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Twirled Products and Group-Covariant Symbols

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Geometric Science of Information (GSI 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14071))

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Abstract

A quantum stochastic product is a binary operation on the convex set of states (density operators) of a quantum system preserving the convex structure. We review the notion of twirled product of quantum states, a group-theoretical construction yielding a remarkable class of group-covariant associative stochastic products. In the case where the relevant group is abelian, we then realize the twirled product in terms of the covariant symbols associated with the quantum states involved in the product. Finally, the special case of the twirled product associated with the group of phase-space translations is considered.

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Acknowledgements

We thank J.-P. Gazeau and P. Bieliavsky for their kind invitation to participate in the session “Geometric and Analytical Aspects of Quantization and Non-Commutative Harmonic Analysis on Lie Groups” (GSI’23).

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Authors and Affiliations

  1. Dipartimento di Fisica “Ettore Pancini”, Università di Napoli “Federico II”, Complesso Universitario di Monte S. Angelo, via Cintia, 80126, Napoli, Italy

    Paolo Aniello

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, via Cintia, 80126, Napoli, Italy

    Paolo Aniello

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  1. Paolo Aniello
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Correspondence to Paolo Aniello .

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Editors and Affiliations

  1. Sony Computer Science Laboratories Inc., Tokyo, Japan

    Frank Nielsen

  2. THALES Land and Air Systems, Meudon, France

    Frédéric Barbaresco

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Aniello, P. (2023). Twirled Products and Group-Covariant Symbols. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14071. Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_50

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  • DOI: https://doi.org/10.1007/978-3-031-38271-0_50

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-38270-3

  • Online ISBN: 978-3-031-38271-0

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