Testing quantum theory by generalizing noncontextuality
- URL: http://arxiv.org/abs/2112.09719v3
- Date: Mon, 2 Oct 2023 19:51:48 GMT
- Title: Testing quantum theory by generalizing noncontextuality
- Authors: Markus P. Mueller, Andrew J. P. Garner
- Abstract summary: We prove that only Jordan-algebraic state spaces are exactly embeddable into quantum theory.
We propose an experimental test of quantum theory by probing single physical systems.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: It is a fundamental prediction of quantum theory that states of physical
systems are described by complex vectors or density operators on a Hilbert
space. However, many experiments admit effective descriptions in terms of other
state spaces, such as classical probability distributions or quantum systems
with superselection rules. Which kind of effective statistics would allow us to
experimentally falsify quantum theory as a fundamental description of nature?
Here, we address this question by introducing a methodological principle that
generalizes Spekkens' notion of noncontextuality: processes that are
statistically indistinguishable in an effective theory should not require
explanation by multiple distinguishable processes in a more fundamental theory.
We formulate this principle in terms of linear embeddings and simulations of
one probabilistic theory by another, show how this concept subsumes standard
notions of contextuality, and prove a multitude of fundamental results on the
exact and approximate embedding of theories (in particular into quantum
theory). We prove that only Jordan-algebraic state spaces are exactly
embeddable into quantum theory, and show how results on Bell inequalities can
be used for the certification of non-approximate embeddability. From this, we
propose an experimental test of quantum theory by probing single physical
systems without assuming access to a tomographically complete set of procedures
or calibration of the devices, arguably avoiding a significant loophole of
earlier approaches.
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