Optimal observables to determine entanglement of a two qubit state

Experimental determination of entanglement is important not only to characterize the state and use it in quantum information, but also in understanding complicated phenomena such as phase transitions. In this paper we show that in many cases, it is possible to determine entanglement of a two qubit state, as represented by concurrence, with a few observables, most of which are local. In particular, rank 1 and rank 2 states need exclusively measurement of local observables while rank 3 states need measurement of just one correlation observable in addition to local observables. Only the rank 4 states are shown to require a more detailed tomography. The analysis also sheds light on the other measure, non separability since it is a lower bound on concurrence.

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