Abstract
Born's rule, one of the cornerstones of quantum mechanics, relates detection probabilities to the modulus square of the wave function. 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. We here extend this formalism to many-particle interferences and find that they exhibit a much richer structure. We demonstrate, in particular, 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.
Highlights
Born’s rule relates detection probabilities to the modulus square of the wave function
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 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
Summary
Marc-Oliver Pleinert ,1,2 Joachim von Zanthier, and Eric Lutz3 1Institut für Optik, Information und Photonik, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), D-91058 Erlangen, Germany. Born’s rule states that the probability of a measurement outcome is given by the modulus square of the corresponding probability amplitude [21] This fundamental postulate of quantum mechanics establishes a link between the (deterministic) mathematical formalism and experiment. The parameter has been measured in three- and five-slit experiments with single photons [15,16,17] and single molecules [18,19], and has been found to be smaller than 3 × 10−5 in the classical light regime and 2 × 10−3 in the quantum regime [17] These findings rule out higher-order single-particle interference [39] and confirm Born’s law to that level of precision. It is of interest from a fundamental point of view [40,41,42,43,44,45,46,59], but has been exploited in imaging [47,48], metrology [49,60], and for quantum information processing [50,61]
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