From the Bloch sphere to phase space representations with the Gottesman-Kitaev-Preskill encoding

L. García-Álvarez, A. Ferraro, G. Ferrini

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Abstract

In this work, we study the Wigner phase-space representation of qubit states encoded in continuous variables (CV) by using the Gottesman-Kitaev-Preskill (GKP) mapping. We explore a possible connection between resources for universal quantum computation in discrete-variable (DV) systems, i.e. non-stabilizer states, and negativity of the Wigner function in CV architectures, which is a necessary requirement for quantum advantage. In particular, we show that the lowest Wigner logarithmic negativity of qubit states encoded in CV with the GKP mapping corresponds to encoded stabilizer states, while the maximum negativity is associated with the most non-stabilizer states, H-type and T-type quantum states.
Original languageEnglish
Title of host publicationInternational Symposium on Mathematics, Quantum Theory, and Cryptography
Pages79-92
DOIs
Publication statusPublished - 23 Oct 2020

Publication series

NameMathematics in Industry
PublisherSpringer
Volume33
ISSN (Print)1612-3956

Bibliographical note

(v1) Accepted for publication in the Springer's "Mathematics for Industry" series. (v2) Typo in the abstract fixed; URL of the conference where the paper has been presented added: International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), held in September 2019 in Fukuoka, Japan (https://www.mqc2019.org/mqc2019/program)

Keywords

  • quant-ph

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