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.
|Title of host publication||International Symposium on Mathematics, Quantum Theory, and Cryptography|
|Publication status||Published - 23 Oct 2020|
|Name||Mathematics in Industry|
(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)