On braid statistics versus parastatistics

• URL: http://arxiv.org/abs/2411.14261v1
• Date: Thu, 21 Nov 2024 16:15:07 GMT
• Title: On braid statistics versus parastatistics
• Authors: Francesco Toppan,
• Abstract summary: In the first scenario simple toy models based on the so-called $2$-bit parastatistics show that, in the multiparticle sector, certain observables can discriminate paraparticles from ordinary bosons/fermions. In the second scenario the notion of (braided) Majorana qubit is introduced as the simplest building block to implement the Kitaev's proposal of a topological quantum computer.
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• Abstract: I report the recent advances in applying (graded) Hopf algebras with braided tensor product in two scenarios: i) paraparticles beyond bosons and fermions living in any space dimensions and transforming under the permutation group; ii) physical models of anyons living in two space-dimensions and transforming under the braid group. In the first scenario simple toy models based on the so-called $2$-bit parastatistics show that, in the multiparticle sector, certain observables can discriminate paraparticles from ordinary bosons/fermions (thus, providing a counterexample to the widespread belief of the "conventionality of parastatistics" argument). In the second scenario the notion of (braided) Majorana qubit is introduced as the simplest building block to implement the Kitaev's proposal of a topological quantum computer which protects from decoherence.

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