Quantum process reconstruction based on mutually unbiased basis

We study a quantum process reconstruction based on the use of mutually unbiased projectors (MUB-projectors) as input states for a D-dimensional quantum system, with D being a power of a prime number. This approach connects the results of quantum-state tomography using mutually unbiased bases (MUB) with the coefficients of a quantum process, expanded in terms of MUBprojectors. We also study the performance of the reconstruction scheme against random errors when measuring probabilities at the MUB-projectors.

[1]  G M D'Ariano,et al.  Quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation. , 2001, Physical review letters.

[2]  A. G. White,et al.  Ancilla-assisted quantum process tomography. , 2003, Physical review letters.

[3]  H. D. Watson.  At 14 , 1979 .

[4]  F. Pastawski,et al.  Selective and efficient estimation of parameters for quantum process tomography. , 2008, Physical review letters.

[5]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[6]  E. S. Gómez,et al.  Experimental quantum tomography of photonic qudits via mutually unbiased basis. , 2010, Optics express.

[7]  Adi Ben-Israel,et al.  Generalized inverses: theory and applications , 1974 .

[8]  L. Sánchez-Soto,et al.  Multicomplementary operators via finite Fourier transform , 2004, quant-ph/0410155.

[9]  T. Ralph,et al.  Quantum process tomography of a controlled-NOT gate. , 2004, Physical review letters.

[10]  Daniel A. Lidar,et al.  Quantum Process Tomography: Resource Analysis of Different Strategies , 2007, quant-ph/0702131.

[11]  A. N. Korotkov,et al.  Two-qubit decoherence mechanisms revealed via quantum process tomography , 2009, 0903.0671.

[12]  P. M. Mathews,et al.  STOCHASTIC DYNAMICS OF QUANTUM-MECHANICAL SYSTEMS , 1961 .

[13]  Metod Saniga,et al.  Mutually unbiased bases and finite projective planes , 2004 .

[14]  L. L. Sanchez-Soto,et al.  Structure of the sets of mutually unbiased bases for N qubits (8 pages) , 2005 .

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

[16]  J. Wrachtrup,et al.  Quantum process tomography and Linblad estimation of a solid-state qubit , 2006, quant-ph/0601167.

[17]  W. Wootters,et al.  Optimal state-determination by mutually unbiased measurements , 1989 .

[18]  Giacomo Mauro D'Ariano,et al.  Imprinting complete information about a quantum channel on its output state. , 2003, Physical review letters.

[19]  Karol Życzkowski,et al.  Dynamics beyond completely positive maps : some properties and applications , 2008 .

[20]  Aephraim M. Steinberg,et al.  Quantum process tomography on vibrational states of atoms in an optical lattice , 2003, quant-ph/0312210.

[21]  S. Deleglise,et al.  Process tomography of field damping and measurement of Fock state lifetimes by quantum nondemolition photon counting in a cavity. , 2008, Physical review letters.

[22]  D. Petz,et al.  Contractivity of positive and trace-preserving maps under Lp norms , 2006, math-ph/0601063.

[23]  E. Knill,et al.  Complete quantum teleportation using nuclear magnetic resonance , 1998, Nature.

[24]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[25]  W. Wootters.  Quantum Measurements and Finite Geometry , 2004, quant-ph/0406032.

[26]  P. Oscar Boykin,et al.  A New Proof for the Existence of Mutually Unbiased Bases , 2002, Algorithmica.

[27]  I. D. Ivonovic.  Geometrical description of quantal state determination , 1981 .

[28]  Fernando Pastawski,et al.  Selective and efficient quantum process tomography , 2009, 0906.3002.

[29]  C. Saavedra,et al.  Optimal quantum-state reconstruction for cold trapped ions , 2008 .

[30]  E. Sudarshan,et al.  How state preparation can affect a quantum experiment: Quantum process tomography for open systems , 2007, 0706.0394.

[31]  J. L. Romero,et al.  Geometrical approach to the discrete Wigner function in prime power dimensions , 2006 .

[32]  Aephraim M. Steinberg,et al.  Improving quantum state estimation with mutually unbiased bases. , 2008, Physical review letters.

[33]  Isaac L. Chuang,et al.  Prescription for experimental determination of the dynamics of a quantum black box , 1997 .

[34]  N. Langford,et al.  Distance measures to compare real and ideal quantum processes (14 pages) , 2004, quant-ph/0408063.

[35]  Andrew G. White,et al.  Measurement of qubits , 2001, quant-ph/0103121.

[36]  C. Ross.  Found , 1869, The Dental register.

[37]  T. Monz,et al.  Process tomography of ion trap quantum gates. , 2006, Physical review letters.

[38]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.