Quantum advantage in postselected metrology

Postselection can improve the rate of Fisher information (the average information learned about an unknown parameter from a trial) to cost in parameter-estimation experiments. This improvement stems from the negativity of a particular quasiprobability distribution, a quantum extension of a probability distribution. Negative quasiprobabilities enable postselected quantum experiments to outperform optimal postselection-free experiments, yielding anomalously large information-cost rates. This advantage is unrealizable in any classically commuting theory. A preparation-and-postselection procedure yielding arbitrarily large Fisher information is constructed.

David R. M. Arvidsson-Shukur, Nicole Yunger Halpern, Hugo V. Lepage, Aleksander A. Lasek, Crispin H. W. Barnes, Seth Lloyd