After Quantum Lunch: Entropy power inequalities for qudits – University of Copenhagen

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After Quantum Lunch: Entropy power inequalities for qudits

Speaker: Māris Ozols, University of Cambridge.

Abstract: Shannon's entropy power inequality (EPI) for continuous random variables can be stated as concavity of von Neumann entropy or its power under a certain scaled addition rule. König and Smith obtained quantum analogues of these inequalities for continuous-variable quantum systems, where random variables are replaced by bosonic fields and the addition rule corresponds to the action of a beamsplitter on those fields. We consider d-level quantum systems (qudits) and establish analogues of EPIs for a large class of functions. In particular, we prove a qudit analogue of the entropy photon number inequality, which is still open in the bosonic case. The addition rule underlying our inequalities is given by a partial swap channel that acts as a finite-dimensional analogue of a beamsplitter. Contrary to previous work, our proofs rely on majorization.

This is joint work with Koenraad Audenaert and Nilanjana Datta (arXiv:1503.04213).