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Fidelity and mistaken identity for symplectic quantum states

Henriksson, Andreas (2021) Fidelity and mistaken identity for symplectic quantum states. [Preprint]

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Abstract

The distinguishability between pairs of quantum states, as measured by quantum fidelity, is formulated on phase space. The fidelity is physically interpreted as the probability that the pair are mistaken for each other upon an measurement. The mathematical representation is based on the concept of symplectic capacity in symplectic topology. The fidelity is the absolute square of the complex-valued overlap between the symplectic capacities of the pair of states. The symplectic capacity for a given state, onto any conjugate plane of degrees of freedom, is postulated to be bounded from below by the Gromov width h/2. This generalize the Gibbs-Liouville theorem in classical mechanics, which state that the volume of a region of phase space is invariant under the Hamiltonian flow of the system, by constraining the shape of the flow. It is shown that for closed Hamiltonian systems, the Schroedinger equation is the mathematical representation for the conservation of fidelity.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Henriksson, Andreasandreas.henriksson@skole.rogfk.no0000-0001-9014-4320
Keywords: Indeterminacy relation, Non-squeezing theorem, Symplectic capacity, Quantum fidelity, Born rule, Gibbs-Liouville theorem, Schroedinger equation
Subjects: Specific Sciences > Physics > Quantum Mechanics
Depositing User: Mr. Andreas Henriksson
Date Deposited: 13 Apr 2021 02:08
Last Modified: 13 Apr 2021 02:08
Item ID: 18903
Subjects: Specific Sciences > Physics > Quantum Mechanics
Date: 2021
URI: http://philsci-archive.pitt.edu/id/eprint/18903

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