A gambling interpretation of some quantum information-theoretic quantities

TL;DR

This paper extends classical gambling interpretations of entropy to quantum systems, linking quantum information measures like von Neumann entropy and discord to operational gambling scenarios involving quantum states and measurements.

Contribution

It introduces a quantum gambling framework that provides operational meanings for quantum entropies and discord, extending classical results to the quantum domain.

Findings

Operational interpretation of von Neumann entropy in quantum gambling

Quantum discord relates to the difference in doubling rates with a helper

Doubling rate bounded by Holevo information in quantum Kelly gambling

Abstract

It is known that repeated gambling over the outcomes of independent and identically distributed (i.i.d.) random variables gives rise to alternate operational meaning of entropies in the classical case in terms of the doubling rates. We give a quantum extension of this approach for gambling over the measurement outcomes of tensor product states. Under certain parameters of the gambling setup, one can give operational meaning of von Neumann entropies. We discuss two variants of gambling when a helper is available and it is shown that the difference in their doubling rates is the quantum discord. Lastly, a quantum extension of Kelly's gambling setup in the classical case gives a doubling rate that is upper bounded by the Holevo information.