Freiburg 2019 – wissenschaftliches Programm

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FM: Fall Meeting

FM 11: Entanglement: Many-Body States I

FM 11.5: Talk

Montag, 23. September 2019, 15:15–15:30, 2004

Optimal measurement strategies for fast entanglement detection — •Nadia Milazzo1,2, Daniel Braun1, and Olivier Giraud21Institut für theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany — 2LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France

The recent emergence of small quantum processors in quantum information technology has seen the increasing need of characterizing their behavior as "truly" quantum mechanical or not. Already for an unknown quantum state, verifying whether the statistics arising from it can be explained by a classical state is challenging, as long as non-classicality measures or witnesses are based on full tomography. Which is then the most efficient measurement strategy to prove that a state is entangled (or more generally: non-classical)? We tackle this problem by introducing the statistics of lengths of measurement sequences that allow one to certify entanglement across a given bi-partition of a multi-qubit system over the possible sequence of measurements of random unknown states. Perfectly suited for this approach is the formalism of "truncated moment sequences", that allows one to deal naturally with incomplete information about a quantum state. We use it to identify the best measurement strategy in the sense of the (on average) shortest measurement sequence of (multi-qubit) Pauli-measurements. We find that the set of measurements corresponding to diagonal entries of the moment matrix associated to the state are particularly efficient. For symmetric states their number grows like the third power of the number of qubits and their efficiency increases rapidly with that number.

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