Complementarity-based complementarity: the choice of mutually unbiased observables shapes quantum uncertainty relations

TL;DR

This paper shows that the uncertainty bounds in quantum systems depend on the specific choice of mutually unbiased bases, with experimental and numerical evidence demonstrating variability in uncertainty relations.

Contribution

It reveals that the uncertainty relations are not uniform but depend on the particular set of mutually unbiased bases chosen, a novel insight in quantum uncertainty research.

Findings

Different sets of MUBs yield distinct uncertainty bounds.

Uncertainty relations vary with the choice of observables within MUBs.

Experimental and numerical results confirm the dependence on observable selection.

Abstract

Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually unbiased bases (MUBs). Uncertainty relations derived from joint properties of the MUBs are generally assumed to be uniform, irrespective of the specific observables chosen within a set. In this work, we demonstrate instead that the uncertainty relations can depend on the choice of observables. Through both experimental observation and numerical methods, we show that selecting different sets of three MUBs in a 5-dimensional quantum system results in distinct uncertainty bounds, i.e. in varying degrees of complementarity, in terms of both entropy and variance.