classical and quantum communication complexities