Experimentally Bounding Deviations From Quantum Theory in the Landscape of Generalized Probabilistic Theories

  title={Experimentally Bounding Deviations From Quantum Theory in the Landscape of Generalized Probabilistic Theories},
  author={Michael D. Mazurek and Matthew F Pusey and Kevin J. Resch and Robert W. Spekkens},
  journal={PRX Quantum},
Many experiments in the field of quantum foundations seek to adjudicate between quantum theory and speculative alternatives to it. To do so, one must analyse the experimental data in a manner that does not presume the correctness of the quantum formalism. The mathematical framework of generalized probabilistic theories (GPTs) provides a means of doing so. We present a scheme for determining what GPTs are consistent with a given set of experimental data. It proceeds by performing tomography on… 
Testing classical and quantum theory with single photons
To date, quantum theory is the most successful physical theory that has been discovered. However, there is still the possibility that an inconsistency between experimental observations and the
Characterization of the probabilistic models that can be embedded in quantum theory
It is shown that the embeddable models are exactly those that correspond to the Euclidean special Jordan algebras: quantum theory over the reals, the complex numbers, or the quaternions, and "spin factors" (qubits with more than three degrees of freedom), and direct sums thereof.
Contextuality without access to a tomographically complete set
Tests of contextuality are designed that are immune to this effect for a given number of extra measurements in the tomographically complete set, even if nothing is known about their statistics, which allows contextuality to be demonstrated with weaker assumptions.
Contextual Advantage for State Discrimination
This work identifies quantitative limits on the success probability for minimum error state discrimination in any experiment described by a noncontextual ontological model, and identifies noncontextuality inequalities that are violated by quantum theory, and implies a quantum advantage for state discrimination relative to non contextual models.
Quantum Darwinism and the spreading of classical information in non-classical theories
Quantum Darwinism posits that the emergence of a classical reality relies on the spreading of classical information from a quantum system to many parts of its environment. But what are the essential
Almost Quantum Correlations are Inconsistent with Specker's Principle
Ernst Specker considered a particular feature of quantum theory to be especially fundamental, namely that pairwise joint measurability of sharp measurements implies their global joint measurability
Characterization of Noncontextuality in the Framework of Generalized Probabilistic Theories
It is argued that simplex-embeddability constitutes an intuitive and freestanding notion of classicality for GPTs, which has applications to witnessing nonclassicality in prepare-measure experiments.
An open-source linear program for testing nonclassicality
This work provides an open-source linear program for testing whether or not any given prepare-measure experiment is classically-explainable in this sense, and generalizes all results to arbitrary generalized probabilistic theories.
Deriving robust noncontextuality inequalities from algebraic proofs of the Kochen-Specker theorem: the Peres-Mermin square
When a measurement is compatible with each of two other measurements that are incompatible with one another, these define distinct contexts for the given measurement. The Kochen-Specker theorem rules
Contextuality in entanglement-assisted one-shot classical communication
The results show that the task of entanglement-assisted oneshot classical communication provides a fertile ground to study the interplay of the Kochen-Specker theorem, Spekkens contextuality, and Bell nonlocality.


Generalized probability theories: what determines the structure of quantum theory?
It turns out that non-classical features of single systems can equivalently result from higher-dimensional classical theories that have been restricted, and entanglement and non-locality are shown to be genuine non- classical features.
Probabilistic Theories: What Is Special about Quantum Mechanics?
Quantum Mechanics (QM) is a very special probabilistic theory, yet we don’t know which operational principles make it so. All axiomatization attempts suffer at least one postulate of a mathematical
Quantum Theory and Beyond: Is Entanglement Special?
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic
Evidence for the epistemic view of quantum states: A toy theory
We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a
The Problem of Hidden Variables in Quantum Mechanics
Forty years after the advent of quantum mechanics the problem of hidden variables, that is, the possibility of imbedding quantum theory into a classical theory, remains a controversial and obscure
Quantum Theory: Informational Foundations and Foils
This book provides the first unified overview of the burgeoning research area at the interface between Quantum Foundations and Quantum Information, with fourteen original contributions from leading experts in the field covering some of the most promising research directions that have emerged in the new wave of quantum foundations.
Information processing in generalized probabilistic theories
A framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others, is introduced, and a tensor product rule for combining separate systems can be derived.
Tomography of quantum detectors
Measurement connects the world of quantum phenomena to the world of classical events. It has both a passive role—in observing quantum systems—and an active one, in preparing quantum states and
Experimental violation of a Bell's inequality with efficient detection
Here, correlations in the classical properties of massive entangled particles (9Be+ ions): these correlations violate a form of Bell's inequality, and the high detection efficiency of the apparatus eliminates the so-called ‘detection’ loophole.
Ruling Out Multi-Order Interference in Quantum Mechanics
A three-slit experiment with photons was performed and bounded the magnitude of three- path interference to less than 10−2 of the expected two-path interference, thus ruling out third- and higher-order interference and providing a bound on the accuracy of Born’s rule.