Measuring a Quantum Measure Exceeding Unity

Sanchari Chakraborti; Rafael D. Sorkin; Urbasi Sinha

doi:10.22331/q-2026-09-24-2215

Measuring a Quantum Measure Exceeding Unity

Sanchari Chakraborti¹, Rafael D. Sorkin^2,3,5, and Urbasi Sinha^1,4

¹Raman Research Institute, C.V.Raman Avenue, Sadashivanagar, Bengaluru-560080, Karnataka, India
²Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada
³Department of Physics, Syracuse University, Syracuse, NY 13244-1130, U.S.A.
⁴Department of Physics and Astronomy, University of Calgary, Alberta T2N 1N4, Canada
⁵School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Ireland

Published:	2026-09-24, volume 10, page 2215
Editor:	Leon Loveridge
Eprint:	arXiv:2407.15702v3
Doi:	https://doi.org/10.22331/q-2026-09-24-2215
Citation:	Quantum 10, 2215 (2026).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

The history based formalism known as Quantum Measure Theory (QMT) generalizes the concept of probability-measure so as to incorporate quantum interference. The resulting quantum measure $\mu$ is defined for arbitrary events (sets of histories), not just for observables at a fixed moment of time. Thanks to interference effects, $\mu$ can exceed unity, exhibiting its non-classical nature in a particularly striking manner. Here, in an optical experiment, we illustrate an ancilla based filtering scheme that gives operational meaning to the quantum measure. For a specific photonic event $E$, we report a measured value of $\mu(E)=1.172^{+0.013}_{-0.019}$, which within errors agrees with the theoretical value of $5/4$, while exceeding the maximum value permissible for a classical probability (namely $1$) by $13.32$ upper or $8.89$ lower percentile widths. The directly observed quantity is an ordinary detector probability $p_D\le 1$ (or, with laser light, an equivalent power ratio); the value $\mu(E)\gt1$ is inferred via the calibrated relation $\mu(E)=2p_D$ for our filter.
If an unconventional theoretical concept is to play a role in meeting the foundational challenges of quantum theory, it seems important to bring it into contact with experiment as much as possible. Our experiment does this for the quantum measure.

Featured image: Event-filtering of quantum histories. A coherent optical field explores multiple possible histories through the interferometric system. The event filter selects a chosen set of histories while preserving the interference needed to determine their quantum measure. The measured result, $\mu(E)\approx1.17\gt1$, exceeds the classical probability bound of unity, even though the directly observed detector probability itself remains between zero and one.

Popular summary

Quantum mechanics is usually described in terms of the state of a system at a particular time and the outcomes obtained when we measure it. A complementary viewpoint is to describe a quantum system through its possible histories, meaning the different ways it can evolve between preparation and detection.

Quantum Measure Theory assigns a generalized measure to sets of such histories, incorporating the interference between them. Unlike an ordinary probability, this quantum measure can exceed one.
The difficulty is that a general set of histories does not necessarily correspond to a sequence of ordinary measurements, so its quantum measure is not straightforward to access experimentally.

Here we overcome this problem using an ancilla-assisted optical event-filter. In our photonic implementation, polarization is used to tag, select and coherently recombine a chosen set of path histories. The output of the filter is an ordinary detector probability, which always remains between zero and one, but is related by a known factor to the quantum measure of the selected history-event.

For the event studied here, the ideal quantum measure is 1.25. Experimentally, we obtain a median value of approximately 1.17, in close agreement with a realistic theoretical model of the apparatus, which predicts about 1.18, and clearly above the classical probability bound of one.

The significance goes beyond observing a number greater than one. The experiment gives operational access to a quantity associated with an entire quantum history-event, rather than simply with a final measurement outcome. Histories-based formulations are also natural in attempts to formulate quantum physics for spacetime and quantum gravity, although the present work is a quantum-optics experiment and does not test quantum gravity.

If an unconventional theoretical concept is to play a role in meeting the foundational challenges of quantum theory, it seems important to bring it into contact with experiment as much as possible. Our experiment does this for the quantum measure.

► BibTeX data

@article{Chakraborti2026measuringquantum,
  doi = {10.22331/q-2026-09-24-2215},
  url = {https://doi.org/10.22331/q-2026-09-24-2215},
  title = {Measuring a {Q}uantum {M}easure {E}xceeding {U}nity},
  author = {Chakraborti, Sanchari and Sorkin, Rafael D. and Sinha, Urbasi},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2215},
  month = sep,
  year = {2026}
}

► References

[1] Álvaro Mozota Frauca and Rafael Dolnick Sorkin. How to measure the quantum measure. International Journal of Theoretical Physics, 56(1):232–258, jan 2017. https://doi.org/10.1007/s10773-016-3181-x.
https://doi.org/10.1007/s10773-016-3181-x

[2] A. J. Leggett. Experimental approaches to the quantum measurement paradox. Foundations of Physics, 18(9):939–952, 1988. https://doi.org/10.1007/bf01855943.
https://doi.org/10.1007/bf01855943

[3] A J Leggett. Realism and the physical world. Reports on Progress in Physics, 71(2):022001, jan 2008. https://doi.org/10.1088/0034-4885/71/2/022001.
https://doi.org/10.1088/0034-4885/71/2/022001

[4] Yakir Aharonov, David Z. Albert, and Lev Vaidman. How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett., 60:1351–1354, Apr 1988. https://doi.org/10.1103/PhysRevLett.60.1351.
https://doi.org/10.1103/PhysRevLett.60.1351

[5] I. M. Duck, P. M. Stevenson, and E. C. G. Sudarshan. The sense in which a "weak measurement" of a spin-1/2 particle's spin component yields a value 100. Phys. Rev. D, 40:2112–2117, Sep 1989. https://doi.org/10.1103/PhysRevD.40.2112.
https://doi.org/10.1103/PhysRevD.40.2112

[6] A. Matzkin. Weak values from path integrals. Phys. Rev. Res., 2:032048, August 2020. https://doi.org/10.1103/PhysRevResearch.2.032048.
https://doi.org/10.1103/PhysRevResearch.2.032048

[7] Rafael D. Sorkin. Quantum mechanics as quantum measure theory. Modern Physics Letters A, 09(33):3119–3127, 1994. https://doi.org/10.1142/S021773239400294X.
https://doi.org/10.1142/S021773239400294X

[8] Robert B. Griffiths. Consistent histories and the interpretation of quantum mechanics. Journal of Statistical Physics, 36(1–2):219–272, 1984. https://doi.org/10.1007/BF01015734.
https://doi.org/10.1007/BF01015734

[9] Robert B. Griffiths. Consistent interpretation of quantum mechanics using quantum trajectories. Phys. Rev. Lett., 70:2201–2204, Apr 1993. https://doi.org/10.1103/PhysRevLett.70.2201.
https://doi.org/10.1103/PhysRevLett.70.2201

[10] James B. Hartle. Spacetime quantum mechanics and the quantum mechanics of spacetime, 1993. https://doi.org/10.48550/arXiv.gr-qc/9304006.
https://doi.org/10.48550/arXiv.gr-qc/9304006

[11] Murray Gell-Mann and James B. Hartle. Classical equations for quantum systems. Phys. Rev. D, 47:3345–3382, Apr 1993. https://doi.org/10.1103/PhysRevD.47.3345.
https://doi.org/10.1103/PhysRevD.47.3345

[12] Roland Omnès. Logical reformulation of quantum mechanics. I. Foundations. Journal of Statistical Physics, 53(3–4):893–932, 1988. https://doi.org/10.1007/BF01014230.
https://doi.org/10.1007/BF01014230

[13] C. J. Isham and N. Linden. Information entropy and the space of decoherence functions in generalized quantum theory. Phys. Rev. A, 55:4030–4040, Jun 1997. https://doi.org/10.1103/PhysRevA.55.4030.
https://doi.org/10.1103/PhysRevA.55.4030

[14] Stanley P. Gudder and Rafael D. Sorkin. Two-site quantum random walk. General Relativity and Gravitation, 43(12):3451–3475, Dec 2011. https://doi.org/10.1007/s10714-011-1245-z.
https://doi.org/10.1007/s10714-011-1245-z

[15] Nicolaas P. Landsman. Born Rule and its Interpretation, pages 64–70. Springer Berlin Heidelberg, Berlin, Heidelberg, 2009. https://doi.org/10.1007/978-3-540-70626-7_20.
https://doi.org/10.1007/978-3-540-70626-7_20

[16] Wendell H. Furry. Conference on the foundations of quantum mechanics. 1962. https://www.exhibit.xavier.edu/conf_qm_1962/2/.
https://www.exhibit.xavier.edu/conf_qm_1962/2/

[17] Matthew Leifer. Is the quantum state real? An extended review of $\psi$-ontology theorems. Quanta, 3(1):67–155, 2014. https://doi.org/10.12743/quanta.v3i1.22.
https://doi.org/10.12743/quanta.v3i1.22

[18] Wojciech H. Zurek. Decoherence and the Transition from Quantum to Classical. Physics Today, 44(10):36–44, 10 1991. https://doi.org/10.1063/1.881293.
https://doi.org/10.1063/1.881293

[19] George F.R. Ellis. On the limits of quantum theory: Contextuality and the quantum–classical cut. Annals of Physics, 327(7):1890–1932, 2012. July 2012 Special Issue. https://doi.org/10.1016/j.aop.2012.05.002.
https://doi.org/10.1016/j.aop.2012.05.002

[20] R. P. Feynman. Space-time approach to non-relativistic quantum mechanics. Rev. Mod. Phys., 20:367–387, Apr 1948. https://doi.org/10.1103/RevModPhys.20.367.
https://doi.org/10.1103/RevModPhys.20.367

[21] Sukanya Sinha and Rafael D. Sorkin. A sum-over-histories account of an EPR(B) experiment. Foundations of Physics Letters, 4(4):303–335, Aug 1991. https://doi.org/10.1007/BF00665892.
https://doi.org/10.1007/BF00665892

[22] James B. Hartle. The spacetime approach to quantum mechanics. Vistas in Astronomy, 37:569–583, 1993. https://doi.org/10.1016/0083-6656(93)90097-4.
https://doi.org/10.1016/0083-6656(93)90097-4

[23] Roger Penrose. On the gravitization of quantum mechanics 1: Quantum state reduction. Foundations of Physics, 44(5):557–575, jan 2014. https://doi.org/10.1007/s10701-013-9770-0.
https://doi.org/10.1007/s10701-013-9770-0

[24] C. J. Isham and N. Linden. Quantum temporal logic and decoherence functionals in the histories approach to generalized quantum theory. Journal of Mathematical Physics, 35(10):5452–5476, 10 1994. https://doi.org/10.1063/1.530759.
https://doi.org/10.1063/1.530759

[25] Rafael D. Sorkin. On the Role of Time in the Sum Over Histories Framework for Gravity. Int. J. Theor. Phys., 33:523–534, 1994. https://doi.org/10.1007/BF00670514.
https://doi.org/10.1007/BF00670514

[26] Rafael D. Sorkin. Quantum measure theory and its interpretation, 1997. https://doi.org/10.48550/arXiv.gr-qc/9507057.
https://doi.org/10.48550/arXiv.gr-qc/9507057

[27] J. B. Hartle. Quantum kinematics of spacetime. II. A model quantum cosmology with real clocks. Phys. Rev. D, 38:2985–2999, Nov 1988. https://doi.org/10.1103/PhysRevD.38.2985.
https://doi.org/10.1103/PhysRevD.38.2985

[28] Bo-Sture K Skagerstam. On the three-slit experiment and quantum mechanics. Journal of Physics Communications, 2(12):125014, 2018. https://doi.org/10.1088/2399-6528/aaf683.
https://doi.org/10.1088/2399-6528/aaf683

[29] E. C. G. Sudarshan. Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams. Phys. Rev. Lett., 10:277–279, Apr 1963. https://doi.org/10.1103/PhysRevLett.10.277.
https://doi.org/10.1103/PhysRevLett.10.277

Cited by

[1] "Physicists have a new tool for quantum measurement", Nature India (2026).

[2] Sam Powers, Guangpeng Xu, Herbert Fotso, Tim Thomay, and Dejan Stojkovic, "Statistical model for quantum spin and photon number states", Physical Review A 111 1, 012217 (2025).

The above citations are from Crossref's cited-by service (last updated successfully 2026-10-23 08:19:14) and SAO/NASA ADS (last updated successfully 2026-10-22 19:51:10). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch ADS cited-by data during last attempt 2026-10-23 08:19:14: Cannot retrieve data from ADS due to rate limitations.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.