An approach to $p$-adic qubits from irreducible representations of $SO(3)_p$

• URL: http://arxiv.org/abs/2112.03362v3
• Date: Wed, 13 Jul 2022 07:43:45 GMT
• Title: An approach to $p$-adic qubits from irreducible representations of $SO(3)_p$
• Authors: Ilaria Svampa, Stefano Mancini, Andreas Winter
• Abstract summary: We introduce the notion of $p$-adic quantum bit ($p$-qubit) In this approach, physics takes place in three-dimensional $p$-adic space rather than Euclidean space.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce the notion of $p$-adic quantum bit ($p$-qubit) in the context of the $p$-adic quantum mechanics initiated and developed by Volovich and his followers. In this approach, physics takes place in three-dimensional $p$-adic space rather than Euclidean space. Based on our prior work describing the $p$-adic special orthogonal group, we outline a programme to classify its continuous unitary projective representations, which can be interpreted as a theory of $p$-adic angular momentum. The $p$-adic quantum bit arises from the irreducible representations of minimal nontrivial dimension two, of which we construct examples for all primes $p$.

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