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arXiv:1611.05761 · Physical Review A

Proposed experiment to test fundamentally binary theories

Matthias Kleinmann, Tamás Vértesi, Adán Cabello

Published Sep 5, 2017• 12 citations
arXivHTMLPDF

Abstract

Fundamentally binary theories are nonsignaling theories in which measurements of many outcomes are constructed by selecting from binary measurements. They constitute a sensible alternative to quantum theory and have never been directly falsified by any experiment. Here we show that fundamentally binary theories are experimentally testable with current technology. For that, we identify a feasible Bell-type experiment on pairs of entangled qutrits. In addition, we prove that, for any $n$, quantum $n$-ary correlations are not fundamentally $(n\ensuremath{-}1)$-ary. For that, we introduce a family of inequalities that hold for fundamentally $(n\ensuremath{-}1)$-ary theories but are violated by quantum $n$-ary correlations.

DOI
10.1103/physreva.96.032104

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Fundamentally binary theories are nonsignaling theories in which measurements of many outcomes are constructed by selecting from binary measurements. They constitute a sensible alternative to quantum theory and have never been directly falsified by any experiment. Here we show that fundamentally binary theories are experimentally testable with current technology. For that, we identify a feasible Bell-type experiment on pairs of entangled qutrits. In addition, we prove that, for any nnn, quantum nnn-ary correlations are not fundamentally (n\ensuremath−1)(n\ensuremath{-}1)(n\ensuremath−1)-ary. For that, we introduce a family of inequalities that hold for fundamentally (n\ensuremath−1)(n\ensuremath{-}1)(n\ensuremath−1)-ary theories but are violated by quantum nnn-ary correlations.
We present the first experimental confirmation of the quantum-mechanical prediction of stronger-than-binary correlations. These are correlations that cannot be explained under the assumption that the occurrence of a particular outcome of an n≥3-outcome measurement is due to a two-step process in which, in the first step, some classical mechanism precludes n-2 of the outcomes and, in the second step, a binary measurement generates the outcome. Our experiment uses pairs of photonic qutrits distributed between two laboratories, where randomly chosen three-outcome measurements are performed. We report a violation by 9.3 standard deviations of the optimal inequality for nonsignaling binary correlations.
We show that, for any n, there are m-outcome quantum correlations, with m>n, which are stronger than any nonsignaling correlation produced from selecting among n-outcome measurements. As a consequence, for any n, there are m-outcome quantum measurements that cannot be constructed by selecting locally from the set of n-outcome measurements. This is a property of the set of measurements in quantum theory that is not mandatory for general probabilistic theories. We also show that this prediction can be tested through high-precision Bell-type experiments and identify past experiments providing evidence that some of these strong correlations exist in nature. Finally, we provide a modified version of quantum theory restricted to having at most n-outcome quantum measurements.
The qubit, the simplest system and unit of information, is sometimes compared to a quantum coin: a coin with infinitely many sets of two sides which can only be tossed when specifying the desired set. However, this picture fails to capture the richness of the world, where qubit measurements are not necessarily binary. Consequently, when pairs of entangled qubits are measured locally, theory predicts correlations that can neither be explained as produced by locally tossing classical coins nor explained by locally tossing coins. However, this last prediction was unconfirmed until now since it requires the observation of a very small effect on an almost perfectly entangled qubit-qubit state. Here we present an experiment on pairs of entangled photonic qubits violating by more than 8 standard deviations a new Bell-like correlation inequality, which is valid only for binary measurements. By also providing device-independent evidences that our system is best described by two qubits, we prove that measurements on a qubit can be fundamentally non-binary. Since non-binary measurements on a qubit cannot be sharp, this constitutes the first device-independent certification of a genuine generalized measurement.
We show that, for any n, there are m-outcome quantum correlations, with m>n, which are stronger than any nonsignaling correlation produced from selecting among n-outcome measurements. As a consequence, for any n, there are m-outcome quantum measurements that cannot be constructed by selecting locally from the set of n-outcome measurements. This is a property of the set of measurements in quantum theory that is not mandatory for general probabilistic theories. We also show that this prediction can be tested through high-precision Bell-type experiments and identify past experiments providing evidence that some of these strong correlations exist in nature. Finally, we provide a modified version of quantum theory restricted to having at most n-outcome quantum measurements.