A new interpretation of entanglement entropy is proposed: entanglement entropy of a pure state with respect to a division of a Hilbert space into two subspaces 1 and 2 is an amount of information, which can be transmitted through 1 and 2 from a system interacting with 1 to another system interacting with 2. The transmission medium is quantum entanglement between 1 and 2. In order to support the...

– It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantummechanical definition. But the latter is problematic from quantum information point of view. Consequently we introduce a new definition of entropy that reflects the inherent uncertainty of qua...

We present an entropy concept measuring phase-space localization in dynamical systems based on time-averaged phase-space densities. This entropy has a direct classical counterpart; its local scaling with ln h ?1=2 is the information dimension of the underlying invariant sets of the classical dynamics. The proposed entropy concept allows to visualize the global phase-space structure of the quant...

The effects of quantum entropy on the bag constant are studied at low temperatures and small chemical potentials. The inclusion of the quantum entropy of the quarks in the equation of state provides the hadronic bag with an additional heat which causes a decrease in the effective latent heat inside the bag. We have considered two types of baryonic bags, ∆ and Ω−. In both cases we have found tha...

We construct a strong extractor against quantum storage that works for every min-entropy k, has logarithmic seed length, and outputs Ω(k) bits, provided that the quantum adversary has at most βk qubits of memory, for any β < 1 2 . The construction works by first condensing the source (with minimal entropy-loss) and then applying an extractor that works well against quantum adversaries when the ...

The entropy of a subalgebra, which has been used in quantum ergodic theory to construct a noncommutative dynamical entropy, coincides for N-level systems and Abelian subalgebras with the notion of maximal mutual information of quantum communication theory. The optimal decompositions of mixed quantum states singled out by the entropy of Abelian subalgebras correspond to optimal detection schemes...

The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and entanglement measures can be realized from it. As such, there has been broad interest in generalizing the notion to further understand its most basic properti...

when two systems are under consideration. In classical information theory, one employs the Kullback – Leibler relative entropy for this purpose which also has its quantum version. These are also additive measures and the Tsallis counterparts of these have been put forward and employed in the quantum context as well [10, 11]. There is promise in future work using the Tsallis approach to problems...

Abstract. In this paper a notion of entropy transmission of quantum channels is introduced as a natural extension of Ohya’s entropy. Here by quantum channel is meant unital completely positive mappings (ucp) of B(H) into itself, where H is an infinite dimensional Hilbert space. Using a representation theorem of ucp mapping we associate to every ucp map a uniquely determined state, and prove tha...

Entropy of distribution P can be defined in at least three different ways: 1) as the expectation of the Kullback-Leibler (KL) divergence of P from elementary δ -measures (in this case, it is interpreted as expected surprise); 2) as a negative KL-divergence of some reference measure ν from the probability measure P; 3) as the supremum of Shannon’s mutual information taken over all channels such ...