Marcelo A. Marchiolli

Publications (13)0 Total impact

• Article: Spin squeezing and entanglement via finite-dimensional discrete phase-space description

  Marcelo A. Marchiolli, Diógenes Galetti, Tiago Debarba
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  ABSTRACT: We show how mapping techniques inherent to $N^{2}$-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the modified Lipkin-Meshkov-Glick (LMG) model in order to obtain the time evolution of certain special parameters related to the Robertson-Schr\"{o}dinger (RS) uncertainty principle and some particular proposals of entanglement measure based on collective angular-momentum generators. Our results reinforce the connection between both the squeezing and entanglement effects, as well as allow to investigate the basic role of spin correlations through the discrete representatives of quasiprobability distribution functions. Entropy functionals are also discussed in this context. The main sequence correlations -> entanglement -> squeezing of quantum effects embraces a new set of insights and interpretations in this framework, which represents an effective gain for future researches in different spin systems.
  11/2012;
• Source

  Available from: ArXiv

  Article: An alternative fidelity measure for quantum states

  Paulo E. M. F. Mendonca, R. d. J. Napolitano, Marcelo A. Marchiolli, C. J. Foster, Yeong-Cherng Liang
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  ABSTRACT: In this paper, we propose an alternative definition for the fidelity measure between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. The new fidelity measure is a simple function of the linear entropy and the Hilbert-Schmidt inner product between the given states and is thus, in comparison, not as computationally demanding. It also features several remarkable properties such as being jointly concave and satisfying all of "Jozsa's axioms". The tradeoff, however, is that it is super-multiplicative and does not behave monotonically under quantum operations. In addition, new metrics for the space of density matrices are identified and the joint concavity of Uhlmann-Jozsa fidelity for qubit states is established.
  07/2008;
• Source

  Available from: Diógenes Galetti

  Article: Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model

  Marcelo A. Marchiolli, Evandro C. Silva, Diogenes Galetti
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  ABSTRACT: We show how quasiprobability distribution functions defined over $N^{2}$-dimensional discrete phase spaces can be used to treat physical systems described by a finite space of states which exhibit spin tunneling effects. This particular approach is then applied to the Lipkin-Meshkov-Glick model in order to obtain the time evolution of the discrete Husimi function, and as a by-product the energy gap for a symmetric combination of ground and first excited states. Moreover, we also show how an angle-based potential approach can be efficiently employed to explain qualitatively certain features of the energy gap in terms of a spin tunneling. Entropy functionals are also discussed in this context. Such results reinforce not only the formalism per se but also the possibility of some future potential applications in other branches of physics. Comment: 7 pages, 8 figures, title modified, new setences and references included, to appear in Physical Review A
  05/2008;
• Source

  Available from: Diógenes Galetti

  Article: Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

  Marcelo A. Marchiolli, Diogenes Galetti
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  ABSTRACT: We introduce a new class of unitary transformations based on the su(1,1) Lie algebra that generalizes, for certain particular representations of its generators, well-known squeezing transformations in quantum optics. To illustrate our results, we focus on the two-mode bosonic representation and show how the parametric amplifier model can be modified in order to generate such a generalized squeezing operator. Furthermore, we obtain a general expression for the bipartite Wigner function which allows us to identify two distinct sources of entanglement, here labelled by dynamical and kinematical entanglement. We also establish a quantitative estimate of entanglement for bipartite systems through some basic definitions of entropy functionals in continuous phase-space representations. Comment: 16 pages
  09/2007;
• Source

  Available from: Diógenes Galetti

  Article: Discrete squeezed states for finite-dimensional spaces

  Marcelo A. Marchiolli, Maurizio Ruzzi, Diogenes Galetti
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  ABSTRACT: We show how discrete squeezed states in an $N^{2}$-dimensional phase space can be properly constructed out of the finite-dimensional context. Such discrete extensions are then applied to the framework of quantum tomography and quantum information theory with the aim of establishing an initial study on the interference effects between discrete variables in a finite phase-space. Moreover, the interpretation of the squeezing effects is seen to be direct in the present approach, and has some potential applications in different branches of physics.
  03/2007;
• Source

  Available from: arxiv.org

  Article: Using continuous measurement to protect a universal set of quantum gates within a perturbed decoherence-free subspace

  Paulo E. M. F. Mendonca, Marcelo A. Marchiolli, Reginaldo D. J. Napolitano
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  ABSTRACT: We consider a universal set of quantum gates encoded within a perturbed decoherence-free subspace of four physical qubits. Using second-order perturbation theory and a measuring device modeled by an infinite set of harmonic oscillators, simply coupled to the system, we show that continuous observation of the coupling agent induces inhibition of the decoherence due to spurious perturbations. We thus advance the idea of protecting or even creating a decoherence-free subspace for processing quantum information.
  02/2005;
• Source

  Available from: Victor V. Dodonov

  Article: Marginal and correlation distribution functions in the squeezed-states representation

  Marcelo A. Marchiolli, Salomon S. Mizrahi, Victor V. Dodonov
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  ABSTRACT: Here we consider the Husimi function P for the squeezed states and calculate the marginal and correlation distribution functions when P is projected onto the photon number states. According to the value of the squeezing parameter one verifies the occurence of oscillations and beats as already appointed in the literature. We verify that these phenomena are entirely contained in the correlation function. In particular, we show that since Husimi and its marginal distribution functions satisfy partial differential equations where the squeeze parameter plays the role of time, the solutions (the squeezed functions obtained from initial unsqueezed functions) can be expressed by means of kernels responsible for the propagation of squeezing. From the calculational point of view, this method presents advantages for calculating the marginal distribution functions (compared to a direct integration over one of the two phase-space variables of P) since one can use the symmetry properties of the differential equations. Comment: 11 pages, 12 EPS figures, figures 1(a)-(d) can be obtained with the first author, accepted for publication in Journal Physics A
  10/1999;
• Article: Dissipative mass-accreting quantum oscillator

  Marcelo A Marchiolli, Salomon S Mizrahi
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  ABSTRACT: We begin by revisiting the so-called Caldirola - Kanai Hamiltonian and discuss its inherent ambiguity: does it represent a dissipative harmonic oscillator (HO) subject to a friction force, or does it describe an HO with a time-dependent mass (TDM)? Although classically both descriptions do coexist, in the quantum domain the solution of the Schrödinger equation (or Heisenberg equations of motion) with a TDM does not present inconsistencies, however, the dissipative Hamiltonian shows violation of the Heisenberg uncertainty principle. This violation is avoided by introducing a stochastic force in the equations of motion, which will take care of the fluctuations due to the environment. Once the distinction between the dissipative and amplifying Hamiltonian is made clear, we consider the problem of the quantum TDM HO subject to dissipation, showing that both phenomena may be merged and described by a single Hamiltonian, the amplifying - dissipative Hamiltonian. We obtain the solutions of the Heisenberg equations of motion for the canonical momentum and position; next, we specialize on the weak damping limit and analyse the effects of the amplifying - dissipative process on the mean values of the physical variables.
  Journal of Physics A General Physics 12/1998; 30(8):2619.
• Article: Nonclassical statistical properties of finite-coherent states in the framework of the Jaynes–Cummings model

  Marcelo A. Marchiolli
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  ABSTRACT: Adopting the framework of the nonresonant Jaynes–Cummings model, we investigate the nonclassical statistical properties of coherent states defined in a finite-dimensional Hilbert space, considering the single-mode cavity field prepared in a finite and discrete harmonic oscillator-like coherent state with a small average number of photons. Explicit expressions for the time evolution of various functions characterizing the quantum state, such as the Mandel's Q parameter, the photon-number distribution and its respective entropy, the discrete Wigner function, and the number-phase uncertainty relation, are investigated in detail. We also show that the atomic inversion possesses regular structures with collapses and revivals in the Rabi oscillations since the detuning between atom and field is large as compared to the coupling constant, i.e., (κ/2g)2⪢1. The numerical and analytical results obtained in this work turn evident the quantum interference effects between the components of the finite-coherent states. Furthermore, we present a discussion about unitary depolarizers in finite-dimensional Hilbert space and their connection to quantum information theory.
  Physica A: Statistical Mechanics and its Applications.
• Source

  Available from: arxiv.org

  Article: Alternative fidelity measure between quantum states

  Paulo E. M. F. Mendonca, Reginaldo D. J. Napolitano, Marcelo A. Marchiolli, Christopher J. Foster, Yeong-Cherng Liang
  [show abstract] [hide abstract]
  ABSTRACT: We propose an alternative fidelity measure (namely, a measure of the degree of similarity) between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple function of the linear entropy and the Hilbert-Schmidt inner product between the given states and is thus, in comparison, not as computationally demanding. It also features several remarkable properties such as being jointly concave and satisfying all of Jozsa's axioms. The trade-off, however, is that it is supermultiplicative and does not behave monotonically under quantum operations. In addition, metrics for the space of density matrices are identified and the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is established.
• Article: Quantum-interference effects on the superposition of N displaced number states

  Marcelo A. Marchiolli, Luciano F. da Silva, Paulo S. Melo, Célia M.A. Dantas
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  ABSTRACT: We describe properties of a quantum system prepared in a superposition of N displaced number states, with emphasis on the interference effects among the state components. Explicit expressions for wavefunctions in the coordinate and Fock-state representations, photon number distribution, variances and quantum correlation coefficient of the quadrature operators, and quasiprobability distributions are calculated in detail. Nonclassical effects due to such interference and the analogy with diffraction patterns arising in an N slit Young-type experiment are the main results in the present work. In particular, we show that interference and correlation effects in phase space are connected with the nondiagonal term of the quasiprobability distributions, providing further insight into the phenomenon.
  Physica A: Statistical Mechanics and its Applications.
• Source

  Available from: Victor V. Dodonov

  Article: Signal-to-noise ratio of preamplified homodyne detection in quantum tomography

  Marcelo A. Marchiolli, Salomon S. Mizrahi, Victor V. Dodonov
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  ABSTRACT: The operational theory of homodyne detection by nonideal detectors, used in quantum tomography, was recently modified in order to incorporate the preamplification (before homodyne detection) of the input signal, thus enabling one to beat the handicap of the lower than 0.5 detector efficiency. In the present work we set expressions for the Mandel Q parameter and the signal-to-noise ratio in terms of the operational (measured) moments of the preamplified homodyne detection formalism. These quantities furnish important information on the statistical properties of the input signal field and the photocounts at the output. We illustrate the theory by considering several kinds of fields (for the input signal) and determine the effects of the preamplification on the output signal-to-noise ratios. Here we essentially verify that (i) the preamplification shifts the statistics towards the super-Poissonian limit, without jeopardizing the capacity of reconstructing a sub-Poissionan input signal, and (ii) the preamplification is more effective, i.e., the rate of increase of the signal-to-noise ratio of the output photocount is larger for low-efficiency detectors than for ideal ones.
  Phys. Rev. A. 57(5).
• Source

  Available from: Victor V. Dodonov

  Article: Operational approach for reconstruction of quantum distributions in a preamplified homodyne-detection scheme

  Marcelo A. Marchiolli, Salomon S. Mizrahi, Victor V. Dodonov
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  ABSTRACT: We use the operational theory of homodyne detection, introduced by Banaszek and Wódkiewicz [Phys. Rev. A 55, 3117 (1997)], to express a generic quantum phase space quasiprobability distribution (in the sense of Cahill and Glauber) of an electromagnetic field in terms of the photocount moments. We adapt the method of degenerate parametric (pre)amplification of a signal, within the operational theory, in order to overcome the drawback of nonunit efficiency of the detector. Simulations show that as the gain parameter of the amplification is increased, the quasiprobability distribution goes closer to the original one, even for an efficiency lower than 0.5. We also express the mean value of an arbitrary observable in terms of the same photocount moments.
  Phys. Rev. A. 56(5).