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
In a recent paper, Chang et al. have proposed studying “quantum
limit of modal quantum theories over finite fields
, 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
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
, and we determine the corresponding unitary group. Next, we obtain a typical no-cloning result in the general realm of quantum
. 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
, it is also valid in any other quantum theory (and thus also in classical quantum theory in complex Hilbert spaces).
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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.
Thas K. Absolute Quantum Theory (after Chang, Lewis, Minic and Takeuchi), and a Road to Quantum Deletion. Symmetry. 2019; 11(2):174.
Thas, Koen. 2019. "Absolute Quantum Theory (after Chang, Lewis, Minic and Takeuchi), and a Road to Quantum Deletion." Symmetry 11, no. 2: 174.
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