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Q: Fachverband Quantenoptik und Photonik

Q 8: QI Poster I (joint session QI/Q)

Q 8.1: Poster

Monday, March 6, 2023, 16:30–19:00, Empore Lichthof

Towards multi-photon tests of hyper-complex quantum mechanics — •Ece Ipek Saruhan, Marc-Oliver Pleinert, and Joachim von Zanthier — Quantum Optics and Quantum Information, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 1, 91058 Erlangen, Germany

Axioms of quantum mechanics do not tell much about the structure of the Hilbert space such as, e.g., the number system, which could be real, complex, or hyper-complex. Probabilities are amplitude squares of wave functions, which are defined on a complex space in general. Can one consider the result of a dot product to be a hyper-complex number? Asher Peres proposed a way to test hyper-complex quantum mechanics with a single particle scattered from 3 different scatterers [1]. We adapt this test to a 3-slit interference setup and extend it to multi-slit and multi-particle scenarios. We construct Peres-like functions to see if the multitude of paths and particles show different sensitivity to, still hypothetical, hyper-complex phases.

[1] A. Peres, Phys. Rev. Lett. 42, 683 (1979).