Connections Between Mutually Unbiased Bases and Quantum Random Access Codes
Edgar A. Aguilar, Jakub J. Borka{\l}a, Piotr Mironowicz, Marcin, Paw{\l}owski
TL;DR
This paper introduces a new quantum communication protocol called promise--Quantum Random Access Code, which provides a novel measure of unbiasedness for bases in Hilbert spaces and uses Semi-Definite Programming to explore the existence of mutually unbiased bases.
Contribution
It proposes a new measure of unbiasedness with operational meaning and links it to the existence of mutually unbiased bases via Semi-Definite Programming.
Findings
New measure of unbiasedness for Hilbert space bases
Operational interpretation of the measure
Method to investigate mutually unbiased bases existence
Abstract
We present a new quantum communication complexity protocol, the promise--Quantum Random Access Code, which allows us to introduce a new measure of unbiasedness for bases of Hilbert spaces. The proposed measure possesses a clear operational meaning and can be used to investigate whether a specific number of mutually unbiased bases exist in a given dimension by employing Semi--Definite Programming techniques.
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