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The usefulness of negativity: Quantum advantage in post-selected metrology

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In this talk, I will show that post-selection offers a non-classical advantage in metrology. In every parameter-estimation experiment, the final measurement or the post-processing incurs some cost. Post-selection can improve the rate of Fisher information (the average information learned about an unknown parameter from an experimental trial) to cost. This improvement, we will see, stems from the negativity of the Kirkwood-Dirac (KD) quasi-probability distribution, a quantum extension of a probability distribution. In a classical theory, in which all observables commute, the KD distribution can be expressed as real and non-negative. In a quantum-mechanical theory, however, I will show that non-commutation forces the KD distribution to include negative or non-real quasi-probabilities. The distribution’s non-classically negative values enable post-selected experiments to outperform even post-selection-free experiments whose input states and final measurements are optimised: Post-selected quantum experiments can yield anomalously large information-cost rates. Finally, I will outline a preparation-and-post-selection procedure that can result in an arbitrarily large Fisher information. In collaboration with Aephraim Steinberg’s quantum-optics group, we are currently conducting an experiment to demonstrate this result.


1) D. Arvidsson-Shukur et al., Nature Comms., 11, 3775, (2020)



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