The Grothendieck formalism applied to physical examples in a single quantum system
Year: 2024
Type: conference-paper
Abstract: The Grothendieck formalism considers a classical quadratic form C(θ), and a quantum quadratic form Q(θ). It shows that if C(θ) ≤ 1, the Q(θ) might take values greater than 1, up to the complex Grothendieck constant k G . The region (1, k G ) is ‘ultra-quantum’ in the sense that Q can take values in it, but C cannot take values in it. The mathematical formalism is applied to various physical examples. It is shown that many physically interesting density matrices give Q(θ) ≤ 1. In some examples Q is the Wigner and Weyl functions, and in that case also Q(θ) ≤ 1. In many examples Fourier dual density matrices both give Q(θ) ≤ 1, and in this sense Fourier duality does not play an important role within the Grothendieck formalism. Therefore quantumness according to Grothendieck (Q ε (1, k G )) is different from quantumness according to other criteria.
Author: A. Vourdas
Institution: University of Bradford
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405241208