Programmable quantum-state discriminator by nuclear magnetic resonance (8 pages)

A programmable quantum-state discriminator is implemented by using nuclear magnetic resonance. We use a two-qubit spin-1/2 system, one for the data qubit and one for the ancilla (program) qubit. This device does the unambiguous (error-free) discrimination of a pair of states of the data qubit that are symmetrically located about a fixed state. The device is used to discriminate both linearly polarized states and elliptically polarized states. The maximum probability of successful discrimination is achieved by suitably preparing the ancilla qubit. It is also shown that the probability of discrimination depends on the angle of the unitary operator of the protocol and ellipticity of the data qubit state.

[1]  Anthony Chefles.  Unambiguous discrimination between linearly dependent states with multiple copies , 2001, quant-ph/0105016.

[2]  C. Helstrom.  Quantum detection and estimation theory , 1969 .

[3]  David Collins,et al.  Scaling issues in ensemble implementations of the Deutsch-Jozsa algorithm , 2003 .

[4]  Lov K. Grover.  Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[5]  N. Gershenfeld,et al.  Experimental Implementation of Fast Quantum Searching , 1998 .

[6]  Shengyu Zhang,et al.  Upper bound for the success probability of unambiguous discrimination among quantum states , 2001 .

[7]  S Lloyd,et al.  A Potentially Realizable Quantum Computer , 1993, Science.

[8]  Timothy F. Havel,et al.  Ensemble quantum computing by NMR spectroscopy , 1997, Proc. Natl. Acad. Sci. USA.

[9]  Observation of geometric phases for mixed states using NMR interferometry. , 2003, Physical review letters.

[10]  Ranabir Das,et al.  Use of quadrupolar nuclei for quantum-information processing by nuclear magnetic resonance: Implementation of a quantum algorithm , 2003 .

[11]  M. Dušek,et al.  Quantum-controlled measurement device for quantum-state discrimination , 2002 .

[12]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[13]  E. Knill,et al.  EFFECTIVE PURE STATES FOR BULK QUANTUM COMPUTATION , 1997, quant-ph/9706053.

[14]  S. Barnett.  Minimum-error discrimination between multiply symmetric states , 2001 .

[15]  T. S. Mahesh,et al.  Toward quantum information processing by nuclear magnetic resonance: pseudopure states and logical operations using selective pulses on an oriented spin 3/2 nucleus , 2001 .

[16]  Miloslav Dusek,et al.  Unambiguous state discrimination in quantum cryptography with weak coherent states , 2000 .

[17]  Timothy F. Havel,et al.  Nuclear magnetic resonance spectroscopy: an experimentally accessible paradigm for quantum computing , 1997, quant-ph/9709001.

[18]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[19]  Experimental demonstration of a programmable quantum computer by NMR. , 2004, Journal of magnetic resonance.

[20]  Anthony Chefles.  Quantum state discrimination , 2000 .

[21]  R. Feynman.  Simulating physics with computers , 1999 .

[22]  M. Dušek,et al.  Probabilistic quantum multimeters , 2003, quant-ph/0308111.

[23]  G. M. D'Ariano,et al.  Quantum universal detectors , 2004 .

[24]  Gisin,et al.  Unambiguous quantum measurement of nonorthogonal states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[25]  S. Barnett,et al.  Optimum unambiguous discrimination between linearly independent symmetric states , 1998, quant-ph/9807023.

[26]  Arvind,et al.  Implementing quantum-logic operations, pseudopure states, and the Deutsch-Jozsa algorithm using noncommuting selective pulses in NMR , 1999, quant-ph/9906027.

[27]  M. Dušek,et al.  Universal measurement apparatus controlled by quantum software. , 2002, Physical review letters.

[28]  A. Peres.  How to differentiate between non-orthogonal states , 1988 .

[29]  I. Chuang,et al.  Programmable Quantum Gate Arrays , 1997, quant-ph/9703032.

[30]  D. Leung,et al.  Experimental realization of a quantum algorithm , 1998, Nature.

[31]  J. A. Jones,et al.  Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer , 1998, quant-ph/9801027.

[32]  M. Dušek,et al.  Experimental realization of a programmable quantum-state discriminator and a phase-covariant quantum multimeter , 2004, quant-ph/0401166.

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

[34]  I. D. Ivanović.  How to differentiate between non-orthogonal states , 1987 .

[35]  Charles H. Bennett,et al.  The thermodynamics of computation—a review , 1982 .

[36]  Implementation of conditional phase-shift gate for quantum information processing by NMR, using transition-selective pulses. , 2002, Journal of magnetic resonance.

[37]  J. Paz,et al.  Quantum gate arrays can be programmed to evaluate the expectation value of any operator , 2003, quant-ph/0306143.

[38]  Jonathan A. Jones,et al.  Implementation of a quantum search algorithm on a quantum computer , 1998, Nature.

[39]  J. Cirac,et al.  Storing quantum dynamics in quantum states: a stochastic programmable gate. , 2001, Physical review letters.

[40]  Jiangfeng Du,et al.  Experimental implementation of the quantum random-walk algorithm , 2002, quant-ph/0203120.

[41]  T. S. Mahesh,et al.  Ensemble quantum-information processing by NMR: Spatially averaged logical labeling technique for creating pseudopure states , 2001 .

[42]  N. Gershenfeld,et al.  Bulk Spin-Resonance Quantum Computation , 1997, Science.

[43]  Jozef Gruska,et al.  Quantum Computing , 2008, Wiley Encyclopedia of Computer Science and Engineering.

[44]  D. Leung,et al.  Bulk quantum computation with nuclear magnetic resonance: theory and experiment , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[45]  T. S. Mahesh,et al.  Implementing logic gates and the Deutsch-Jozsa quantum algorithm by two-dimensional NMR using spin- and transition-selective pulses. , 2001, Journal of magnetic resonance.

[46]  D. Bouwmeester,et al.  The Physics of Quantum Information , 2000 .

[47]  V. Buzek,et al.  Probabilistic implementation of universal quantum processors , 2001, quant-ph/0106088.

[48]  David C. Collins.  Modified Grover's algorithm for an expectation-value quantum computer , 2001, quant-ph/0111108.

[49]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[50]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .