Continuous-Variable Wigner Representation of Gottesman-Kitaev-Preskill-Encoded Qudits

Easily understandable representations of quantum systems are key to gaining an intuition, both mathematical and visual, for how they work and how they can be used—for example, in quantum computation. The Wigner function for a continuous-variable system is such a representation. It is a quasiprobability distribution—i.e., it obeys all conditions for a probability distribution except positivity. The analogous Wigner function used to describe discrete-variable systems, however, only exists for a subset of dimensions, and we lack physical intuition as to why this may be the case. To address this gap, we will develop a new quasiprobability representation by applying the continuous-variable Wigner function to discrete-variable states encoded in continuous variables using the Gottesman-Kitaev-Preskill (GKP) code. We will then compare our version to the known discrete-variable Wigner function. By this approach, we expect that two outcomes are possible. Either the current mathematical description of discrete-variable systems is missing something important, or there is something physically fundamental about discrete-variable systems that keeps the mathematical description existing only in a subset of possible dimensions. We expect that, by using our method, we will gain insight into which of the mentioned outcomes is the case and fill in the missing information.

Lucky Antonopoulos

RMIT University

Kanellos Antonopoulos, who also goes by his preferred name, Lucky, is an enthusiastic student of RMIT University. Having finished a bachelor’s degree in mechanical engineering at Swinburne University in 2017, he followed his true passion—physics—by enrolling at RMIT the following year. Currently halfway through his degree in physics, Lucky is pursuing his interests in quantum mechanics. Participation in a summer research project in 2018, where he developed an understanding of Spekkens’ toy model, has well equipped him in his continued aspiration as a future researcher. Lucky’s continued drive, interest, curiosity and enthusiasm are his tool set that makes him a great student and budding researcher.

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