Conjectured Strong Complementary Information Tradeoff

TL;DR

This paper introduces a new entropic uncertainty principle for quantum systems with side information, generalizing previous relations and exploring implications for quantum cryptography and system decoupling.

Contribution

It conjectures a novel entropic uncertainty relation for complementary quantum observations with side information, extending prior work and providing a proof for specific cases.

Findings

Proposes a new entropic uncertainty conjecture for quantum systems.

Proves a special case for certain conjugate observables.

Discusses applications to quantum cryptography and system decoupling.

Abstract

We conjecture a new entropic uncertainty principle governing the entropy of complementary observations made on a system given side information in the form of quantum states, generalizing the entropic uncertainty relation of Maassen and Uffink [Phys. Rev. Lett. 60, 1103 (1988)]. We prove a special case for certain conjugate observables by adapting a similar result found by Christandl and Winter pertaining to quantum channels [IEEE Trans. Inf. Theory 51, 3159 (2005)], and discuss possible applications of this result to the decoupling of quantum systems and for security analysis in quantum cryptography.