931 research outputs found

    On a conjecture regarding Fisher information

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    Fisher's information measure plays a very important role in diverse areas of theoretical physics. The associated measures as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the protagonists of our present considerations. The product of them has been conjectured to exhibit a non trivial lower bound in [Phys. Rev. A (2000) 62 012107]. We show here that such is not the case. This is illustrated, in particular, for pure states that are solutions to the free-particle Schr\"odinger equation. In fact, we construct a family of counterexamples to the conjecture, corresponding to time-dependent solutions of the free-particle Schr\"odinger equation. We also give a new conjecture regarding any normalizable time-dependent solution of this equation.Comment: 4 pages; revised equations, results unchange

    Comment on "Quantum discord through the generalized entropy in bipartite quantum states"

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    In [X.-W. Hou, Z.-P. Huang, S. Chen, Eur. Phys. J. D 68, 1 (2014)], Hou et al. present, using Tsallis' entropy, possible generalizations of the quantum discord measure, finding original results. As for the mutual informations and discord, we show here that these two types of quantifiers can take negative values. In the two qubits instance we further determine in which regions they are non-negative. Additionally, we study alternative generalizations on the basis of R\'enyi entropies.Comment: 5 pages, 4 figure

    Repercusiones cu√°nticas de los estados cl√°sicamente correlacionados : Aspectos informacionales y computacionales

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    La Informaci√≥n Cu√°ntica, como disciplina que hereda virtudes y defectos de la Teor√≠a de la Informaci√≥n y de la Mec√°nica Cu√°ntica, ha brindado, durante los √ļltimos a√Īos, un avance considerable en el entendimiento y resoluci√≥n de ciertos problemas de Fundamentos de la Cu√°ntica. El formalismo, sin embargo, no est√° exento de interrogantes propios que son intensamente estudiados. Algunas de las contribuciones m√°s importantes se vinculan con las potencialidades de los sistemas mec√°nico-cu√°nticos como recursos computacionales m√°s poderosos que los implementables mediante sistemas que no evidencian efectos cu√°nticos. La clave, en esos casos, est√° en el tipo de correlaciones que pueden establecerse entre dos o m√°s partes de los sistemas. En este trabajo, presento varios resultados en los que estudio aspectos informacionales de los sistemas cu√°nticos, presentes incluso en los estados denominados cl√°sicamente correlacionados.Quantum Information, as a discipline that inherits the strengths and weaknesses of Information Theory and Quantum Mechanics, has provided, in recent years, considerable progress in understanding and solving certain problems on the Foundations of Quantum Mechanics. The formalism, however, has its own open questions that are intensely studied nowadays. Some of the most important contributions are realated to the potentiality of quantum-mechanical systems as more powerful computational resources than those implementable by means of systems that do not show quantal effects. The key, in those cases, is on the class of correlations that can be established between two or more parts of the systems. In this work, I present several results that explore informational aspects of quantum systems, which show up even in the so-called classically-correlated states.Facultad de Ciencias Exacta

    On a conjecture regarding Fisher information

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    Fisher's information measure I plays a very important role in diverse areas of theoretical physics. The associated measures Ix and Ip, as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the protagonists of our present considerations. The product IxIp has been conjectured to exhibit a nontrivial lower bound in Hall (2000). More explicitly, this conjecture says that for any pure state of a particle in one dimension IxIp ‚Č• 4. We show here that such is not the case. This is illustrated, in particular, for pure states that are solutions to the free-particle Schr√∂dinger equation. In fact, we construct a family of counterexamples to the conjecture, corresponding to time-dependent solutions of the free-particle Schr√∂dinger equation. We also conjecture that any normalizable time-dependent solution of this equation verifies IxIp ‚Üí 0 for t ‚Üí ‚ąě.Facultad de Ciencias ExactasInstituto de F√≠sica La Plat

    On a conjecture regarding Fisher information

    Get PDF
    Fisher's information measure I plays a very important role in diverse areas of theoretical physics. The associated measures Ix and Ip, as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the protagonists of our present considerations. The product IxIp has been conjectured to exhibit a nontrivial lower bound in Hall (2000). More explicitly, this conjecture says that for any pure state of a particle in one dimension IxIp ‚Č• 4. We show here that such is not the case. This is illustrated, in particular, for pure states that are solutions to the free-particle Schr√∂dinger equation. In fact, we construct a family of counterexamples to the conjecture, corresponding to time-dependent solutions of the free-particle Schr√∂dinger equation. We also conjecture that any normalizable time-dependent solution of this equation verifies IxIp ‚Üí 0 for t ‚Üí ‚ąě.Facultad de Ciencias ExactasInstituto de F√≠sica La Plat

    Quantum information as a non-kolmogorovian generalization of Shannon's theory

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    In this article, we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum information can be considered as a particular case of a huge family of non-commutative extensions of its classical counterpart. In any conceivable information theory, the possibility of dealing with different kinds of information measures plays a key role. Here, we generalize a notion of state spectrum, allowing us to introduce a majorization relation and a new family of generalized entropic measures.Facultad de Ciencias ExactasInstituto de Física La Plat

    Lossless quantum data compression with exponential penalization: an operational interpretation of the quantum Rényi entropy

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    Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum Rényi entropies. In order to do this, we appeal to a very general quantum encoding scheme that satisfies a quantum version of the Kraft-McMillan inequality. Then, in the standard situation, where one is intended to minimize the usual average length of the quantum codewords, we recover the known results, namely that the von Neumann entropy of the source bounds the average length of the optimal codes. Otherwise, we show that by invoking an exponential average length, related to an exponential penalization over large codewords, the quantum Rényi entropies arise as the natural quantities relating the optimal encoding schemes with the source description, playing an analogous role to that of von Neumann entropy.Facultad de Ciencias Exacta
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