Uncertainty Relation for Mutual Information

Authors

James Schneeloch, University of Rochester
Curtis J. Broadbent, University of Rochester
John C. Howell, Chapman UniversityFollow

Document Type

Article

Publication Date

12-15-2014

Abstract

We postulate the existence of a universal uncertainty relation between the quantum and classical mutual informations between pairs of quantum systems. Specifically, we propose that the sum of the classical mutual information, determined by two mutually unbiased pairs of observables, never exceeds the quantum mutual information. We call this the complementary-quantum correlation (CQC) relation and prove its validity for pure states, for states with one maximally mixed subsystem, and for all states when one measurement is minimally disturbing. We provide results of a Monte Carlo simulation suggesting that the CQC relation is generally valid. Importantly, we also show that the CQC relation represents an improvement to an entropic uncertainty principle in the presence of a quantum memory, and that it can be used to verify an achievable secret key rate in the quantum one-time pad cryptographic protocol.

Comments

This article was originally published in Physical Review A, volume 90, issue 6, in 2014. https://doi.org/10.1103/PhysRevA.90.062119

Recommended Citation

J. Schneeloch, C. J. Broadbent, and J. C. Howell,Uncertainty Relation for Mutual Information, Phys. Rev. A 90(6), 062119.

Peer Reviewed

1

Copyright

American Physical Society