Since its introduction in the 1930s by Wigner, and its generalisations by Moyal and Weyl, the ability to associate an operator on Hilbert space by a quasi-probability distribution function on phase space has found extensive use in the physics of continuous variable systems. Lacking, however, is finite system applications; to date, such functions have taken a back seat to state vector, path integration, and Heisenberg representations. In recent work we have addressed this lack of application by giving a general framework to generate a Wigner distribution function for any system in displaced parity form. Using this work, we have shown how varied quantum systems can be easily represented in phase space as well as visualise certain quantum properties, such as entanglement, within these systems. In particular, we have applied our formalism to directly measure phase space coordinates of multiple qubit states, including a five-qubit GHZ state, on IBM’s Quantum Experience. The above work makes clear that our finite-state Wigner functions are an optimal method for quantum state analysis, entanglement testing, and state characterisations.
Russell P. Rundle is currently in the final year of his Ph.D as part of the Quantum systems Engineering Research Group in Loughborough University with Mark Everitt and Vince Dwyer. He completed his BSc in Mathematics at Royal Holloway, University of London before going on to do his MSc in Physics at Loughborough University. Russell’s research has centred on the use of phase-space methods to develop quantum and quantum-inspired technologies, where the main focus has been on the verification, validation, and visualisation of quantum states.
Seminar by the NYU-ECNU Institute of Physics at NYU Shanghai