Raman Research Institute, C.V.Raman Avenue, Sadashivanagar, Bengaluru-560080, Karnataka, India · Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada
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Abstract
The history based formalism known as Quantum Measure Theory (QMT) generalizes the concept of probability-measure so as to incorporate quantum interference. The resulting quantum measure μ is defined for arbitrary events (sets of histories), not just for observables at a fixed moment of time. Thanks to interference effects, μ can exceed unity, exhibiting its non-classical nature in a particularly striking manner. Here, in an optical experiment, we illustrate an ancilla based filtering scheme that gives operational meaning to the quantum measure. For a specific photonic event E , we report a measured value of μ ( E ) = 1.172 − 0.019 + 0.013 , which within errors agrees with the theoretical value of 5 / 4 , while exceeding the maximum value permissible for a classical probability (namely 1 ) by 13.32 upper or 8.89 lower percentile widths. The directly observed quantity is an ordinary detector probability p D ≤ 1 (or, with laser light, an equivalent power ratio); the value μ ( E ) > 1 is inferred via the calibrated relation μ ( E ) = 2 p D for our filter.If an unconventional theoretical concept is to play a role in meeting the foundational challenges of quantum theory, it seems important to bring it into contact with experiment as much as possible. Our experiment does this for the quantum measure.
Quantum Measure Theory (QMT) is a framework that extends the idea of probability to quantum systems by assigning a 'quantum measure' to sets of histories rather than just to outcomes at a single moment in time. Unlike ordinary probabilities, which must lie between 0 and 1, this quantum measure can exceed 1 because of interference effects, offering a striking way to reveal the non-classical nature of quantum behavior. Until now, this theoretical possibility had not been directly demonstrated in an experiment.
In this paper, the authors design and carry out an optical experiment using an ancilla-based filtering scheme to give physical meaning to the quantum measure for a specific photonic event. By calibrating the relationship between an ordinary, directly observable detector probability (which cannot exceed 1) and the quantum measure, they infer a value for the quantum measure that is significantly greater than 1, consistent with the theoretical prediction. This represents a concrete experimental contact with an unconventional theoretical concept central to the foundational debates in quantum theory.
Plain-language summary by The Gufo; the paper is the authors’ own text.
Key findings
The quantum measure μ, unlike classical probability, can take values greater than 1 due to quantum interference.
An ancilla-based optical filtering scheme was used to operationally measure the quantum measure for a specific photonic event.
The measured value of μ(E) was found to agree within experimental error with the theoretical prediction of 5/4.
The measured quantum measure exceeded the classical probability bound of 1 by a significant margin in terms of percentile widths, demonstrating non-classical behavior experimentally.
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