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

Laura Serino1, Giovanni Chesi2,*, Benjamin Brecht1, Lorenzo Maccone2, Chiara Macchiavello2, and Christine Silberhorn1

  • 1Integrated Quantum Optics, Institute for Photonic Quantum Systems (PhoQS), Paderborn University, Warburgerstrasse 100, 33098 Paderborn, Germany
  • 2QUIT Group, Physics Department, University of Pavia, INFN Sez. Pavia, Via Bassi 6, 27100 Pavia, Italy

  • *Contact author: giovanni.chesi@unipv.it
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Phys. Rev. Research 7, 033152 – Published 13 August, 2025

DOI: https://doi.org/10.1103/v24q-sl6n

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 five-dimensional quantum system results in distinct uncertainty bounds, i.e., in varying degrees of complementarity, in terms of both entropy and variance.

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Phys. Rev. Research 7, 033152– Published 13 August, 2025
  • Received 29 July 2024
  • Revised 20 January 2025
  • Accepted 23 June 2025
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