On Capacities of Quantum Channels

Ohya, Masanori; Petz, Dénes; Watanabe, Noboru

doi:10.1142/9789812794208_0019

Cited by 28 publications

(47 citation statements)

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“…which is actually a simple consequence of the monotonicity of the relative entropy under state transformation [7], see also [11]. I(X, W ) is the so-called Holevo quantity or classical-quantum mutual information, and it satisfies the identity…”

Section: Interpretation As Capacitymentioning

confidence: 99%

Limit relation for quantum entropy and channel capacity per unit cost

Csiszár

Hiai

Petz

2007

Journal of Mathematical Physics

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Abstract:In a quantum mechanical model, Diósi, Feldmann and Kosloff arrived at a conjecture stating that the limit of the entropy of certain mixtures is the relative entropy as system size goes to infinity. The conjecture is proven in this paper for density matrices. The first proof is analytic and uses the quantum law of large numbers. The second one clarifies the relation to channel capacity per unit cost for classical-quantum channels. Both proofs lead to generalizations of the conjecture.

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Section: Interpretation As Capacitymentioning

confidence: 99%

Limit relation for quantum entropy and channel capacity per unit cost

Csiszár

Hiai

Petz

2007

Journal of Mathematical Physics

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“…Since the Holevo capacity is equal to the relative entropy radius R ran W d,α by [24], this shows that…”

Section: Appendix Cmentioning

confidence: 91%

“…A geometric interpetation of the asymptotic channel capacity was given in [24] (see also [7] for classical channels), where it was shown that the Holevo capacity of a channel is equal to the divergence radius of its image, as measured by the relative entropy. In Theorem 4.1 we show an upper bound on the one-shot capacity of a classical-quantum channel in terms of the divergence radius of its image, as measured by the max-relative entropy.…”

Section: Introductionmentioning

confidence: 99%

Generalized relative entropies and the capacity of classical-quantum channels

Mosonyi

Datta

2009

Journal of Mathematical Physics

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We provide lower and upper bounds on the information transmission capacity of one single use of a classical-quantum channel. The lower bound is expressed in terms of the Hoeding capacity, that we dene similarly to the Holevo capacity, but replacing the relative entropy with the Hoeding distance. Similarly, our upper bound is in terms of a quantity obtained by replacing the relative entropy with the recently introduced max-relative entropy in the denition of the divergence radius of a channel.

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“…The quantum capacity is formulated by taking the supremum of the Ohya mutual entropy with respect to a certain subset of the initial state space. The quantum capacity of quantum channel was studied in [17][18][19][20]. …”

Section: Ohya Mutual Entropy For Density Operatormentioning

confidence: 99%

Note on complexity of quantum transmission processes

Ватанабе¹,

Watanabe²

2013

J. Samara State Tech. Univ., Ser. Phys. & Math. Sci.

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In 1989, Ohya propose a new concept, so-called Information Dynamics (ID), to investigate complex systems according to two kinds of view points. One is the dynamics of state change and another is measure of complexity. In ID, two complexities C S and T S are introduced. C S is a measure for complexity of system itself, and T S is a measure for dynamical change of states, which is called a transmitted complexity. An example of these complexities of ID is entropy for information transmission processes. The study of complexity is strongly related to the study of entropy theory for classical and quantum systems. The quantum entropy was introduced by von Neumann around 1932, which describes the amount of information of the quantum state itself. It was extended by Ohya for C*-systems before CNT entropy. The quantum relative entropy was first defined by Umegaki for σ-finite von Neumann algebras, which was extended by Araki and Uhlmann for general von Neumann algebras and *-algebras, respectively. By introducing a new notion, the so-called compound state, in 1983 Ohya succeeded to formulate the mutual entropy in a complete quantum mechanical system (i.e., input state, output state and channel are all quantum mechanical) describing the amount of information correctly transmitted through the quantum channel. In this paper, we briefly review the entropic complexities for classical and quantum systems. We introduce some complexities by means of entropy functionals in order to treat the transmission processes consistently. We apply the general frames of quantum communication to the Gaussian communication processes. Finally, we discuss about a construction of compound states including quantum correlations.

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On Capacities of Quantum Channels

Cited by 28 publications

References 0 publications

Limit relation for quantum entropy and channel capacity per unit cost

Limit relation for quantum entropy and channel capacity per unit cost

Generalized relative entropies and the capacity of classical-quantum channels

Note on complexity of quantum transmission processes

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