No extension of quantum theory can have improved predictive power
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According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory that removes this indeterminism, as suspected by Einstein, Podolsky and Rosen. Although this has been shown to be impossible, existing results do not imply that the current theory is maximally informative. Here we ask the more general question of whether any improved predictions can be achieved by any extension of quantum theory. Under the assumption that measurements can be chosen freely, we answer this question in the negative: no extension of quantum theory can give more information about the outcomes of future measurements than quantum theory itself. Our result has significance for the foundations of quantum mechanics, as well as applications to tasks that exploit the inherent randomness in quantum theory, such as quantum cryptography. Quantum-mechanical predictions are generally probabilistic. Here, assuming freely chosen measurements, it is shown that enhanced predictions are not possible and, thus, randomness is inherent in quantum theory: a result that has applications in fields such as quantum cryptography.
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Earlier no-go results use assumptions similar to (Q) and (S).
“Theorem 1 may be compared to earlier no-go results, such as7–10,41–43, which also use assumptions similar to (Q) and (S) (although the latter is often implicit).”
From Quantum theory cannot consistently describe the use of itself (2018) · cites this paper as [43]
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Lev Vaidman, A. (2016) · Journal of Physics Conference Series · doi:10.1088/1742-6596/701/1/012020 · Cited by 16 · see citing works
The Completeness of Quantum Theory for Predicting Measurement Outcomes
Colbeck, R., & Renner, R. (2015) · Fundamental theories of physics · doi:10.1007/978-94-017-7303-4_15 · Cited by 15 · see citing works
Self-citationA short note on the concept of free choicePreprint
Colbeck, R., & Renner, R. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1302.4446 · Cited by 14 · see citing works
Self-citationFrom counterportation to local wormholes
Salih, H. (2022) · Quantum Science and Technology · doi:10.1088/2058-9565/ac8ecd · Cited by 14 · see citing works
The post-determined block universe
Stoica, O. C. (2020) · Quantum Studies Mathematics and Foundations · doi:10.1007/s40509-020-00228-4 · Cited by 13 · see citing works
Quantum correlations on the no-signaling boundary: self-testing and more
Chen, K.-S., Tabia, G. N. M., Jebarathinam, C., Mal, S., Wu, J.-Y., & Liang, Y.-C. (2023) · Quantum · doi:10.22331/q-2023-07-11-1054 · Cited by 12 · see citing works
Lack of measurement independence can simulate quantum correlations even when signaling can not
Banik, M. (2013) · Physical Review A · doi:10.1103/physreva.88.032118 · Cited by 13 · see citing works
A New Theory for the Essence and Origin of Electron Spin
Butto, N. (2021) · Journal of High Energy Physics Gravitation and Cosmology · doi:10.4236/jhepgc.2021.74088 · Cited by 11 · see citing works
Weak Interaction and the Mechanisms for Neutron Stability and Decay
Pons, D. J., Pons, A. D., & Pons, A. J. (2014) · Applied Physics Research · doi:10.5539/apr.v7n1p1 · Cited by 12 · see citing works
Belnap, N., Müller, T., & Placek, T. (2021) · doi:10.1093/oso/9780190884314.001.0001 · Cited by 11 · see citing works
Determination of hidden-variable models reproducing the spin singlet
Lorenzo, A. D. (2012) · Physical Review A · doi:10.1103/physreva.86.042119 · Cited by 12 · see citing works
The Quantum Hourglass: approaching time measurement with quantum information theory
Erker, P. (2014) · Repository for Publications and Research Data (ETH Zurich) · doi:10.3929/ethz-a-010514644 · Cited by 11 · see citing works
Effect of Matter Distribution on Relativistic Time Dilation
Pons, D. J., Pons, A. D., & Pons, A. J. (2018) · Journal of Modern Physics · doi:10.4236/jmp.2018.93035 · Cited by 10 · see citing works
Representation of the wave function on the three-dimensional space
Stoica, O. C. (2019) · Physical Review A · doi:10.1103/physreva.100.042115 · Cited by 10 · see citing works
Quantum Secret Aggregation Utilizing a Network of Agents
Ampatzis, M., & Andronikos, T. (2023) · Cryptography · doi:10.3390/cryptography7010005 · Cited by 11 · see citing works
Asymmetrical Neutrino Induced Decay of Nucleons
Pons, D. J., Pons, A. D., & Pons, A. J. (2015) · Applied Physics Research · doi:10.5539/apr.v7n2p1 · Cited by 11 · see citing works
Causality–Complexity–Consistency: Can Space-Time Be Based on Logic and Computation?
Baumeler, Ä., & Wolf, S. (2017) · Tutorials, schools, and workshops in the mathematical sciences · doi:10.1007/978-3-319-68655-4_6 · Cited by 10 · see citing works
Ontological Models in Quantum Mechanics: What do they tell us?Preprint
Ballentine, L. E. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1402.5689 · Cited by 10 · see citing works
A Physical Basis for Entanglement in a Non-Local Hidden Variable Theory
Pons, D. J., Pons, A. D., & Pons, A. J. (2017) · Journal of Modern Physics · doi:10.4236/jmp.2017.88082 · Cited by 9 · see citing works
An impossibility theorem for parameter independent hidden variable theories
Leegwater, G. (2016) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/j.shpsb.2016.01.003 · Cited by 10 · see citing works
- Authors
- Colbeck, R., & Renner, R.
- Affiliations
- Perimeter Institute (CA)
- ETH Zurich (CH)
- Corresponding author
- Colbeck, Roger
- Venue
- Nature Communications
- Published
- 2011-08-02
- Volume
- 2
- Issue
- 1
- Pages
- 411-411
- ISSN
- 2041-1723 (ISSN-L)
- PMC
- PMC3265370
- OpenAlex
- W2144820907
- Cited by
- 223
- References
- 42
- Citations by year
- 2026: 5 · 2025: 7 · 2024: 8 · 2023: 15 · 2022: 7 · 2021: 28 · 2020: 10 · 2019: 11 · 2018: 12 · 2017: 12 · 2016: 23 · 2015: 22 · 2014: 28 · 2013: 20 · 2012: 14
- FWCI
- 10.77
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Nature Communications (publishedVersion, cc-by-nc-sa)
- PubMed Central (publishedVersion, cc-by-nc-sa)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Repository for Publications and Research Data (ETH Zurich) (submittedVersion, cc-by-nc-sa)
- arXiv (Cornell University)
- ETH Zürich Research Collection
- Funders
- National Science Foundation
- Government of Canada
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (119868, 200021)
- Industry Canada
- Institut Périmètre de physique théorique
- FP7 Ideas: European Research Council (258932)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- quantum foundations, quantum indeterminism, EPR paradox, quantum cryptography, probabilistic forecasting
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