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arXiv · 1711.08112

Strong unitary and overlap uncertainty relations: theory and experiment

Kok-Wei Bong·Nora Tischler·Raj B. Patel·Sabine Wollmann·Geoff J. Pryde·Michael J. W. Hall
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Abstract

We derive and experimentally investigate a strong uncertainty relation valid for any $n$ unitary operators, which implies the standard uncertainty relation as a special case, and which can be written in terms of geometric phases. It is saturated by every pure state of any $n$-dimensional quantum system, generates a tight overlap uncertainty relation for the transition probabilities of any $n+1$ pure states, and gives an upper bound for the out-of-time-order correlation function. We test these uncertainty relations experimentally for photonic polarisation qubits, including the minimum uncertainty states of the overlap uncertainty relation, via interferometric measurements of generalised geometric phases.

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Kok-Wei Bong, Nora Tischler, Raj B. Patel, Sabine Wollmann, Geoff J. Pryde, Michael J. W. Hall. 2017-11-22. Strong unitary and overlap uncertainty relations: theory and experiment. https://doi.org/10.1103/physrevlett.120.230402

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