Prescription for experimental determination of the dynamics of a quantum black box

Abstract We give an explicit way to experimentally determine the evolution operators which completely describe the dynamics of a quantum-mechanical black box: an arbitrary open quantum system. We show necessary and sufficient conditions for this to be possible and illustrate the general theory by considering specifically one-and two-quantum-bit systems. These procedures may be useful in the comparative evaluation of experimental quantum measurement, communication and computation systems.

[1]  King,et al.  Experimental Determination of the Motional Quantum State of a Trapped Atom. , 1996, Physical review letters.

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

[3]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[4]  King,et al.  Demonstration of a fundamental quantum logic gate. , 1995, Physical review letters.

[5]  P. Knight,et al.  Quantum error correction in the presence of spontaneous emission. , 1996, quant-ph/9603022.

[6]  Schumacher,et al.  Quantum data processing and error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[7]  Hood,et al.  Measurement of conditional phase shifts for quantum logic. , 1995, Physical review letters.

[8]  C. Macchiavello,et al.  Detection of the density matrix through optical homodyne tomography without filtered back projection. , 1994, Physical Review A. Atomic, Molecular, and Optical Physics.

[9]  I. Chuang,et al.  Creation of a persistent quantum bit using error correction , 1997 .

[10]  Leonhardt,et al.  Discrete Wigner function and quantum-state tomography. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[11]  Unruh.  Maintaining coherence in quantum computers. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[12]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[13]  Sudarshan..  Quantum dynamics, metastable states, and contractive semigroups. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[14]  E. Knill,et al.  Theory of quantum error-correcting codes , 1997 .

[15]  S. Lloyd.  Capacity of the noisy quantum channel , 1996, quant-ph/9604015.

[16]  Schumacher,et al.  Sending entanglement through noisy quantum channels. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[17]  Jones,et al.  Fundamental limits upon the measurement of state vectors. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[18]  Beck,et al.  Complex wave-field reconstruction using phase-space tomography. , 1994, Physical review letters.

[19]  W. Louisell.  Quantum Statistical Properties of Radiation , 1973 .

[20]  Vladimir B. Braginsky,et al.  Quantum Measurement , 1992 .

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

[22]  R. Hughes,et al.  Quantum Cryptography , 1995, quant-ph/9504002.

[23]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[24]  K. Kraus,et al.  States, effects, and operations : fundamental notions of quantum theory : lectures in mathematical physics at the University of Texas at Austin , 1983 .

[25]  Raymond Laflamme,et al.  Quantum Computers, Factoring, and Decoherence , 1995, Science.