Quantum theory based on real numbers can be experimentally falsified
- URL: http://arxiv.org/abs/2101.10873v2
- Date: Mon, 27 Dec 2021 17:26:36 GMT
- Title: Quantum theory based on real numbers can be experimentally falsified
- Authors: Marc-Olivier Renou, David Trillo, Mirjam Weilenmann, Thinh P. Le,
Armin Tavakoli, Nicolas Gisin, Antonio Acin and Miguel Navascues
- Abstract summary: We show that real and complex quantum theory make different predictions in network scenarios comprising independent states and measurements.
This allows us to devise a Bell-like experiment whose successful realization would disprove real quantum theory.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: While complex numbers are essential in mathematics, they are not needed to
describe physical experiments, expressed in terms of probabilities, hence real
numbers. Physics however aims to explain, rather than describe, experiments
through theories. While most theories of physics are based on real numbers,
quantum theory was the first to be formulated in terms of operators acting on
complex Hilbert spaces. This has puzzled countless physicists, including the
fathers of the theory, for whom a real version of quantum theory, in terms of
real operators, seemed much more natural. In fact, previous works showed that
such "real quantum theory" can reproduce the outcomes of any multipartite
experiment, as long as the parts share arbitrary real quantum states. Thus, are
complex numbers really needed in the quantum formalism? Here, we show this to
be case by proving that real and complex quantum theory make different
predictions in network scenarios comprising independent states and
measurements. This allows us to devise a Bell-like experiment whose successful
realization would disprove real quantum theory, in the same way as standard
Bell experiments disproved local physics.
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