Get A course in mathematical physics. Classical dynamical PDF

By Walter E Thirring

ISBN-10: 0387814965

ISBN-13: 9780387814964

Mathematical Physics, Nat. Sciences, Physics, arithmetic

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Example text

Aravind [11] observed that there are natural similarities between quantum entanglements and topological entanglements. As a unitary braid has the power of detecting knots or links, it can often transform a separate quantum state into an entangled one. Kauffman and Lomonaco [12, 13] identified a nontrivial unitary braid representation with a universal quantum gate [14]. Recently, a series of papers have been published on the application of the braid group [10] (or the Yang–Baxter equation [15, 16]) to quantum information and computation, see [13, 17, 18] for unitary solutions of the Yang–Baxter equation as universal quantum gates; see [19, 20, 21] for quantum topology and quantum computation; see 1991 Mathematics Subject Classification.

K. Lo (Wiley-VCH, 2001), 155–173. P. DiVincenzo, Two-bit quantum gates are universal for quantum computation, Phys. Rev. A 51(1995), 1015–1022. [14] W. Hansel, J. Reichel, P. W. Hansch, Trapped-atom interferometer in magnetic microtrap, Phys. Rev. A 64(2001), 063607. [15] D. J. I. W. Gardiner, and P. Zoller, Entanglement of atoms via cold controlled collisions, Phys. Rev. Lett 82(1999), 1975 – 1978. A. L. , 2000. [17] J. Normand, A Lie Group: Rotations in Quantum Mechanics, North-Holland, New York, 1980.

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A course in mathematical physics. Classical dynamical systems by Walter E Thirring

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