Southwest Quantum Information and Technology

Quasi-probabilities on a fermionic phase space

Presenting Author: Ninnat Dangniam, University of New Mexico CQuIC
Contributing Author(s): Christopher Jackson, Christopher Ferrie, Carlton Caves

Sometimes a classical simulation scheme of quantum processes given a restricted set of states and measurements can be naturally interpreted as a statistical simulation of positive quasi-probability distributions on a phase space. To explore the relation between classical simulatability and positivity of quasi-probabilities beyond the Wigner functions, we constructed quasi-probability representations on the compact phase space of fermionic Gaussian states (as opposed to coherent states in the usual Wigner phase space formulation) tailored to a classically simulatable problem of fermionic linear optics and found that fermionic Gaussian states possess negative quasi-probabilities. More generally, we showed that this construction due to Brif and Mann (Phys. Rev. A 59, 971 (1999)) is essentially unique given the group of quantum gates and an input state in the relevant representation.

(Session 9c : Friday from 5:15pm-5:45pm)