相关论文: On the additivity conjecture for channels with arb…

Communication rates over quantum channels can be boosted by entanglement, via superadditivity phenomena or entanglement assistance. Superadditivity refers to the capacity improvement from entangling inputs across multiple channel uses.…

The long-standing conjectures of the optimality of Gaussian inputs for Gaussian channel and Gaussian additivity are solved for a broad class of covariant or contravariant Bosonic Gaussian channels (which includes in particular thermal,…

We present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for high-fidelity quantum communication when assisted by a family of channels that have…

It is known that the minimal output entropy is additive for any product of entanglement breaking (EB) channels. The same is true for the Renyi entropy, where additivity is equivalent to multiplicativity of the $1 \rightarrow q$ norm for all…

This paper considers reliable communications over a multiple-input multiple-output (MIMO) Gaussian channel, where the channel matrix is within a bounded channel uncertainty region around a nominal channel matrix, i.e., an instance of the…

Given a general channel, we first formulate the idetification capacity problem as well as the resolvability problem with input cost constraint in as the general form as possible, along with relevant fundamental theorems. Next, we establish…

Every channel can be expressed as a convex combination of deterministic channels with each deterministic channel corresponding to one particular intrinsic state. Such convex combinations are in general not unique, each giving rise to a…

We present a family of relatively simple and unified lower bounds on the capacity of the Gaussian channel under a set of pointwise additive input constraints. Specifically, the admissible channel input vectors $\bx = (x_1, \ldots, x_n)$…

Seminal work by Edmonds and Lovasz shows the strong connection between submodularity and convexity. Submodular functions have tight modular lower bounds, and subdifferentials in a manner akin to convex functions. They also admit poly-time…

The relative entropy description of Holevo-Schumacher-Westmoreland (HSW) classical channel capacity is applied to single qubit channels. A simple formula for the relative entropy of qubit density matrices in the Bloch sphere representation…

In this note we study restrictions on the recently introduced super-additive and sub-additive transformations, $A\mapsto A^*$ and $A\mapsto A_*$, of an aggregation function $A$. We prove that if $A^*$ has a slightly stronger property of…

Recently, the longstanding Gaussian optimizer conjecture was proven for bosonic Gaussian gauge-covariant or contravariant channels in the work of Giovannetti, Holevo and Garcia-Patron [3]. In the paper of Mari, Giovannetti and Holevo [11]…

This paper concerns the capacity of the discrete noiseless channel introduced by Shannon. A sufficient condition is given for the capacity to be well-defined. For a general discrete noiseless channel allowing non-integer valued symbol…

Memoryless channels with deletion errors as defined by a stochastic channel matrix allowing for bit drop outs are considered in which transmitted bits are either independently deleted with probability $d$ or unchanged with probability…

A strong converse theorem for the classical capacity of a quantum channel states that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of…

We introduce a new form for the bosonic channel minimal output entropy conjecture, namely that among states with equal input entropy, the thermal states are the ones that have slightest increase in entropy when sent through a infinitesimal…

Let $p\ge 1$ and let $\boldsymbol{v} \colon \mathbb R^d \to \mathbb R^d$ be a compactly supported vector field with $\boldsymbol{v} \in L^p(\mathbb R^d)$ and $\operatorname{div} \boldsymbol{v} = 0$ (in the sense of distributions). It was…

For all 1 < p < 2, we demonstrate the existence of quantum channels with non-multiplicative maximal p-norms. Equivalently, the minimum output Renyi entropy of order p of a quantum channel is not additive for all 1 < p < 2. The violations…

The property of the optimal signal ensembles of entanglement assisted channel capacity is studied. A relationship between entanglement assisted channel capacity and one-shot capacity of unassisted channel is obtained. The data processing…

We show that the uniform distribution minimizes entropy among all one-dimensional symmetric log-concave distributions with fixed variance, as well as various generalizations of this fact to R\'enyi entropies of orders less than 1 and with…