Shannon 暗号を超える光通信量子暗号Y-00

Abstract Besides the well-known Shannon entropy, there is a set of Shannon-like entropies which have applications in statistical and quantum physics. These entropies are functions of certain parameters and converge toward Shannon entropy when these parameters approach the value 1. We describe briefly the most important Shannon-like entropies and present their graphical representations. Their graphs look almost identical, though by superimposing them it appears that they are distinct and characteristic of each Shannon-like entropy. We try to formulate the alternative entropic uncertainty relations by means of the Shannon-like entropies and show that all of them equally well express the uncertainty principle of quantum physics.Abstract Besides the well-known Shannon entropy, there is a set of Shannon-like entropies which have applications in statistical and quantum physics. These entropies are functions of certain parameters and converge toward Shannon entropy when these parameters approach the value 1. We describe briefly the most important Shannon-like entropies and present their graphical representations. Their graphs look almost identical, though by superimposing them it appears that they are distinct and characteristic of each Shannon-like entropy. We try to formulate the alternative entropic uncertainty relations by means of the Shannon-like entropies and show that all of them equally well express the uncertainty principle of quantum physics.

Open PhysicsSep 1, 200323 citations

B-10-87 Shannon暗号を超える光通信量子暗号Y-00(B-10.光通信システムA(線路),一般セッション)

修廣田, 勇樹長迫, 哲也清水 +1 more

電子情報通信学会総合大会講演論文集Mar 4, 20090 citations

A characterization of the Shannon ordering of communication channels

Rajai Nasser

The ordering of communication channels was first introduced by Shannon. In this paper, we aim to find a characterization of the Shannon ordering. We show that W' contains W if and only if W is the skew-composition of W' with a convex-product channel. This fact is used to derive a characterization of the Shannon ordering that is similar to the Blackwell-Sherman-Stein theorem. Two channels are said to be Shannon-equivalent if each one is contained in the other. We investigate the topologies that can be constructed on the space of Shannon-equivalent channels. We introduce the strong topology and the BRM metric on this space. Finally, we study the continuity of a few channel parameters and operations under the strong topology.The ordering of communication channels was first introduced by Shannon. In this paper, we aim to find a characterization of the Shannon ordering. We show that W' contains W if and only if W is the skew-composition of W' with a convex-product channel. This fact is used to derive a characterization of the Shannon ordering that is similar to the Blackwell-Sherman-Stein theorem. Two channels are said to be Shannon-equivalent if each one is contained in the other. We investigate the topologies that can be constructed on the space of Shannon-equivalent channels. We introduce the strong topology and the BRM metric on this space. Finally, we study the continuity of a few channel parameters and operations under the strong topology.

arXiv:1705.01394IEEE International Symposium on Information Theory (ISIT)Jun 1, 20174 citations

光通信量子暗号(Y-00)への攻撃は真の攻撃か? Part I

修廣田

India Software Engineering ConferenceMar 11, 20050 citations

Properties of classical and quantum Jensen-Shannon divergence

Jop Briët, Peter Harremöes D

Jensen-Shannon divergence (JD) is a symmetrized and smoothed version of the most important divergence measure of information theory, Kullback divergence. As opposed to Kullback divergence it determines in a very direct way a metric; indeed, it is the square of a metric. We consider a family of divergence measures (${\text{JD}}_{\ensuremath{\alpha}}$ for $\ensuremath{\alpha}>0$), the Jensen divergences of order $\ensuremath{\alpha}$, which generalize JD as ${\text{JD}}_{1}=\text{JD}$ . Using a result of Schoenberg, we prove that ${\text{JD}}_{\ensuremath{\alpha}}$ is the square of a metric for $\ensuremath{\alpha}∊(0,2]$, and that the resulting metric space of probability distributions can be isometrically embedded in a real Hilbert space. Quantum Jensen-Shannon divergence (QJD) is a symmetrized and smoothed version of quantum relative entropy and can be extended to a family of quantum Jensen divergences of order $\ensuremath{\alpha}$ $({\text{QJD}}_{\ensuremath{\alpha}})$. We strengthen results by Lamberti and co-workers by proving that for qubits and pure states, ${\text{QJD}}_{\ensuremath{\alpha}}^{1/2}$ is a metric space which can be isometrically embedded in a real Hilbert space when $\ensuremath{\alpha}∊(0,2]$. In analogy with Burbea and Rao's generalization of JD, we also define general QJD by associating a Jensen-type quantity to any weighted family of states. Appropriate interpretations of quantities introduced are discussed and bounds are derived in terms of the total variation and trace distance.Jensen-Shannon divergence (JD) is a symmetrized and smoothed version of the most important divergence measure of information theory, Kullback divergence. As opposed to Kullback divergence it determines in a very direct way a metric; indeed, it is the square of a metric. We consider a family of divergence measures (${\text{JD}}_{\ensuremath{\alpha}}$ for $\ensuremath{\alpha}>0$), the Jensen divergences of order $\ensuremath{\alpha}$, which generalize JD as ${\text{JD}}_{1}=\text{JD}$. Using a result of Schoenberg, we prove that ${\text{JD}}_{\ensuremath{\alpha}}$ is the square of a metric for $\ensuremath{\alpha}∊(0,2]$, and that the resulting metric space of probability distributions can be isometrically embedded in a real Hilbert space. Quantum Jensen-Shannon divergence (QJD) is a symmetrized and smoothed version of quantum relative entropy and can be extended to a family of quantum Jensen divergences of order $\ensuremath{\alpha}$ $({\text{QJD}}_{\ensuremath{\alpha}})$. We strengthen results by Lamberti and co-workers by proving that for qubits and pure states, ${\text{QJD}}_{\ensuremath{\alpha}}^{1/2}$ is a metric space which can be isometrically embedded in a real Hilbert space when $\ensuremath{\alpha}∊(0,2]$. In analogy with Burbea and Rao's generalization of JD, we also define general QJD by associating a Jensen-type quantity to any weighted family of states. Appropriate interpretations of quantities introduced are discussed and bounds are derived in terms of the total variation and trace distance.

arXiv:0806.4472Physical Review AMay 12, 2009207 citations

{\text{JD}}_{1}=\text{JD}

. Using a result of Schoenberg, we prove that ${\text{JD}}_{\ensuremath{\alpha}}$ is the square of a metric for $\ensuremath{\alpha}∊(0,2]$, and that the resulting metric space of probability distributions can be isometrically embedded in a real Hilbert space. Quantum Jensen-Shannon divergence (QJD) is a symmetrized and smoothed version of quantum relative entropy and can be extended to a family of quantum Jensen divergences of order $\ensuremath{\alpha}$ $({\text{QJD}}_{\ensuremath{\alpha}})$. We strengthen results by Lamberti and co-workers by proving that for qubits and pure states, ${\text{QJD}}_{\ensuremath{\alpha}}^{1/2}$ is a metric space which can be isometrically embedded in a real Hilbert space when $\ensuremath{\alpha}∊(0,2]$. In analogy with Burbea and Rao's generalization of JD, we also define general QJD by associating a Jensen-type quantity to any weighted family of states. Appropriate interpretations of quantities introduced are discussed and bounds are derived in terms of the total variation and trace distance.