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Q: Fachverband Quantenoptik und Photonik

Q 13: Quanteninformation: Konzepte III

Q 13.1: Vortrag

Montag, 2. März 2009, 16:30–16:45, VMP 6 HS-D

Quantitative verification of entanglement from incomplete measurement data — •Harald Wunderlich^1,2 and Martin B. Plenio^2,3 — ¹Fachbereich Physik, Universität Siegen, Siegen — ²Institute for Mathematical Sciences, Imperial College London, London, UK — ³QOLS, Blackett Laboratory, Imperial College London, London, UK

Many experiments in quantum information aim at creating multi-partite entangled states. Quantifying the amount of actually generated entanglement can, in principle, be accomplished using full-state tomography. However, this method requires a number of measurement settings growing exponentially in the number of qubits. Non-trivial bounds on experimentally achieved entanglement can also be obtained from partial information on the density matrix. The fundamental question is then formulated as: What is the entanglement content of the least entangled quantum state that is compatible with the available measurement data?

We formulate the problem mathematically employing methods from the theory of semi-definite programming and then address this problem for the case, where the goal of the experiment is the creation of graph states. The observables that we consider are the generators of the stabilizer group, thus the number of measurement settings grows only linearly in the number of qubits. We provide analytical solutions as well as numerical methods that may be applied directly to experiments, and compare the obtained bounds with results from full-state tomography for simulated data.