Jesús Urías

Instituto de Física
Zona Universitaria
San Luis Potosi, SLP, México

Oficina: C-07 IF, 3er Piso
Tel: [52](444) 826 - 2362 al 65, ext 147
FAX: [52](444) 813 - 3874

J. Urias
Mezquitic, SLP

Interests: Quantum mechanics and dynamical systems.

Partial list of publications
  • Fractal dimensions for Poincaré recurrences. Elsevier (2006)
    ISBN–13: 978-0-444-52189-7, ISBN–10: 0-444-52189-5
    With V. Afraimovich and E. Ugalde.
  • Translated to russian by Prof. Mikhail Mallkin and published by R&C Dynamics (Moscow, 2011).
    ISBN: 978-5-93972-903-1
  1. Amplitudes for multiphoton quantum processes in linear optics. J. Phys. A: Math. & Theor. 44 (2011) 305303 (13pp).
    Summary. An extended version of Wick's theorem for the expectation value of products of linear operators, in general, is proved. The theorem is applied to extract the combinatorics of interfering amplitudes in multi-photon quantum processes in linear optics. Computation of probability amplitudes simplifies to a concise procedural rule with a natural physical meaning. The generation of high-photon-number entangled states by interferometrically mixing coherent light with spontaneously down-converted light is treated in full detail.
  2. Householder factorizations of unitary matrices. J. Math. Phys. 51, 072204 (2010) [9pp].
    Selected for the August 2010 issue of Virtual Journal of Quantum Information.
    Summary. The strong superposition principle of quantum mechanics tells us that every orthonormal basis represents an exhaustive test. However, the principle does not tell us how to actually perform the test. A bridge from U(N) to the hardware is to represent a quantum operation as the product of simpler unitary factors. Here, I prove that A is in U(N) if, and only if, A is the product of Housholder reflections. The proof is constructive and provides a method to construct all representations of U(N) as the product of Householder factors. Earlier constructions are shown to be extreme cases of the unifying scheme that I present here.
  3. Optimal multi-setting witness operators for two qudits. Physics Letters A, 373 (2009) 720-726
    Summary. A new class of observables to detect quantum entanglement in bipartite systems is introduced. They are a relaxed form of Bell operators and I call them pseudo Bell (pB) operators. Every pB operator may be transformed into (at least) an optimal witness operator. The transformation is indicated. I provide a class of pB operators for pairs of qudits (or qunits), based on multiple two-dimensional local measuring settings. The spectral resolution of all these multi-setting pB operators is provided. Each of them admits two optimal (multi-setting) witness operators. Then, I explain how pB operators provide estimates of the sets of separable and of entangled states. A class of Werner-like entangled states of pairs of qudits is identified.
  4. Filtering by non-linear systems. Chaos, 18 (2008) 043118.
    With E. Campos Cantón and J.S. González.
  5. Closing the detection loophole in the Bell test for local models based upon three hidden variables. Phys. Lett. A 372 (2008) 600 - 603.
    Summary. In the Bell test the spin projections of two spatially separated spin-1/2 particles, that have been prepared in the singlet state, are measured. Spin correlations in local hidden variable models with two outcomes (“spin-up” or “spin-down”) obey an upper bound that is exceeded experimentally. However, local hidden variable models with three outcomes are consistent with the experimental spin correlations. Such models are justified by the fact that experiments have very low detection efficiencies and the extra third outcome is interpreted as a sample being missed by the detectors. The situation is known as the detection loophole in the Bell test. In this article I prove that locality and fair sampling are contradictory assumptions in hidden variable models of the Bell test that are based upon a 3-dimensional sample space. This result makes the class of 3-dimensional hidden variable models incompatible with quantum mechanics, independently of detection efficiencies.
  6. Spectral decomposition of Bell operators for multiquibit systems. J. Math. Physics 48 (2007) 072111.
    Selected for the August 2007 issue of Virtual Journal of Quantum Information.
    Summary. The (pure) state space of multiparty quantum systems have a very rich structure with respect to entanglement and the full class of entangled states that can be characterized by the violation of Bell inequalities is not known. For the special case of n-qubits the complete set of independent full correlation inequalities is known. The corresponding class of Bell operators is complete. In this article I provide their spectral decomposition and discuss its implications in the characterization of the entanglement of pure n-qubit states.
  7. Poincaré planes in non-linear electronics. International Journal of Bifurcation and Chaos 17 (2007) 199–208.
    With E. Campos Cantón and J.S. González.

  8. Finite random approximations of chaotic maps. Chapter of the book L. Larson, J.–M. Liu and L.S. Tsimring (Editors), Digital Communications Using Chaos and Nonlinear Dynamics. Springer-Verlag (2006).
    ISBN: 0-387-29787-1
    With E. Campos and N. Rulkov.

  9. Master-slave synchronization of affine cellular automaton pairs. Discrete and Continuous Dynamical Systems, 13 (2005) 491-502.
    With G. Salazar and E. Ugalde.

  10. Filters display inverse limit spaces. Chaos 14 (2004) 963–968.

  11. Multimodal synchronization of chaos. Chaos 14 (2004) 48-54.
    With E. Campos and N.F. Rulkov.

  12. Some characteristics of complex behavior of orbits in dynamical systems. Nonlinear Science and Numerical Simulation 8, 171–181 (2003).
    With V. Afraimovich.

  13. Smooth-Hölder transition in chaos synchronization. Phys. Letters A 308, 37–40 (2003).
    With J.S. Murguía.

  14. A class of cellular automata modeling winnerless competition. Chaos 12, 279–288 (2002)
    With V. Afraimovich and F.C. Ordaz.

  15. Dimension-like characteristics of invariant sets in dynamical systems. Chapter I of book, A. Maass et al. (eds.) Dynamics and Randomness, pp1–30, Kluwer (2002). ISBN: 1–4020–0591–1
    With V. Afraimovich.

  16. Spectrum of dimensions for Poincaré recurrences of Markov maps. Discrete and Continuous Dynamical Systems 8, 835–849 (2002)
    With B. Fernandez and E. Ugalde.

  17. On the wavelet formalism for multifractal analysis. Chaos, 11, 1054 (2001).
    With J.S. Murguía.

  18. An asymptotically perfect pseudorandom generator, Discrete and Continuous Dynamical Systems 7, 115–126 (2001).
    With Marcela Mejía.

  19. Poincaré recurrences for rythmical dynamics, Far East J. Dynamical Systems 2, 53–67 (2000).
    With V. Afraimovich and E. Ugalde.

  20. Spectra of dimensions for Poincaré recurrences, Discrete and Continuous Dynamical Systems 6, 901–914 (2000).
    With V. Afraimovich, J. Schmeling and E. Ugalde.

  21. Symbolic dynamics for sticky sets in Hamiltonian systems, Nonlinearity 13, 617–637 (2000).
    With Valentin Afraimovich and Alejandro Maass.

Student supervision
Ph.D. M.Sc. B.Sc.
Nehemias Leija Martinez (2010) Guillermo Rodriguez Garcia (2009)
J. Salvador González Salas (2006) Elba I. Gordillo Martínez (2005) J. Abel Aguilar Torres (2004)
Francisco Cruz Ordaz (2004) F. Alfonso Alba Cadena (2001) Leticia A. Ramírez Hdez. (2001)
Eric Campos Cantón (2003) J. Carmelo Flores Gutiérrez (2001) Fco. G. Pérez Rodríguez (1997)
J. Salomé Murguía Ibarra (2003) J. Salomé Murguía Ibarra (1999) J. G. Jiménez Guerrero (1997)
Marcela Mejía Carlos (2001) Eric Campos Cantón (1999) D. C. Hernández Guevara (1997)
Agustín Enciso Muñoz (1996) J. Salvador González Salas (1998) Félix Rosendo Francisco (1997)
Pedro Villaseñor González (1986) F. Cruz Ordaz Salazar (1998) Gabriel Velarde Torres (1996)
J. Martin Luna Rivera (1998) Genaro Durán Rodríguez (1994)
Gabriel Velarde Torres (1997) María A. Araiza Esquivel (1994)
Marcela Mejía Carlos (1997) Rosa M. López Gutiérrez (1994)
Gelasio Salazar Anaya (1993) J. María Ruiz Palomo (1994)
Edgardo Ugalde Saldaña (1992) Raúl Reyes Guerra (1994)
Ramiro Hernández Banda (1992) Marcela Mejía Carlos (1992)
Adolfo Vidales Roque (1990) Manuel N. López López (1990)
J. Refugio Martínez (1990) Victor J. Gallardo Palomo (1987)
Facundo Ruiz (1988) Jaime L. Castillo Sánchez (1982)
Pedro Alvarado Leyva (1987) M. Cecilia Peña de la Maza (1982)
Gerardo Muñiz Rivera (1986) S.A. Palomares Sánchez (1982)
J. Carlos Ruiz Suarez (1983)
J.M. Montejano Carrizales (1983)