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 -