Abstract
Entanglement witnesses (EW) allow the detection of entanglement in a quantum system, from the measurement of some few observables. They do not require the complete determination of the quantum state, which is regarded as a main advantage. On this paper it is experimentally analyzed an entanglement witness recently proposed in the context of Nuclear Magnetic Resonance experiments to test it in some Bell-diagonal states. We also propose some optimal entanglement witness for Bell-diagonal states. The efficiency of the two types of EW’s are compared to a measure of entanglement with tomographic cost, the generalized robustness of entanglement. It is used a GRAPE algorithm to produce an entangled state which is out of the detection region of the EW for Bell-diagonal states. Upon relaxation, the results show that there is a region in which both EW fails, whereas the generalized robustness still shows entanglement, but with the entanglement witness proposed here with a better performance.
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Filgueiras, J.G., Maciel, T.O., Auccaise, R.E. et al. Experimental implementation of a NMR entanglement witness. Quantum Inf Process 11, 1883–1893 (2012). https://doi.org/10.1007/s11128-011-0341-z
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DOI: https://doi.org/10.1007/s11128-011-0341-z