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arXiv:1612.08563 · Physical Review A

Experimental test of Born's rule by inspecting third-order quantum interference on a single spin in solids

Fangzhou Jin, Ying Liu, Jianpei Geng, Pu Huang, Wenchao Ma, Mingjun Shi, Chang‐Kui Duan, Fazhan Shi, Xing Rong, Jiangfeng Du

Published Jan 9, 2017• 26 citations
arXivHTMLPDF

Abstract

As a fundamental postulate of quantum mechanics, Born's rule assigns probabilities to the measurement outcomes of quantum systems and excludes multiorder quantum interference. Here we report an experiment on a single spin in diamond to test Born's rule by inspecting the third-order quantum interference. The ratio of the third-order quantum interference to the second order in our experiment is bounded to the scale of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, which provides a stringent constraint on the potential breakdown of Born's rule.

DOI
10.1103/physreva.95.012107

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As a fundamental postulate of quantum mechanics, Born's rule assigns probabilities to the measurement outcomes of quantum systems and excludes multiorder quantum interference. Here we report an experiment on a single spin in diamond to test Born's rule by inspecting the third-order quantum interference. The ratio of the third-order quantum interference to the second order in our experiment is bounded to the scale of 1\ifmmode×\else\texttimes\fi10\ensuremath−31\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}1\ifmmode×\else\texttimes\fi10\ensuremath−3, which provides a stringent constraint on the potential breakdown of Born's rule.
This paper is based on work published in [1]. It describes a triple slit experiment using single photons that has been used to provide a bound on one of the most fundamental axioms of quantum mechanics i.e. Born’s rule for probabilities [2]. In spite of being one of the most successful theories which describes various natural phenomena, quantum mechanics has enough intricacies and “weirdness” associated with it which makes many physicists believe that it may not be the final theory and hints towards the possibility of more generalized versions. Quantum interference as shown by a double slit diffraction experiment only occurs from pairs of paths. Even in multi‐slit versions, interference can only occur between pairs of possibilities and increasing the number of slits does not increase the complexity of the theory that still remains second‐order. However, more generalized versions of quantum mechanics may allow for multi‐path i.e. higher than second order interference. This experiment also provides a bound on the magnitude of such higher order interference. We have been able to bound 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.
The Born rule is at the foundation of quantum mechanics and transforms the classical understanding of probabilities by predicting that interference occurs between pairs of independent paths of a single object. One consequence of the Born rule is that three-way (or three-path) quantum interference does not exist. In order to test the consistency of the Born rule, we examine detection probabilities in three-path interference using an ensemble of spin-1/2 quantum registers in liquid state nuclear magnetic resonance. As a measure of the consistency, we evaluate the ratio of three-way interference to two-way interference. Our experiment bounded the ratio to the order of 10 −3 ± 10 −3 , and hence it is consistent with Born's rule.
Born's rule relates detection probabilities to the modulus square of the wave function.It is one of the central principles of quantum mechanics together with that of linear superposition.Single-particle interference is accordingly limited to pairs of quantum paths and higher-order interferences are prohibited.Deviations from Born's law have been quantified via the Sorkin parameter which is proportional to the third-order term.However, while the linearity of quantum theory has been experimentally tested to the level of 10 -20 eV, the Sorkin parameter has only been measured to an accuracy of 2 × 10 -3 in the quantum regime.We here investigate Born's law using many-particle interferences and demonstrate that all interference terms of order (2M + 1) and greater vanish for M particles.We further introduce a family of many-particle Sorkin parameters and show that they are exponentially more sensitive to deviations from Born's rule than their single-particle counterpart.
Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be generalized to achieve unification. For example, Born's rule--one of the axioms of quantum mechanics--could be violated. Born's rule predicts that quantum interference, as shown by a double-slit diffraction experiment, occurs from pairs of paths. A generalized version of quantum mechanics might allow multipath (i.e., higher-order) interference, thus leading to a deviation from the theory. We performed a three-slit experiment with photons 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. Our experiment is consistent with the postulate both in semiclassical and quantum regimes.