Related papers: A semidefinite programming upper bound of quantum …
A generalization of the superactivation of quantum channel capacities to the case of n>2 channels is considered. An explicit example of such superactivation for the 1-shot quantum zero-error capacity is constructed for n=3. Some…
We study the quantum channel version of Shannon's zero-error capacity problem. Motivated by recent progress on this question, we propose to consider a certain operator space as the quantum generalisation of the adjacency matrix, in terms of…
Inspired by the power of abstraction in information theory, we consider quantum rebound protocols as a way of providing a unifying perspective to deal with several information-processing tasks related to and extending quantum channel…
We study commitment scheme for classical-quantum channels. To accomplish this we define various notions of commitment capacity for these channels and prove matching upper and lower bound on it in terms of the conditional entropy. Our…
We present a family of additive quantum error-correcting codes whose capacities exceeds that of quantum random coding (hashing) for very noisy channels. These codes provide non-zero capacity in a depolarizing channel for fidelity parameters…
Coding theorems and (strong) converses for memoryless quantum communication channels and quantum sources are proved: for the quantum source the coding theorem is reviewed, and the strong converse proven. For classical information…
Quantum Information Processing (QIP) tasks can be efficiently formulated in terms of quantum dynamical maps, whose formalism is able to provide the appropriate mathematical representation of the evolution of open quantum systems. A key QIP…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
We introduce potential capacities of quantum channels in an operational way and provide upper bounds for these quantities, which quantify the ultimate limit of usefulness of a channel for a given task in the best possible context.…
Quantum error correction codes protect information from realistic noisy channels and lie at the heart of quantum computation and communication tasks. Understanding the optimal performance and other information-theoretic properties, such as…
Superactivation is the property that two channels with zero quantum capacity can be used together to yield positive capacity. Here we demonstrate that this effect exists for a wide class of inequivalent channels, none of which can simulate…
A fundamental model of quantum computation is the programmable quantum gate array. This is a quantum processor that is fed by a program state that induces a corresponding quantum operation on input states. While being programmable, any…
We develop a systematic approach, based on convex programming and real analysis, for obtaining upper bounds on the capacity of the binary deletion channel and, more generally, channels with i.i.d. insertions and deletions. Other than the…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural convex relaxation via the standard (Shor) semidefinite program…
We study quantum channels that are close to another channel with weakly additive Holevo information and derive upper bounds on their classical capacity. Examples of channels with weakly additive Holevo information are entanglement-breaking…
A new bound for the quantum capacity of the $d$-dimensional depolarizing channels is presented. Our derivation makes use of a flagged extension of the map where the receiver obtains a copy of a state $\sigma_0$ whenever the messages are…
Semidefinite programming (SDP) is a unifying framework that generalizes both linear programming and quadratically-constrained quadratic programming, while also yielding efficient solvers, both in theory and in practice. However, there exist…
Approximate message passing (AMP) is a family of iterative algorithms that generalize matrix power iteration. AMP algorithms are known to optimally solve many average-case optimization problems. In this paper, we show that a large class of…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…