Incoherent noise and quantum information processing.

Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modeled as a distribution of unitary processes arising from slowly varying experimental parameters. We show how it introduces artifacts in quantum process tomography and we explain how the resulting estimate of the superoperator may not be completely positive. We then go on to attack the inverse problem of extracting an effective distribution of unitaries that characterizes the incoherence via a perturbation theory analysis of the superoperator eigenvalue spectra.

[1]  T. P. Das,et al.  Mathematical Analysis of the Hahn Spin-Echo Experiment , 1954 .

[2]  Timothy F. Havel,et al.  Robust method for estimating the Lindblad operators of a dissipative quantum process from measurements of the density operator at multiple time points , 2003 .

[3]  A.,et al.  FAST FOURIER TRANSFORMS FOR NONEQUISPACED DATA * , 2022 .

[4]  J. A. Jones,et al.  Use of composite rotations to correct systematic errors in NMR quantum computation , 1999, quant-ph/9911072.

[5]  Man-Duen Choi.  Completely positive linear maps on complex matrices , 1975 .

[6]  Steane,et al.  Error Correcting Codes in Quantum Theory. , 1996, Physical review letters.

[7]  A. Uhlmann,et al.  Stochasticity and Partial Order: Doubly Stochastic Maps and Unitary Mixing , 1982 .

[8]  David G. Cory,et al.  Experimental demonstration of an entanglement swapping operation and improved control in NMR quantum-information processing , 2003 .

[9]  J. J. Sakurai,et al.  Modern Quantum Mechanics , 1986 .

[10]  K. Kraus.  General state changes in quantum theory , 1971 .

[11]  Andrew G. Glen,et al.  APPL , 2001 .

[12]  P. Zoller,et al.  Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate , 1996, quant-ph/9611013.

[13]  Pines,et al.  Broadband and adiabatic inversion of a two-level system by phase-modulated pulses. , 1985, Physical review. A, General physics.

[14]  Timothy F. Havel,et al.  Robust control of quantum information , 2003, quant-ph/0307062.

[15]  C. Pillet.  Quantum Dynamical Systems , 2006 .

[16]  A. J. Shaka,et al.  Composite pulses with dual compensation , 1983 .

[17]  V. Buzek,et al.  Erratum: Dynamics of open quantum systems initially entangled with environment: Beyond the Kraus representation [Phys. Rev. A 64, 062106 (2001)] , 2003 .

[18]  Timothy F. Havel.  Robust procedures for converting among Lindblad, Kraus and matrix representations of quantum dynamical semigroups , 2002, quant-ph/0201127.

[19]  J. A. Jones,et al.  Tackling systematic errors in quantum logic gates with composite rotations , 2003 .

[20]  William M. Steen,et al.  Atom-Photon Interactions Basic Processes and Applications , 1992 .

[21]  G. Bodenhausen,et al.  Principles of nuclear magnetic resonance in one and two dimensions , 1987 .

[22]  U. Weiss.  Quantum Dissipative Systems , 1993 .

[23]  Pechukas,et al.  Reduced dynamics need not be completely positive. , 1994, Physical review letters.

[24]  R. Tycko,et al.  Broadband Population Inversion , 1983 .

[25]  L. J. Landau,et al.  On Birkhoff's theorem for doubly stochastic completely positive maps of matrix algebras , 1993 .

[26]  Hoult,et al.  Selective spin inversion in nuclear magnetic resonance and coherent optics through an exact solution of the Bloch-Riccati equation. , 1985, Physical review. A, General physics.

[27]  Debbie W. Leung,et al.  Realization of quantum process tomography in NMR , 2000, quant-ph/0012032.

[28]  Vladimir Buzek,et al.  Dynamics of open quantum systems initially entangled with environment: Beyond the Kraus representation , 2001, quant-ph/0108136.