The measurement postulates of quantum mechanics are not redundant

Adrian Kent

doi:10.22331/q-2025-05-20-1749

The measurement postulates of quantum mechanics are not redundant

Adrian Kent

Centre for Quantum Information and Foundations, DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, U.K.
Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada.

Published:	2025-05-20, volume 9, page 1749
Editor:	Alexander Wilce
Eprint:	arXiv:2307.06191v3
Doi:	https://doi.org/10.22331/q-2025-05-20-1749
Citation:	Quantum 9, 1749 (2025).

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Abstract

Masanes, Galley and Müller [39] argue that the measurement postulates of non-relativistic quantum mechanics follow from the structural postulates together with an assumption they call the "possibility of state estimation". Their argument also relies on what they term a "theory-independent characterization of measurements for single and multipartite systems". We refute their conclusion, giving explicit examples of non-quantum measurement and state update rules that satisfy all their assumptions. We also show that their "possibility of state estimation" assumption is neither necessary nor sufficient to ensure a sensible notion of state estimation within a theory whose states are described by the quantum formalism. We further show their purportedly "theory-independent" characterization assumes several properties of quantum measurements that exclude plausible alternative types of measurement. We illustrate all these points with specific alternative measurement postulates and post-measurement state update rules. We conclude that, contrary to some folklore, quantum mechanics is by no means an island in theory-space. It can consistently be extended by rules for obtaining information about quantum states other than via POVMs. Whether such rules are realised in nature, for example in linking quantum theory and gravity, is an empirical question that cannot be resolved by theoretical analysis alone.

► BibTeX data

@article{Kent2025measurement,
  doi = {10.22331/q-2025-05-20-1749},
  url = {https://doi.org/10.22331/q-2025-05-20-1749},
  title = {The measurement postulates of quantum mechanics are not redundant},
  author = {Kent, Adrian},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1749},
  month = may,
  year = {2025}
}

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[2] Vincenzo Fiorentino and Stefan Weigert, "Beyond the projection postulate and back: Quantum theories with generalized state-update rules", Physical Review A 113 1, 012204 (2026).

[3] Samuel Fedida and Adrian Kent, "Mixture equivalence principles and postquantum theories of gravity", Physical Review D 111 12, 126016 (2025).

[4] Samuel Fedida and Adrian Kent, "Thermodynamics of readout devices and semiclassical gravity", Physical Review A 113 1, 012214 (2026).

[5] Zachary P. Bradshaw, Jeffrey J. Dale, and Ethan N. Evans, "Introduction to quantum error correction with stabilizer codes", Annals of Physics 487, 170353 (2026).

[6] Alireza Tavanfar, Sahar Alipour, and Ali T. Rezakhani, "Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories", Universe 11 5, 162 (2025).

[7] Adrian Kent, "Fundamental physics, existential risks and human futures", Philosophical Transactions of the Royal Society of London Series A 383 2296, 20230376 (2025).

[8] Lluís Masanes, Thomas D. Galley, and Markus P. Müller, "Response to "The measurement postulates of quantum mechanics are not redundant"", arXiv:2309.01650, (2023).

[9] Blake C. Stacey, "Contradictions or Curiosities? On Kent's Critique of the Masanes--Galley--Müller Derivation of the Quantum Measurement Postulates", arXiv:2405.17733, (2024).

[10] Lluís Masanes, Thomas D. Galley, and Markus P. Müller, "Response to "The measurement postulates of quantum mechanics are not redundant"", Quantum 9, 1592 (2025).

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