$n$-fold unbiased bases: an extension of the MUB condition

TL;DR

This paper introduces n-fold unbiased bases as an extension of MUBs, providing new bounds for quantum random access codes and raising questions about quantum state geometry.

Contribution

It defines nUB conditions extending MUBs to multiple bases, linking them to QRAC optimization and quantum state geometry.

Findings

nUB bases give close-to-tight bounds on QRAC success probabilities

The existence of nUB bases in general dimensions remains an open question

nUB conditions relate to the geometry of quantum states

Abstract

I introduce a new notion, that extends the mutually unbiased bases (MUB) conditons to more than two bases. These, I call the nUB conditions, and the corresponding bases $n$-fold unbiased. They naturally appear while optimizing generic $n$-to-one quantum random access code (QRAC) strategies. While their existence in general dimensions is an open question, they nevertheless give close-to-tight upper bounds on QRAC success probabilities, and raise fundamental questions about the geometry of quantum states.