Entanglement in Liquid-State NMR

In a beautiful example of how technology can stimulate fundamental physics, the proposals for implementing quantum computing via liquid-state NMR have sparked a debate recently on the very nature of quantum computing. - N. Linden and S. Popescu [Phys. Rev. Lett. 87 (2001) 047901-1] 

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Indeed, in current liquid-state NMR experiments e 3 x 10-5 on n < 10 qubits. So we may conclude that in all liquid-state NMR experiments to-date no entangled state has been accessed [Braunstein 1999]. So that resolves one issue. Our first intuition was that entanglement is everything in quantum computation, but recall that the Jozsa-Linden theorem does not actually say that for mixed states. Maybe one can still obtain a speed-up without entanglement It turns out that this was no less controversial than the first question. 

So, how to quantify entanglement For two qubits, the elements of the Bell basis represent maximally entangled states, but as the number of qubits increases, the quantification of entanglement becomes difficult. For an arbitrary number of qubits, nobody knows how to quantify entanglement. Notice that these difficulties are present to any physical system where noise is present or not, and by no means is exclusive to NMR. Indeed, any quantum system in the presence of white noise can be written in the form (6.1.3). The difference is that in experiments of liquid-state NMR made at room temperature, that form is intrinsic. For discussions about general aspects, characterization and quantification of entanglement, see [2,3]. 

The general conclusion of the authors is that there is more to quantum information processing than entanglement and that, keeping in mind the limitations of room temperature liquid-state experiments, the NMR of these systems is an excellent test bed for the principles of quantum information and quantum computation. 

However, the exponential loss of sensitivity of the NMR signal upon increasing the number of qubits, severely limits the practical applications of such systems for quantum computation, and cannot be considered for a large scale real quantum processor. Besides, as discussed in the previous chapter, it has been shown that entanglement phenomenon cannot be implemented at room-temperature liquids, in spite of the fact that NMR possesses the ideal tools for that. Just to remind the problem, suppose that a n-qubit system is in the pseudo-pure state 00... 0) ... 

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