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Mirjam Weilenmann, IQOQI Vienna, Austria

Quantum Physics Needs Complex Numbers

Abstract: As it is explicitly formulated in terms of operators acting on complex Hilbert spaces, Quantum Theory seems to rely crucially on complex numbers. This has, nonetheless, puzzled countless physicists, including some of the fathers of the theory, for whom a real version of quantum physics seemed more natural. We address this problem by asking whether Real Quantum Theory -- where states and measurements are formulated over real Hilbert spaces instead -- can lead to the same experimental predictions as usual Quantum Theory. In fact, previous works showed that Real Quantum Theory can reproduce the outcome probabilities of any multipartite experiment, as long as the parts share arbitrary real quantum states. Thus, are complex Hilbert spaces really needed for a quantum description of nature? In our recent work, we found this to be the case, by proving that the two theories make different predictions in network scenarios comprising independent quantum state sources. This allows us to devise a Bell-type quantum experiment whose input-output correlations cannot be approximated by any real quantum model. The successful realization of such an experiment would disprove Real Quantum Theory, in the same way as standard Bell experiments disproved local physics.
This is joint work with Marc-Olivier Renou, David Trillo, Le Phuc Thinh, Armin Tavakoli, Nicolas Gisin, Antonio Acín and Miguel Navascués.


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