Why the `coarse-graining' of Wigner function is always coarse

Joachim J. Włodarz

Tyler Keating, Adam T. C. Steege, Arjendu K. Pattanayak

The negativity of a given state's Wigner function has been proposed as a measure of quantumness of that state in a unipartite system. This otherwise physically intuitive and useful phase-space measure however does not yield the right correspondence principle limit, and also turns out to yield infinite values for the infinite square well. We show that both these issues can be sensibly resolved using coarse-graining of the Wigner function.

T.B. Smith

Olivia Di Matteo, Luis Lorenzo Sánchez-Soto, Gerd Leuchs +1 more

We develop a systematic coarse-graining procedure for systems of $N$ qubits. We exploit the underlying geometrical structures of the associated discrete phase space to produce a coarse-grained version with reduced effective size. Our coarse-grained spaces inherit key properties of the original ones. In particular, our procedure naturally yields a subset of the original measurement operators, which can be used to construct a coarse discrete Wigner function. These operators also constitute a systematic choice of incomplete measurements for the tomographer wishing to probe an intractably large system.

Francisco Soto, P. Claverie

Dragomir M Davidović, D. Lalović