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arXiv:2506.10760 · Journal of the Indian Institute of Science

Comparing Probability Distributions: Application to Quantum States of Light

Soumyabrata Paul, V. Balakrishnan, S. Ramanan, S. Lakshmibala

Published Jan 1, 2025• 2 citations
arXivHTMLPDF
DOI
10.1007/s41745-025-00474-8

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The Scrooge distribution is a probability distribution over the set of pure states of a quantum system. Specifically, it is the distribution that, upon measurement, gives up the least information about the identity of the pure state compared with all other distributions that have the same density matrix. The Scrooge distribution has normally been regarded as a purely quantum mechanical concept with no natural classical interpretation. In this paper, we offer a classical interpretation of the Scrooge distribution viewed as a probability distribution over the probability simplex. We begin by considering a real-amplitude version of the Scrooge distribution for which we find that there is a non-trivial but natural classical interpretation. The transition to the complex-amplitude case requires a step that is not particularly natural but that may shed light on the relation between quantum mechanics and classical probability theory.
This paper explores the application of dynamic topology to quantum probability models, aiming to enhance quantum system capabilities through adaptive probability distributions. We present a novel framework that dynamically adjusts probability distributions based on quantum system states and environmental influences. The core mechanism relies on the construction of dynamic topology, allowing for automated optimization of probability distributions tailored to the system's characteristics. The work demonstrates a significant improvement in computational performance and system adaptability compared to traditional approaches. This research contributes to a deeper understanding of the potential for dynamic topology to revolutionize quantum computation.