Minimal tomography with entanglement witnesses

Abstract

We introduce informationally complete measurements whose outcomes are entanglement witnesses and so answer the question of how many witnesses need to be measured to decide whether an arbitrary state is entangled or not: as many as the dimension of the state space. The optimized witness-based measurement can provide exponential improvement with respect to witness efficiency in high-dimensional Hilbert spaces, at the price of a reduction in the tomographic efficiency. We describe a systematic construction, and illustrate the matter at the example of two qubits.

5 pages, 1 figure

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• Product measurements and fully symmetric measurements in qubit-pair tomography: A numerical study
• Detecting entanglement of unknown states by violating the Clauser-Horne-Shimony-Holt inequality
• Numerical Estimation Schemes for Quantum Tomography