A method for performing quantum state tomography for quadrupole nuclei is presented in this paper. First, it is shown that upon appropriate phase cycling, the nuclear-magnetic-resonance (NMR) intensities of quadrupole nuclei depend only on diagonal elements of the density-matrix. Thus, a method for obtaining the density-matrix elements, which consists of dragging off-diagonal elements into the main diagonal using fine phase-controlled selective radio-frequency pulses, was derived. The use of the method is exemplified through $^{23}\mathrm{Na}$ NMR (nuclear spin $I=3∕2$ ) in a lyotropic liquid crystal at room temperature, in three applications: (a) the tomography of pseudopure states, (b) the tomography of the quadrupole free evolution of the density matrix, and (c) the unitary state evolution of each qubit in the system over the Bloch sphere upon the application of a Hadamard gate. Further applications in the context of pure NMR and in the context of quantum information processing, as well as generalizations for higher spins, are discussed.A method for performing quantum state tomography for quadrupole nuclei is presented in this paper. First, it is shown that upon appropriate phase cycling, the nuclear-magnetic-resonance (NMR) intensities of quadrupole nuclei depend only on diagonal elements of the density-matrix. Thus, a method for obtaining the density-matrix elements, which consists of dragging off-diagonal elements into the main diagonal using fine phase-controlled selective radio-frequency pulses, was derived. The use of the method is exemplified through $^{23}\mathrm{Na}$ NMR (nuclear spin $I=3∕2$) in a lyotropic liquid crystal at room temperature, in three applications: (a) the tomography of pseudopure states, (b) the tomography of the quadrupole free evolution of the density matrix, and (c) the unitary state evolution of each qubit in the system over the Bloch sphere upon the application of a Hadamard gate. Further applications in the context of pure NMR and in the context of quantum information processing, as well as generalizations for higher spins, are discussed.

Physical Review AApr 29, 200442 citations

Analysis of density matrix reconstruction in NMR quantum computing

Gui‐Lu Long, Hu Yong Yan, Yang Sun

Reconstruction of density matrices is important in NMR quantum computing. An analysis is made for a 2-qubit system using the error matrix method. It is found that the state tomography method determines well the parameters that are necessary for reconstructing the density matrix in NMR quantum computations. Analysis is also made for a simplified state tomography procedure that uses fewer read-outs. The result of this analysis with the error matrix method demonstrates that a satisfactory accuracy in the density matrix reconstruction can be achieved even in a measurement with the number of read-outs being largely reduced.Reconstruction of density matrices is important in NMR quantum computing. An analysis is made for a 2-qubit system using the error matrix method. It is found that the state tomography method determines well the parameters that are necessary for reconstructing the density matrix in NMR quantum computations. Analysis is also made for a simplified state tomography procedure that uses fewer read-outs. The result of this analysis with the error matrix method demonstrates that a satisfactory accuracy in the density matrix reconstruction can be achieved even in a measurement with the number of read-outs being largely reduced.

arXiv:quant-ph/0012047Journal of Optics B Quantum and Semiclassical OpticsNov 13, 200161 citations

Efficient quantum state tomography

Gregory S. Kanter, Prem Kumar

Nature PhotonicsOct 31, 20237 citations

Efficient quantum state tomography

M. Cramer, Martin Bodo Plenio, Steven T. Flammia +6 more

arXiv:1101.4366Nature CommunicationsDec 21, 2010671 citations

^{23}\mathrm{Na}

NMR (nuclear spin

I=3∕2

) in a lyotropic liquid crystal at room temperature, in three applications: (a) the tomography of pseudopure states, (b) the tomography of the quadrupole free evolution of the density matrix, and (c) the unitary state evolution of each qubit in the system over the Bloch sphere upon the application of a Hadamard gate. Further applications in the context of pure NMR and in the context of quantum information processing, as well as generalizations for higher spins, are discussed.