Choice of mutually unbiased bases and outcome labelling affects measurement outcome secrecy

TL;DR

This paper reveals that the choice and labelling of mutually unbiased bases (MUBs) in quantum measurements can significantly influence the secrecy of measurement outcomes, impacting quantum information protocols.

Contribution

It demonstrates that specific properties of MUB sets, including outcome labelling, affect measurement secrecy, highlighting the importance of basis selection in quantum information tasks.

Findings

Outcome secrecy can be fully lost with certain MUB choices

Secrecy is partially retained depending on basis selection

Measurement outcome labelling influences information security

Abstract

Mutually unbiased bases (MUBs) are a crucial ingredient for many protocols in quantum information processing. Measurements performed in these bases are unbiased to the maximally possible extent, which is used to prove randomness or secrecy of measurement results. In this work we show that certain properties of sets of MUBs crucially depend on their specific choice, including, somewhat surprisingly, measurement outcome labelling. If measurements are chosen in a coherent way, the secrecy of the result can be completely lost for specific sets of MUB measurements, while partially retained for others. This can potentially impact a broad spectrum of applications, where MUBs are utilized.