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

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

doi:10.1007/978-981-15-5191-8_9

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 proceeding › Conference contribution

43 Downloads (Pure)

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 language	English
Title of host publication	International Symposium on Mathematics, Quantum Theory, and Cryptography
Pages	79-92
DOIs	https://doi.org/10.1007/978-981-15-5191-8_9
Publication status	Published - 23 Oct 2020

Publication series

Name	Mathematics in Industry
Publisher	Springer
Volume	33
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

Access to Document

10.1007/978-981-15-5191-8_9Licence: CC BY

From the Bloch Sphere to Phase-Space Representations with the Gottesman–Kitaev–Preskill Encoding
Copyright 2020 the authors. This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
Accepted author manuscript, 2.98 MBLicence: CC BY

Cite this

@inproceedings{6de344908c88461fa1292ada77f35788,

title = "From the Bloch sphere to phase space representations with the Gottesman-Kitaev-Preskill encoding",

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. ",

keywords = "quant-ph",

author = "L. Garc{\'i}a-{\'A}lvarez and A. Ferraro and G. Ferrini",

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)",

year = "2020",

month = oct,

day = "23",

doi = "10.1007/978-981-15-5191-8_9",

language = "English",

series = "Mathematics in Industry",

publisher = "Springer",

pages = "79--92",

booktitle = "International Symposium on Mathematics, Quantum Theory, and Cryptography",

}

TY - GEN

T1 - From the Bloch sphere to phase space representations with the Gottesman-Kitaev-Preskill encoding

AU - García-Álvarez, L.

AU - Ferraro, A.

AU - Ferrini, G.

N1 - (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)

PY - 2020/10/23

Y1 - 2020/10/23

N2 - 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.

AB - 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.

KW - quant-ph

U2 - 10.1007/978-981-15-5191-8_9

DO - 10.1007/978-981-15-5191-8_9

M3 - Conference contribution

T3 - Mathematics in Industry

SP - 79

EP - 92

BT - International Symposium on Mathematics, Quantum Theory, and Cryptography

ER -

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

Abstract

Publication series

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this