Happy to announce new work with Sergii Strelchuk, in which we study the role of positivity in Kirkwood–Dirac (KD) quasiprobability distributions from the perspective of quantum computation. While KD quasiprobabilities have been widely used in quantum foundations, metrology, and thermodynamics, their computational meaning has remained unexplored. This is unlike for the discrete Wigner distribution, where positive distributions and positivity-preserving unitaries are known to describe stabilizer states and Clifford gates.

By classifying positivity-preserving unitaries for a wide class of KD distributions, we prove some interesting contrasts to the Wigner case: positivity preservation in the KD setting does not coincide with stochastic evolution of quasiprobabilities, or with preservation of total non-positivity (a.k.a. the distribution’s \(l_1\)-norm)! We also adapt the well-known classical simulation algorithm of Pashayan, Wallman and Bartlett to the KD setting. This leads to some surprising constraints for resource theories of KD non-positivity for Fourier-conjugate KD distributions in squarefree semiprime dimensions.

The full paper is available on arXiv: https://arxiv.org/abs/2502.11784.