Quantum process tomography

Another interesting implementation of the QFT in a three-qubit system (the three of alanine) was reported by Weinstein et al. [15]. With the technique, the authors measured the periodicity of an input state, which was followed by quantum state tomography. Their result is shown in Figure 5.6. Other interesting NMR implementation of QFT can be found in Lee et al. [16] and Weinstein et al. [17]. The first applied QFT to phase estimation and quantum counting, and the second performed the quantum process tomography of QFT. 

Y.S. Weinstein, T.F. Havel, J. Emerson, N. Boulant, M. Saraceno, S. Lloyd, D.G. Cory, Quantum process tomography of the Quantum Fourier Transform, J. Chem. Phys. 121 (2004) 6117. 

H. Kampermann, W.S. Veeman, Characterization of quantum algorithms by quantum process tomography using quadrupolar spins in solid-state nuclear magnetic resonance, J. Chem. Phys. 122 (2005) 214108. 

Therefore, performing measurements of observables which are the products of the Pauli matrices, it is possible to determine all the elements of the density matrix operator p, with an arbitrary precision. This process is referred to as Quantum State Tomography, and is a procedure for measuring the quantum state of a system. 

Figure 4.8 shows experimental results for the deviation density matrix obtained after applying each operation for a 2-qubit system Uq, U, and U2 as well as the average state (see also Problems P4.3 and P4.4). The deviation density matrices were obtained using the quantum state tomography process, which will be described in the next section. As it can be seen, the final averaged deviation density matrix is very similar to that of the pure state 100). 

R. Das, T.S. Mahesh, A. Kumar, Efficient quantum-state tomography for quantum-information processing using a two-dimensional Fourier-transform technique, Phys. Rev. A 67 (6) (2003) Art. No. 62304-1. 

Entanglement transfer experiment in NMR quantum information processing - This paper of 2002 by Boulant and co-workers [18] describes an experiment of entanglement transfer by NMR. The aim is to transfer an entangled state of a pair of qubits to another pair of qubits, a process which was first demonstrated using photons in 1998, by Pan and collaborators. The authors used the four nuclei of crotonic acid as qubits. The process was followed by quantum state tomography and the efficacy of the experiment was quantified by a measured called attenuated correlation. A value of 0.65 for this measure at the end of the protocol, indicated that the pseudo-entangled state was indeed transferred from one pair of qubits to the other. 

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