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

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Abstract

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.

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[1] Thomas D. Galley, Flaminia Giacomini, and John H. Selby, "A no-go theorem on the nature of the gravitational field beyond quantum theory", arXiv:2012.01441.

[2] Martin Plávala, "General probabilistic theories: An introduction", arXiv:2103.07469.

[3] 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).

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