Artículos de revistas
A Clifford Algebra Of Signature (n,3n) And The Density Operators Of Quantum Information Theory
Registro en:
Advances In Applied Clifford Algebras. , v. 23, n. 1, p. 143 - 152, 2013.
1887009
10.1007/s00006-012-0341-9
2-s2.0-84874214221
Autor
Melo N.
Lavor C.
Institución
Resumen
This paper presents an algebraic language for fundamental elements of quantum information theory (the density operators), based in the properties of a Clifford algebra of signature (n,3n). We prove that the new description of these elements preserves the same mathematical properties obtained with the classical description. We also extend some results presented in the literature that relate Clifford algebra and quantum information. © 2012 Springer Basel AG. 23 1 143 152 Alves, R., Lavor, C., Clifford algebra applied to grover's algorithm (2010) Advances in Applied Clifford Algebras, 20 (3-4), pp. 477-488 Benenti, G., Casati, G., Strini, G., (2004) Principles of Quantum Computation and Information, , Singapore: World Scientific Chevalley, C., (1996) Collected Works / Claude Chevalley V.2. The Algebraic Theory of Spinors and Clifford Algebras, , Berlin: Springer Corrochano, E.B., Sobczyk, G., (2001) Geometric Algebra with Applications in Science and Engeneering, , Boston: Birkuser Gull, S., Lasenby, A., Doran, C., Imaginary numbers are not real - the geometric algebra of spacetime (1993) Foundations of Physics, 23, pp. 1175-1201 Havel, T.F., Doran, C., Geometric algebra in quantum information processing (2002) AMS Comtemporary Mathematics Series, 305, pp. 81-100 Hestenes, D., (1999) New Foundations for Classical Mechanics, , Boston: Kluwer Hestenes, D., Spacetime physics with geometric algebra (2003) American Journal of Physics, 71, pp. 691-714 Lang, S., (1997) Algebra, , 3rd edn., Massachusetts: Addison-Wesley Publishing Company Lounesto, P., (1997) Clifford Algebras and Spinors, , Cambridge: Cambridge University Press Melo, N., A Clifford Algebra of Signature (n, 3n) and the Density Operators of Quantum Information Theory (in Portuguese), , PhD thesis, UNICAMP, 2011 Nielsen, M.A., Chuang, I.L., (2000) Quantum Computation and Quantum Information, , Cambridge: Cambridge University Press Preskill, J., Quantum information and computation, , Lecture Notes for Physics 229 - California Institute of Technology, 1998 Somaroo, S., Cory, D.G., Havel, T.F., Expressing the operations of quantum computing in multiparticle geometric algebra (1998) Physics Letters A, 240, pp. 1-7 Somaroo, S., Lasenby, A., Doran, C., Geometric algebra and the causal approach to multiparticle quantum mechanics (1999) Journal of Mathematical Physics, 40, pp. 3327-3340