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Symmetry 2019, 11(2), 174; https://doi.org/10.3390/sym11020174

Absolute Quantum Theory (after Chang, Lewis, Minic and Takeuchi), and a Road to Quantum Deletion

Department of Mathematics, Ghent University, Krijgslaan 281, S25, B-9000 Ghent, Belgium
Received: 22 November 2018 / Revised: 16 January 2019 / Accepted: 24 January 2019 / Published: 2 February 2019
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Abstract

In a recent paper, Chang et al. have proposed studying “quantum F u n ”: the q 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 u n , and we determine the corresponding unitary group. Next, we obtain a typical no-cloning result in the general realm of quantum F u n . 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 u n , it is also valid in any other quantum theory (and thus also in classical quantum theory in complex Hilbert spaces). View Full-Text
Keywords: København quantum theory; modal quantum theories; field with one element; no-cloning; quantum deletion; almost unitary operator København quantum theory; modal quantum theories; field with one element; no-cloning; quantum deletion; almost unitary operator
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Thas, K. Absolute Quantum Theory (after Chang, Lewis, Minic and Takeuchi), and a Road to Quantum Deletion. Symmetry 2019, 11, 174.

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