Related papers: Simplification of additivity conjecture in quantum…
The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minimum output entropy of a channel, often…
We show that the minimum Renyi entropy output of a quantum channel is locally additive for Renyi parameter alpha>1. While our work extends the results of [10] (in which local additivity was proven for alpha=1), it is based on several new…
The super-additivity of quantum channel capacity is an important feature of quantum information theory different from classical theory, which has been attracting attention. Recently a special channel called ``platypus channel'' exhibits…
We present explicit quantum channels with strictly sub-additive minimum output R\'enyi entropy for all $p>1$, improving upon prior constructions which handled $p>2$. Our example is provided by explicit constructions of linear subspaces with…
We consider bistochastic quantum channels generated by unitary representations of the discret group. The proof of the additivity conjecture for the quantum depolarizing channel $\Phi$ based on the decreasing property of the relative entropy…
The continuity properties of the convex closure of the output entropy of infinite dimensional channels and their applications to the additivity problem are considered. The main result of this paper is the statement that the superadditivity…
When classical information is sent through a quantum channel of nonorthogonal states, there is a possibility that transmittable classical information exceeds a channel capacity in a single use of the initial channel by extending it into…
Quantum channels can be described via a unitary coupling of system and environment, followed by a trace over the environment state space. Taking the trace instead over the system state space produces a different mapping which we call the…
It is shown that for real finite dimensional Hilbert spaces the additivity property of the minimum output entropy for quantum channels is always true.
We give a survey of the two remarkable analytical problems of quantum information theory. The main part is a detailed report of the recent (partial) solution of the quantum Gaussian optimizers problem which establishes an optimal property…
The design of error-correcting codes used in modern communications relies on information theory to quantify the capacity of a noisy channel to send information [1]. This capacity can be expressed using the mutual information between input…
We prove a lemma which allows one to extend results about the additivity of the minimal output entropy from highly symmetric channels to a much larger class. A similar result holds for the maximal output $p$-norm. Examples are given showing…
Quantum channel capacities give the fundamental performance limits for information flow over a communication channel. However, the prevalence of superadditivity is a major obstacle to understanding capacities, both quantitatively and…
We make a number of simplifications in Gour and Friedland's proof of local additivity of minimum output entropy of a quantum channel. We follow them in reframing the question as one about entanglement entropy of bipartite states associated…
Additivity of minimal entropy output is proven for the class of quantum channels $\Lambda_t (A):=t A^{T}+(1-t)\tau (A)$ in the parameter range $-2/(d^2-2)\le t \le 1/(d+1)$.
In this paper we give a self contained introduction to the conceptional and mathematical foundations of quantum information theory. In the first part we introduce the basic notions like entanglement, channels, teleportation etc. and their…
We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In…
Inspired by Montanaro's work, we introduce the concept of additivity rates of a quantum channel $L$, which give the first order (linear) term of the minimum output $p$-R\'enyi entropies of $L^{\otimes r}$ as functions of $r$. We lower bound…
Information theory, though originally developed for communications engineering, provides mathematical tools with broad applications across science. These tools characterize the fundamental limits of data compression and transmission in the…
When can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity -- a fundamental synergy which…