Unitarity constrains the quantum information metrics for particle interactions

• URL: http://arxiv.org/abs/2412.12585v1
• Date: Tue, 17 Dec 2024 06:38:58 GMT
• Title: Unitarity constrains the quantum information metrics for particle interactions
• Authors: Hobbes Sprague, Shanmuka Shivashankara,
• Abstract summary: Unitarity provides mathematical and physical constraints on quantum information systems. The language of non-relativistic quantum mechanics is presented to derive the density matrix for hard scattering. For the inelastic scattering of an electron from a proton, the language of relativistic quantum mechanics is used to derive the momentum entropy or Sackur-Tetrode equation.
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• Abstract: Unitarity provides mathematical and physical constraints on quantum information systems. e.g., in entanglement swapping, unitarity requires that the same entanglement generation occurs for either an act of measurement or particle interaction. The article's presentation allows particle physicists to readily begin calculating quantum information metrics for any particle interaction. The language of non-relativistic quantum mechanics is presented to derive the density matrix for hard scattering. Unitarity allows for finding the latter's cross section without using the scattering amplitude or the Lippmann-Schwinger equation plus Green's function. For the inelastic scattering of an electron from a proton, the language of relativistic quantum mechanics is used to derive the momentum entropy or Sackur-Tetrode equation. The latter entropy derives from a Shannon entropy and another entropy that evokes the uncertainty principle.

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