Related papers: Error recognition in the Cantor cube

We give asymptotically converging semidefinite programming hierarchies of outer bounds on bilinear programs of the form $\mathrm{Tr}\big[M(X\otimes Y)\big]$, maximized with respect to semidefinite constraints on $X$ and $Y$. Applied to the…

Information-theoretic key agreement is impossible to achieve from scratch and must be based on some - ultimately physical - premise. In 2005, Barrett, Hardy, and Kent showed that unconditional security can be obtained in principle based on…

In the original BB84 protocol by Bennett and Brassard, an eavesdropper is detected because his attempts to intercept information result in a quantum bit error rate (QBER) of at least 25%. Here we design an alternative quantum key…

We show that, for the space of Borel probability measures on a Borel subset of a Polish metric space, the extreme points of the Prokhorov, Monge-Wasserstein and Kantorovich metric balls about a measure whose support has at most n points,…

The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth…

Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…

In 1933, Borsuk proposed the following problem: Can every bounded set in $\mathbb{E}^n$ be divided into $n+1$ subsets of smaller diameters? This problem has been studied by many authors, and a lot of partial results have been discovered. In…

We prove that any pair of reasonable cross norms defined on the tensor product of $n$ Banach spaces induce $(2k)^{n-1}$-Lipschitz equivalent metrics (and thus, a unique topology) on the set $S^k_{X_1,\ldots, X_n}$ of vectors of rank $\leq…

We study the simultaneous message passing (SMP) model of communication complexity, for the case where one party is quantum and the other is classical. We show that in an SMP protocol that computes some function with the first party sending…

I. This paper is devoted to the problem of error detection with quantum codes. In the first part we examine possible problem settings for quantum error detection. Our goal is to derive a functional that describes the probability of…

This paper ist concerned with recent progress in the context of coorbit space theory. Based on a square integrable group representation, the coorbit theory provides new families of associated smoothness spaces, where the smoothness of a…

A set of integers $A$ is computably encodable if every infinite set of integers has an infinite subset computing $A$. By a result of Solovay, the computably encodable sets are exactly the hyperarithmetic ones. In this paper, we extend this…

We study the problem of designing optical receivers to discriminate between multiple coherent states using coherent processing receivers---i.e., one that uses arbitrary coherent feedback control and quantum-noise-limited direct…

Beyond its widespread application in signal and image processing, \emph{compressed sensing} principles have been greatly applied to secure information transmission (often termed 'compressive security'). In this scenario, the measurement…

In 1996, Ricardo Ricardo Ma\~n\'e discovered that Mather measures are in fact the minimizers of a "universal" infinite dimensional linear programming problem. This fundamental result has many applications, one of the most important is to…

Let $d$ be a positive integer. For a finite set $X \subseteq \mathbb{R}^d$, we define its integer cone as the set $\mathsf{IntCone}(X) := \{ \sum_{x \in X} \lambda_x \cdot x \mid \lambda_x \in \mathbb{Z}_{\geq 0} \} \subseteq \mathbb{R}^d$.…

We compare three secrecy-coding schemes for the degraded wiretap binary symmetric channel (BSC) in the finite-blocklength regime: (i) polar wiretap coset codes, (ii) PAC codes used as wiretap coset codes, and (iii) the invertible-extractor…

We consider the problem of communicating over a channel that randomly "tears" the message block into small pieces of different sizes and shuffles them. For the binary torn-paper channel with block length $n$ and pieces of length ${\rm…

We show that every correctable subsystem for an arbitrary noise operation can be recovered by a unitary operation, where the notion of recovery is more relaxed than the notion of correction insofar as it does not protect the subsystem from…

In this paper we give a general integral representation for separable states in the tensor product of infinite dimensional Hilbert spaces and provide the first example of separable states that are not countably decomposable. We also prove…