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Absolute quantum theory (after Chang, Lewis, Minic and Takeuchi), and a road to quantum deletion

Tijdschriftbijdrage - Tijdschriftartikel

In a recent paper, Chang et al. have proposed studying "quantum F-un": the q bar right arrow 1 limit of modal quantum theories over finite fields F-q, motivated by the fact that such limit theories can be naturally interpreted in classical quantum theory. In this letter, we first make a number of rectifications of statements made in that paper. For instance, we show that quantum theory over F-1 does have a natural analogon of an inner product, and so orthogonality is a well-defined notion, contrary to what was claimed in Chang et al. Starting from that formalism, we introduce time evolution operators and observables in quantum F-un, and we determine the corresponding unitary group. Next, we obtain a typical no-cloning result in the general realm of quantum F-un. Finally, we obtain a no-deletion result as well. Remarkably, we show that we can perform quantum deletion by almost unitary operators, with a probability tending to 1. Although we develop the construction in quantum F-un, it is also valid in any other quantum theory (and thus also in classical quantum theory in complex Hilbert spaces).
Tijdschrift: SYMMETRY-BASEL
ISSN: 2073-8994
Issue: 2
Volume: 11
Jaar van publicatie:2019
BOF-keylabel:ja
IOF-keylabel:ja
BOF-publication weight:0.1
Auteurs:National
Authors from:Higher Education
Toegankelijkheid:Open