Using Fisher Information to Analyse Inter-measurement Quantum Particles

A debated question in quantum mechanics is how to describe and interpret a quantum particle between observations. Previous discussions have mainly been centred on controversial and interpretation-dependent weak values. In this talk we provide an operational methodology for the analysis of inter-measurement quantum particles. We assume that absolutely perfect quantum evolutions are impossible, and that all interactions include some disturbances. By calculating the quantum Fisher information with respect to these disturbances we obtain a quantitative tool to map out the past path of quantum particles and to investigate the “quantumness” of post-selected experiments. We relate the Fisher information to the Kirkwood-Dirac quasiprobability distribution by decomposing the density matrix of the quantum state in terms of the projectors of the final measurement and the generator eigenbasis of the relevant interaction. We then show that when the Fisher information of a post-selected experiment exceeds its standard maximum, there exist negative quasiprobabilities in the representation, revealing violations of noncontextuality. Our methodology provides a new approach to investigating the foundations of quantum mechanics.