Tom Rivlin Atominstitut (TU Wien): Complete characterisation of quantum phase space quasiprobabilities and their connection to generalised contextuality
Abstract: Some of the earliest attempts to understand quantum theory involved constructing quantum analogues of classical (and statistical-mechanical) phase spaces. But it was quickly realised that this approach inevitably led to paradoxical negative probabilities. Since then, much progress has been made in understanding these ‘quasiprobabilities’, including as descriptions of quantum optical phase spaces and as witnesses of nonclassicality. Three well-known quasiprobabilities, the Wigner, Husimi, and Glauber-Sudarshan distributions, are unified by a so-called s-parametrisation scheme, and in this talk, I will show how the s-parametrised family is connected to another well-known quasiprobability called the Kirkwood-Dirac distribution, which has recently been subject to significant renewed interest as a useful tool in quantum foundations, metrology, and thermodynamics. I will show how the connections between these different quasiprobabilities leads to a complete characterisation of all the representations of a quantum optical phase space. I will also discuss the connections between these quasiprobabilities and Spekkens’ generalised contextuality, which has emerged in recent years as a leading signifier of nonclassicality.