Related papers: Comments on Hastings' Additivity Counterexamples
A quantum channel is sufficient with respect to a set of input states if it can be reversed on this set. In the approximate version, the input states can be recovered within an error bounded by the decrease of the relative entropy under the…
Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…
We provide a counterexample to Cover's conjecture that the feedback capacity $C_\textrm{FB}$ of an additive Gaussian noise channel under power constraint $P$ be no greater than the nonfeedback capacity $C$ of the same channel under power…
We prove the quantum conditional Entropy Power Inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional…
We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based…
We show the equivalence of two different notions of quantum channel capacity: that which uses the entanglement fidelity as its criterion of success in transmission, and that which uses the minimum fidelity of pure states in a subspace of…
The Besson-Courtois-Gallot theorem is proven for noncompact finite volume Riemannian manifolds. In particular, no bounded geometry assumptions are made. This proves the minimal entropy conjecture for nonuniform rank one lattices.
This was significantly extended from the previous article quant-ph/9705043,especially in an information theoretic aspect, by adding new results.
Originated from the superposition principle in quantum mechanics, coherence has been extensively studied as a kind important resource in quantum information processing. We investigate the distinguishability of coherence-breaking channels…
We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive.…
Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao over torsion-free groups. Next, we prove…
The additivity of the minimal output entropy and that of the $\chi$-capacity are known to be equivalent for finite-dimensional irreducibly covariant channels. In this paper we formulate a list of conditions allowing to establish similar…
We derive a novel chain rule for a family of channel conditional entropies, covering von Neumann and sandwiched R\'{e}nyi entropies. In the process, we show that these channel conditional entropies are equal to their regularized version,…
Quantum channels represent a broad spectrum of operations crucial to quantum information theory, encompassing everything from the transmission of quantum information to the manipulation of various resources. In the domain of states, the…
If Bekenstein's conjectured bound on the microcanonical entropy, S < 2 pi E R, is applied to a closed subsystem of maximal linear size R and excitation energy up through E, it can be violated by an arbitrarily large factor by a scalar field…
It shown that when one of the components of a product channel is entanglement breaking, the output state with maximal p-norm is always a product state. This result complements Shor's theorem that both minimal entropy and Holevo capacity are…
In this work, novel upper and lower bounds for the capacity of channels with arbitrary constraints on the support of the channel input symbols are derived. As an immediate practical application, the case of multiple-input multiple-output…
This paper is an exposition, with some new applications, of our results on the growth of entropy of convolutions. We explain the main result on $\mathbb{R}$, and derive, via a linearization argument, an analogous result for the action of…
The channel output entropy of a transmitted word is the entropy of the possible channel outputs and similarly, the input entropy of a received word is the entropy of all possible transmitted words. The goal of this work is to study these…
We begin by deriving bounds for the entanglement of a spin with an (adjacent and non-adjacent) interval of spins in an arbitrary pure Finitely Correlated States (FCS). The bounds we derive become exact in the case where one considers the…