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Physics Letters B

New nonextensive quantum entropy and strong evidences for equilibrium of quantum hadronic states

D. B. Ion, Rodica‐Mariana Ion

Published Oct 1, 2001• 5 citations
Publisher

Abstract

In this Letter by introduction of the nonextensivity conjugated entropy S̄Jθ(p,q) we proved new nonextensive entropic uncertainty relations (NC-EUR) as well as new entropic uncertainty bands (NC-EUB). Moreover, we obtained not only consistent experimental tests of the optimal NC-EUR and NC-EUB, but also strong experimental evidences for the principle of minimum distance in space of quantum states (PMD-SQS).

DOI
10.1016/s0370-2693(01)01066-8

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In this Letter by introduction of the nonextensivity conjugated entropy S̄Jθ(p,q) we proved new nonextensive entropic uncertainty relations (NC-EUR) as well as new entropic uncertainty bands (NC-EUB). Moreover, we obtained not only consistent experimental tests of the optimal NC-EUR and NC-EUB, but also strong experimental evidences for the principle of minimum distance in space of quantum states (PMD-SQS).
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Nonclassical states of quantized light, except for the Gaussian states, also possess non-Gaussian phase-space distributions. Despite several attempts, a unified description of nonclassicality (NC) and non-Gaussianity (NG) of quantum states of light has not been developed as-of-yet. Here, we propose an experimentally verifiable scheme for quantification of NC, in terms of Wehrl entropy, that further leads to the simultaneous quantification of NC and NG. While requiring no optimization, present work recovers earlier results qualitatively as well as explores several new possibilities on the conjugation of nonclassical and non-Gaussian character of quantum states. Moreover, current formalism, due to its possible extension to the finite-dimensional systems, bridges the gap between discrete and continuous variable systems. Our work, thus, becomes crucial in describing NC of quantum processes including open quantum systems as well as understanding the role of NC and NG as resources in several information theoretic tasks processing such as entanglement distillation, quantum network, quantum computation etc.
We conjecture a new entropic uncertainty principle governing the entropy of complementary observations made on a system given side information in the form of quantum states, generalizing the entropic uncertainty relation of Maassen and Uffink [Phys. Rev. Lett. 60, 1103 (1988)]. We prove a special case for certain conjugate observables by adapting a similar result found by Christandl and Winter pertaining to quantum channels [IEEE Trans. Inf. Theory 51, 3159 (2005)], and discuss possible applications of this result to the decoupling of quantum systems and for security analysis in quantum cryptography.
Uncertainty relations play a central role in quantum mechanics. Entropic uncertainty relations in particular have gained significant importance within quantum information, providing the foundation for the security of many quantum cryptographic protocols. Yet, rather little is known about entropic uncertainty relations with more than two measurement settings. In this note we review known results and open questions. The uncertainty principle is one of the fundamental ideas of quantum mechanics. Since Heisenberg’s uncertainty relations for canonically conjugate variables, they have been one of the most prominent examples of how quantum mechanics differs from the classical world (Heisenberg, 1927). Uncertainty relations today are probably best known in the form given by (Robertson, 1929), who extended Heisenberg’s result to two arbitrary observables A and B. Robertson’s relation states that if we prepare many copies of the state |ψ〉, and measure each copy individually using either A or B, we have