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arXiv:2501.09438

Testing Born's rule via photoionization of helium

Peter Robert Förderer, Andreas Buchleitner, David Busto, Christoph Dittel

Published Jan 16, 2025• 0 citations
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Abstract

It is shown how state-of-the-art attosecond photoionization experiments can test Born's rule -- a postulate of quantum mechanics -- via the so-called Sorkin test. A simulation of the Sorkin test under consideration of typical experimental noise and data acquisition efficiencies infers an achievable measurement precision in the range of the best Sorkin tests to date. The implementation of further fundamental tests of quantum mechanics is discussed.

DOI
10.48550/arxiv.2501.09438

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It is shown how state-of-the-art attosecond photoionization experiments can test Born's rule -- a postulate of quantum mechanics -- via the so-called Sorkin test. A simulation of the Sorkin test under consideration of typical experimental noise and data acquisition efficiencies infers an achievable measurement precision in the range of the best Sorkin tests to date. The implementation of further fundamental tests of quantum mechanics is discussed.
Abstract State-of-the-art attosecond photoionization experiments are identified as a new platform to test Born’s rule—a postulate of quantum mechanics. A simulation of the so-called Sorkin test under typical experimental conditions infers an achievable measurement precision in the range of the best Sorkin tests to date, demonstrating new opportunities for high-precision tests of Born’s rule via nonlinear matter-wave interferometry. The potential of attosecond photoionization for further fundamental tests of quantum mechanics is discussed.
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We use quantum computers to test the foundations of quantum mechanics through quantum algorithms that implement some of the experimental tests as the basis of the theory's postulates. These algorithms can be used as a test of the physical theory under the premise of a perfect hardware or as a test of the hardware under the premise that quantum theory is correct. In this paper, we show how the algorithms can be used to test the efficacy of a quantum computer in obeying the postulates of quantum mechanics. We study the effect of different types of errors on the results of experimental tests of the postulates. A salient feature of this error analysis is that it is deeply rooted in the fundamentals of quantum mechanics as it highlights how systematic errors affect the quantumness of the quantum computer.
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.
We present two complementary viewpoints for combining quantum computers and the foundations of quantum mechanics.On the one hand, ideal devices can be used as test beds for experimental tests of the foundations of quantum mechanics: We provide algorithms for the Peres test for complex numbers in quantum superpositions and the Sorkin test of Born's rule.On the other hand, noisy intermediate-scale quantum devices can be benchmarked using these same tests.These are deep quantum benchmarks based on the foundations of quantum theory itself.We present test data from Rigetti hardware.