Related papers: A Classical Bound on Quantum Entropy
We prove that the classical capacity of an arbitrary quantum channel assisted by a free classical feedback channel is bounded from above by the maximum average output entropy of the quantum channel. As a consequence of this bound, we…
We give new upper and lower bounds on the concavity of quantum entropy. Comparisons are given with other results in the literature.
We show that classical mechanics can be recovered as the high-entropy limit of quantum mechanics. That is, the high entropy masks quantum effects, and mixed states of high enough entropy can be approximated with classical distributions. The…
Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative $q$-entropy is generally unbounded for $q>1$. Upper bounds on the quantum relative $q$-entropy in terms…
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 Hoeffding capacity, that we define similarly to the Holevo capacity,…
We present an upper bound for the Kolmogorov-Sinai entropy of quantum systems having a mixing quantum phase space. The method for this estimation is based on the following ingredients: i) the graininess of quantum phase space in virtue of…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy…
We present some basic inequalities between the classical and quantum values of free energy, entropy and mean energy. We investigate the transition from the deterministic case (classical mechanics) to the probabilistic case (quantum…
We define classical-quantum multiway channels for transmission of classical information, after recent work by Allahverdyan and Saakian. Bounds on the capacity region are derived in a uniform way, which are analogous to the classically known…
We provide an upper bound on the quasi-relative entropy in terms of the trace distance. The bound is derived for two cases: 1) any operator monotone decreasing function and full rank mixed qubit or classical states; 2) a large class of…
The standard notion of a classical limit, represented schematically by $\hbar\rightarrow 0$, provides a method for approximating a quantum system by a classical one. In this work we explain why the standard classical limit fails when…
We prove a variety of new and refined uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimensional systems. We obtain the first tight continuity estimate…
Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. Classical cross entropy plays a central role in machine learning. We define its quantum generalization, the quantum cross entropy,…
Entangled quantum states share properties that do not have classical analogs, in particular, they show correlations that can violate Bell inequalities. It is therefore an interesting question to see what happens to entanglement measures --…
Quantum speed limits set an upper bound to the rate at which a quantum system can evolve. Adopting a phase-space approach we explore quantum speed limits across the quantum to classical transition and identify equivalent bounds in the…
We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators. Thanks to the hermicity constraints, we obtain positive-definite…
Whereas the entropy of any deterministic classical system described by a principle of least action is zero, one can assign a "quantum information" to quantum mechanical degree of freedom equal to Hausdorff area of the deviation from a…
In these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent treatment of entropy which can be applied…
Quantum entropy inequalities are studied. Some quantum entropy inequalities are obtained by several methods. For entanglement breaking channel, we show that the entanglement-assisted classical capacity is upper bounded by $\log d$. A…