Quantum information processing by NMR: preparation of pseudopure states and implementation of unitary operations in a single-qutrit system

Theoretical Quantum Information Processing (QIP) has matured from the use of qubits to the use of qudits (systems having states >2). Whereas most of the experimental implementations have been performed using qubits, little experimental work has been carried out using qudits as yet. In this paper we demonstrate experimental realization of a qutrit system by nuclear magnetic resonance (NMR), utilizing deuterium (spin-1) nuclei partially oriented in liquid crystalline phase. Preparation of pseudopure states and implementation of unitary operations are demonstrated in this single-qutrit system, using transition selective pulses.

[1]  W. Munro,et al.  Bounds on entanglement in qudit subsystems , 2002, quant-ph/0203037.

[2]  J. A. Jones.  NMR quantum computation , 2000 .

[3]  M. Żukowski,et al.  Security of Quantum Key Distribution with entangled Qutrits. , 2002, quant-ph/0207057.

[4]  N. B. Freeman.  An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer , 1998, quant-ph/9808039.

[5]  Carlton M. Caves,et al.  Qutrit Entanglement , 1999 .

[6]  Matthias Christandl,et al.  Quantum cryptography based on qutrit Bell inequalities , 2003 .

[7]  J. C. Retamal,et al.  Qutrit quantum computer with trapped ions , 2003 .

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

[9]  M Fitzi,et al.  Quantum solution to the Byzantine agreement problem. , 2001, Physical review letters.

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

[11]  G. Long,et al.  General scheme for superdense coding between multiparties , 2001, quant-ph/0110112.

[12]  K. B. Whaley,et al.  Theory of decoherence-free fault-tolerant universal quantum computation , 2000, quant-ph/0004064.

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

[14]  K. V. Ramanathan,et al.  Quantum-information processing by nuclear magnetic resonance: Experimental implementation of half-adder and subtractor operations using an oriented spin-7/2 system , 2002 .

[15]  D. Kaszlikowski,et al.  Three-qutrit correlations violate local realism more strongly than those of three qubits , 2002 .

[16]  B. Fung,et al.  Nuclear magnetic resonance quantum logic gates using quadrupolar nuclei , 2000 .

[17]  I. Chuang,et al.  UvA-DARE ( Digital Academic Repository ) Simulating quantum operations with mixed environments , 1999 .

[18]  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.

[19]  Efficient quantum-state tomography for quantum-information processing using a two-dimensional Fourier-transform technique , 2002, quant-ph/0212116.

[20]  W. Munro,et al.  Qudit quantum-state tomography , 2002 .

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

[22]  B. M. Fung,et al.  NMR simulation of an eight-state quantum system , 2001 .

[23]  G. Bowen.  Classical information capacity of superdense coding , 2001 .

[24]  A. Saupe,et al.  Observation of a Biaxial Nematic Phase in Potassium Laurate-1-Decanol-Water Mixtures , 1980 .

[25]  D. Abbott,et al.  Quantum version of the Monty Hall problem , 2001, quant-ph/0109035.

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

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

[28]  Rafael Brüschweiler,et al.  One- and two-dimensional ensemble quantum computing in spin Liouville space , 1998 .

[29]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[30]  Hong-xiang Sun,et al.  Method of multifrequency excitation for creating pseudopure states for NMR quantum computing , 2001 .

[31]  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 .

[32]  K. B. Whaley,et al.  Exact gate sequences for universal quantum computation using the XY interaction alone , 2001, quant-ph/0112014.

[33]  Jason Twamley,et al.  Entanglement distribution between N distant users via a center , 2001 .