Related papers: Coding theorems for compound problems via quantum …
A variety of new measures of quantum Renyi mutual information and quantum Renyi conditional entropy have recently been proposed, and some of their mathematical properties explored. Here, we show that the Renyi mutual information attains…
We use the Tomita-Takesaki modular theory and the Kubo-Ando operator mean to write down a large class of multi-state quantum $f$-divergences and prove that they satisfy the data processing inequality. For two states, this class includes the…
We analyze a task in which classical and quantum messages are simultaneously communicated via a noisy quantum channel, assisted with a limited amount of shared entanglement. We derive direct and converse bounds for the one-shot capacity…
A missing piece in quantum information theory, with very few exceptions, has been to provide the random coding exponents for quantum information-processing protocols. We remedy the situation by providing these exponents for a variety of…
Capacity of a quantum channel characterizes the limits of reliable communication through a noisy quantum channel. This fundamental information theoretic question is very well studied specially in the setting of many independent uses of the…
Explicit classical states achieving maximal $f$-divergence are given, allowing for a simple proof of Matsumoto's Theorem, and the systematic extension of any inequality between classical $f$-divergences to quantum $f$-divergences. Our…
Hypothesis exclusion is an information-theoretic task in which an experimenter aims at ruling out a false hypothesis from a finite set of known candidates, and an error occurs if and only if the hypothesis being ruled out is the ground…
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…
We discuss single-shot decoding of quantum Calderbank-Shor-Steane codes with faulty syndrome measurements. We state the problem as a joint source-channel coding problem. By adding redundant rows to the code's parity-check matrix we obtain…
We study lower bounds on the optimal error probability in classical coding over classical-quantum channels at rates below the capacity, commonly termed quantum sphere-packing bounds. Winter and Dalai have derived such bounds for…
Sandwiched (quantum) $\alpha$-R\'enyi divergence has been recently defined in the independent works of Wilde et al. (arXiv:1306.1586) and M\"uller-Lennert et al (arXiv:1306.3142v1). This new quantum divergence has already found applications…
We prove new inner bounds for several multiterminal channels with classical inputs and quantum outputs. Our inner bounds are all proved in the one-shot setting, and are natural analogues of the best classical inner bounds for the respective…
This paper starts by considering the minimization of the Renyi divergence subject to a constraint on the total variation distance. Based on the solution of this optimization problem, the exact locus of the points $\bigl( D(Q\|P_1),…
In the problem of binary quantum channel discrimination with product inputs, the supremum of all type II error exponents for which the optimal type I errors go to zero is equal to the Umegaki channel relative entropy, while the infimum of…
Quantum replacer codes are codes that can be protected from errors induced by a given set of quantum replacer channels, an important class of quantum channels that includes the erasures of subsets of qubits that arise in quantum error…
In the simple quantum hypothesis testing problem, upper bound with asymmetric setting is shown by using a quite useful inequality by Audenaert et al, quant-ph/0610027, which was originally invented for symmetric setting. Using this upper…
We prove fully smooth one shot multipartite covering, aka convex split, results as well as fully smooth multipartite decoupling results for quantum states. Fully smooth one shot results for these problems were not known earlier, though the…
Variational techniques have been recently developed to find tighter bounds on the von Neumann entropy in a completely device-independent (DI) setting. This, in turn, has led to significantly improved key rates of DI protocols, in both the…
Bounds on information combining are a fundamental tool in coding theory, in particular when analyzing polar codes and belief propagation. They usually bound the evolution of random variables with respect to their Shannon entropy. In recent…
An abstract convergence theorem for a class of generalized descent methods that explicitly models relative errors is proved. The convergence theorem generalizes and unifies several recent abstract convergence theorems. It is applicable to…