Quasiprobability distributions

Perry R. Rice

Calle Luis, Enrique Erro

Arkadiusz Orłowski, Harry Paul, B. Böhmer

Karl Vogel, H. Risken

It is shown that the probability distribution for the rotated quadrature phase [${a}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$exp(i\ensuremath{\theta})+a exp(-i\ensuremath{\theta})]/2 can be expressed in terms of quasiprobability distributions such as P, Q, and Wigner functions and that also the reverse is true, i.e., if the probability distribution for the rotated quadrature phase is known for every \ensuremath{\theta} in the interval 0\ensuremath{\le}\ensuremath{\theta}<\ensuremath{\pi}, then the quasiprobability distributions can be obtained.

Kok Chuan Tan, Souradeep Sasmal

We show that a Kirkwood-Dirac type quasiprobability distribution is sufficient to reveal any arbitrary quantum resource. This is achieved by demonstrating that it is always possible to identify a set of incompatible measurements that distinguishes between resourceful states and nonresourceful states. The quasiprobability reveals a resourceful quantum state by having at least one quasiprobabilty outcome with a strictly negative numerical value. We also show that there always exists a quasiprobabilty distribution where the total negativity can be interpreted as the geometric distance between a resourceful quantum state to the closest nonresourceful state. It can also be shown that Kirkwood-Dirac type quasiprobability distributions, like the Wigner distribution, can be made informationally complete, in the sense that it can provide complete information about the quantum state while simultaneously revealing nonclassicality whenever a quasiprobability outcome is negative. Moreover, we demonstrate the existence of sufficiently strong anomalous weak values whenever the quasiprobability distribution is negative, which suggests a means to experimentally test such quasiprobability distributions. Since incompatible measurements are necessary in order for the quasiprobability to be negative, this result suggests that measurement incompatibility may underlie any quantum advantage gained from utilizing a nonclassical quantum resource