Entropic bounds for unitary testers and mutually unbiased unitary bases
Abstract
We define the entropic bounds, i.e. minimal uncertainty for pairs of unitary testers in distinguishing between unitary transformations not unlike the well known entropic bounds for observables. We show that in the case of specific sets of testers which pairwise saturate the trivial zero bound, the testers are all equivalent in the sense their statistics are the same. On the other hand, when maximal bounds are saturated by such sets of testers, the unitary operators would form unitary bases which are mutually unbiased. This resembles very much the role of mutually unbiased bases in maximising the entropic bounds for observables. We show how such a bound can be useful in certain quantum cryptographic protocols.
 Publication:

Annals of Physics
 Pub Date:
 January 2020
 DOI:
 10.1016/j.aop.2019.168043
 arXiv:
 arXiv:1910.07665
 Bibcode:
 2020AnPhy.41268043S
 Keywords:

 Entropic bound;
 Tester;
 PPOVM;
 MUUB;
 Quantum Physics
 EPrint:
 Added a more comprehensive background on testers and included some minor changes on notation