An Information-Geometric Reconstruction of Quantum Theory, I: The Abstract Quantum Formalism - Quantum PhysicsReport as inadecuate




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Abstract: In this paper and a companion paper, we show how the framework of informationgeometry, a geometry of discrete probability distributions, can form the basisof a derivation of the quantum formalism. The derivation rests upon a fewelementary features of quantum phenomena, such as the statistical nature ofmeasurements, complementarity, and global gauge invariance. It is shown thatthese features can be traced to experimental observations characteristic ofquantum phenomena and to general theoretical principles, and thus canreasonably be taken as a starting point of the derivation. When appropriatelyformulated within an information geometric framework, these features lead toi the abstract quantum formalism for finite-dimensional quantum systems, iithe result of Wigner-s theorem, and iii the fundamental correspondence rulesof quantum theory, such as the canonical commutation relationships. Theformalism also comes naturally equipped with a metric and associated measureover the space of pure states which is unitarily- and anti-unitarily invariant.The derivation suggests that the information geometric framework is directly orindirectly responsible for many of the central structural features of thequantum formalism, such as the importance of square-roots of probability andthe occurrence of sinusoidal functions of phases in a pure quantum state.Global gauge invariance is seen to play a crucial role in the emergence of theformalism in its complex form.



Author: Philip Goyal

Source: https://arxiv.org/







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