Interference as an information-theoretic game

Sebastian Horvat1 and Borivoje Dakić1,2

1University of Vienna, Faculty of Physics, Vienna Center for Quantum Science and Technology, Boltzmanngasse 5, 1090 Vienna, Austria
2Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Vienna, Austria

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


The double slit experiment provides a clear demarcation between classical and quantum theory, while multi-slit experiments demarcate quantum and higher-order interference theories. In this work we show that these experiments pertain to a broader class of processes, which can be formulated as information-processing tasks, providing a clear cut between classical, quantum and higher-order theories. The tasks involve two parties and communication between them with the goal of winning certain parity games. We show that the order of interference is in one-to-one correspondence with the parity order of these games. Furthermore, we prove the order of interference to be additive under composition of systems both in classical and quantum theory. The latter result can be used as a (semi)device-independent witness of the number of particles in the quantum setting. Finally, we extend our game formulation within the generalized probabilistic framework and prove that tomographic locality implies the additivity of the order of interference under composition. These results shed light on the operational meaning of the order of interference and can be important for the identification of the information-theoretic principles behind second-order interference in quantum theory.

► BibTeX data

► References

[1] Feynman, R.P., Leighton, R.B. and Sands, M., 2005. The Feynman Lectures on Physics: Definitive Edition. Pearson Addison-Wesley. ISBN 0-8053-9046-4.

[2] Sorkin, R.D., 1994. Quantum mechanics as quantum measure theory. Modern Physics Letters A, 9(33), pp.3119-3127. https:/​/​​10.1142/​S021773239400294X.

[3] Dakic, B., Paterek, T. and Brukner, C., 2014. Density cubes and higher-order interference theories. New Journal of Physics, 16(2), p.023028. http:/​/​​10.1088/​1367-2630/​16/​2/​023028.

[4] Barnum, H., Mueller, M.P. and Ududec, C., 2014. Higher-order interference and single-system postulates characterizing quantum theory. New Journal of Physics, 16(12), p.123029. http:/​/​​10.1088/​1367-2630/​16/​12/​123029.

[5] Lee, C.M. and Selby, J.H., 2017. Higher-order interference in extensions of quantum theory. Foundations of Physics, 47(1), pp.89-112. https:/​/​​10.1007/​s10701-016-0045-4.

[6] Barnum, H., Lee, C.M., Scandolo, C.M. and Selby, J.H., 2017. Ruling out higher-order interference from purity principles. Entropy, 19(6), p.253. https:/​/​​10.3390/​e19060253.

[7] Ududec, C., Barnum, H. and Emerson, J., 2011. Three slit experiments and the structure of quantum theory. Foundations of Physics, 41(3), pp.396-405. https:/​/​​10.1007/​s10701-010-9429-z.

[8] Niestegge, G., 2013. Three-slit experiments and quantum nonlocality. Foundations of Physics, 43(6), pp.805-812. https:/​/​​10.1007/​s10701-013-9719-3.

[9] Lee, C.M. and Selby, J.H., 2016. Generalised phase kick-back: the structure of computational algorithms from physical principles. New Journal of Physics, 18(3), p.033023. http:/​/​​10.1088/​1367-2630/​18/​3/​033023.

[10] Hardy, L., 2001. Quantum theory from five reasonable axioms. arXiv preprint quant-ph/​0101012.

[11] Dakic, B. and Brukner, C. Quantum theory and beyond: is entanglement special? Deep Beauty: Understanding the Quantum World Through Mathematical Innovation (ed. Halvorson, H.) (Cambridge Univ. Press, 2011). https:/​/​​10.1017/​CBO9780511976971.011.

[12] Masanes, L. and Mueller, M.P., 2011. A derivation of quantum theory from physical requirements. New Journal of Physics, 13(6), p.063001. http:/​/​​10.1088/​1367-2630/​13/​6/​063001.

[13] Chiribella, G., D Ariano, G.M. and Perinotti, P., 2011. Informational derivation of quantum theory. Physical Review A, 84(1), p.012311. http:/​/​​10.1103/​PhysRevA.84.012311.

[14] Del Santo, F. and Dakić, B., 2018. Two-way communication with a single quantum particle. Physical review letters, 120(6), p.060503. https:/​/​​10.1103/​PhysRevLett.120.060503.

[15] Massa, F., Moqanaki, A., Baumeler, Ä., Del Santo, F., Kettlewell, J.A., Dakić, B. and Walther, P., 2019. Experimental two-way communication with one photon. Advanced Quantum Technologies, 2(11), p.1900050. https:/​/​​10.1002/​qute.201900050.

[16] Hsu, L.Y., Lai, C.Y., Chang, Y.C., Wu, C.M. and Lee, R.K., 2020. Infinite information can be carried using a single quantum particle. arXiv preprint arXiv:2002.10374. https:/​/​​10.1103/​PhysRevA.102.022620.

[17] Horvat, S. and Dakić, B., 2019. Quantum enhancement to information speed. arXiv preprint arXiv:1911.11803.

[18] Oreshkov, O., Costa, F. and Brukner, C., 2012. Quantum correlations with no causal order. Nature communications, 3, p.1092. https:/​/​​10.1038/​ncomms2076.

[19] Feix, A., Araujo, M. and Brukner, C., 2016. Causally nonseparable processes admitting a causal model. New Journal of Physics, 18(8), p.083040. http:/​/​​10.1088/​1367-2630/​18/​8/​083040.

[20] Guerin, P.A., Feix, A., Araujo, M. and Brukner, C., 2016. Exponential communication complexity advantage from quantum superposition of the direction of communication. Physical review letters, 117(10), p.100502. https:/​/​​10.1103/​PhysRevLett.117.100502.

[21] Chiribella, G., D Ariano, G.M. and Perinotti, P., 2008. Quantum circuit architecture. Physical review letters, 101(6), p.060401. https:/​/​​10.1103/​PhysRevLett.101.060401.

[22] Chiribella, G., D Ariano, G.M., Perinotti, P. and Valiron, B., 2013. Quantum computations without definite causal structure. Physical Review A, 88(2), p.022318. https:/​/​​10.1103/​PhysRevA.88.022318.

[23] Allen, J.M.A., Barrett, J., Horsman, D.C., Lee, C.M. and Spekkens, R.W., 2017. Quantum common causes and quantum causal models. Physical Review X, 7(3), p.031021. https:/​/​​10.1103/​PhysRevX.7.031021.

[24] Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V. and Wehner, S., 2014. Bell nonlocality. Reviews of Modern Physics, 86(2), p.419. https:/​/​​10.1103/​RevModPhys.86.419.

[25] Hausladen, P. and Wootters, W.K., 1994. A 'pretty good' measurement for distinguishing quantum states. Journal of Modern Optics, 41(12), pp.2385-2390. https:/​/​​10.1080/​09500349414552221.

[26] Cong, W., Cai, Y., Bancal, J.D. and Scarani, V., 2017. Witnessing irreducible dimension. Physical review letters, 119(8), p.080401. https:/​/​​10.1103/​PhysRevLett.119.080401.

[27] Aguilar, E.A., Farkas, M., Martinez, D., Alvarado, M., Carine, J., Xavier, G.B., Barra, J.F., Canas, G., Pawlowski, M. and Lima, G., 2018. Certifying an irreducible 1024-dimensional photonic state using refined dimension witnesses. Physical Review Letters, 120(23), p.230503. https:/​/​​10.1103/​PhysRevLett.120.230503.

[28] Barrett, J., 2007. Information processing in generalized probabilistic theories. Physical Review A, 75(3), p.032304. https:/​/​​10.1103/​PhysRevA.75.032304.

[29] Haag, R., 2012. Local quantum physics: Fields, particles, algebras. Springer Science $\&$ Business Media. https:/​/​​10.1007/​978-3-642-61458-3.

[30] Sinha, U., Couteau, C., Jennewein, T., Laflamme, R. and Weihs, G., 2010. Ruling out multi-order interference in quantum mechanics. Science, 329(5990), pp.418-421. https:/​/​​10.1126/​science.1190545.

[31] Park, D.K., Moussa, O. and Laflamme, R., 2012. Three path interference using nuclear magnetic resonance: a test of the consistency of Born's rule. New Journal of Physics, 14(11), p.113025. http:/​/​​10.1088/​1367-2630/​14/​11/​113025.

[32] Kauten, T., Keil, R., Kaufmann, T., Pressl, B., Brukner, C. and Weihs, G., 2017. Obtaining tight bounds on higher-order interferences with a 5-path interferometer. New Journal of Physics, 19(3), p.033017. https:/​/​​10.1088/​1367-2630/​aa5d98.

[33] Lee, K.S., Zhuo, Z., Couteau, C., Wilkowski, D. and Paterek, T., 2020. Atomic test of higher-order interference. Physical Review A, 101(5), p.052111. https:/​/​​10.1103/​PhysRevA.101.052111.

[34] Garner, A.J., Krumm, M. and Mueller, M.P., 2020. Semi-device-independent information processing with spatiotemporal degrees of freedom. Physical Review Research, 2(1), p.013112. https:/​/​​10.1103/​PhysRevResearch.2.013112.

[35] Lomonosov, V. and Rosenthal, P., 2004. The simplest proof of Burnside's theorem on matrix algebras. Linear algebra and its applications, 383, pp.45-47. https:/​/​​10.1016/​j.laa.2003.08.012.

Cited by

[1] Martin Plávala, "General probabilistic theories: An introduction", Physics Reports 1033, 1 (2023).

[2] Thomas D. Galley, Flaminia Giacomini, and John H. Selby, "A no-go theorem on the nature of the gravitational field beyond quantum theory", Quantum 6, 779 (2022).

[3] Peter Namdar, Philipp K. Jenke, Irati Alonso Calafell, Alessandro Trenti, Milan Radonjić, Borivoje Dakić, Philip Walther, and Lee A. Rozema, "Experimental higher-order interference in a nonlinear triple slit", Physical Review A 107 3, 032211 (2023).

[4] Yujie Zhang, Xinan Chen, and Eric Chitambar, "Building Multiple Access Channels with a Single Particle", Quantum 6, 653 (2022).

[5] John H. Selby, David Schmid, Elie Wolfe, Ana Belén Sainz, Ravi Kunjwal, and Robert W. Spekkens, "Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality", Physical Review A 107 6, 062203 (2023).

[6] Li-Yi Hsu, Ching-Yi Lai, You-Chia Chang, Chien-Ming Wu, and Ray-Kuang Lee, "Carrying an arbitrarily large amount of information using a single quantum particle", Physical Review A 102 2, 022620 (2020).

[7] Paulo J. Cavalcanti, John H. Selby, Jamie Sikora, and Ana Belén Sainz, "Decomposing all multipartite non-signalling channels via quasiprobabilistic mixtures of local channels in generalised probabilistic theories", Journal of Physics A Mathematical General 55 40, 404001 (2022).

The above citations are from Crossref's cited-by service (last updated successfully 2024-06-22 13:23:50) and SAO/NASA ADS (last updated successfully 2024-06-22 13:23:51). The list may be incomplete as not all publishers provide suitable and complete citation data.