Related papers: A Counterexample to the Optimality Conjecture in C…
In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and…
A converse method is developed for the source broadcast problem. Specifically, it is shown that the separation architecture is optimal for a variant of the source broadcast problem and the associated source-channel separation theorem can be…
An example is given of a qubit quantum channel which requires four inputs to maximize the Holevo capacity. The example is one of a family of channels which are related to 3-state channels. The capacity of the product channel is studied and…
We find a connection between the existence of a factorization of a quantum channel and the existence of low-rank solutions to certain linear matrix equations. Using this, we show that if a quantum channel is factorized by a direct integral…
Network Utility Maximisation (NUM) addresses the problem of allocating resources fairly within a network and explores the ways to achieve optimal allocation in real-world networks. Although extensively studied in classical networks, NUM is…
There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected…
The main purpose of this article is to prove that, under certain assumptions in a linear prediction setting, optimal methods based upon model reduction and even an optimal predictor can be provided. The optimality is formulated in terms of…
Energy minimization has been an intensely studied core problem in computer vision. With growing image sizes (2D and 3D), it is now highly desirable to run energy minimization algorithms in parallel. But many existing algorithms, in…
The limits of quantum feedback control have immediate consequences for quantum information science at large, yet remain largely unexplored. Here, we combine quantum filtering theory and moment-sum-of-squares techniques to construct a…
Divergence chain rules for channels relate the divergence of a pair of channel inputs to the divergence of the corresponding channel outputs. An important special case of such a rule is the data-processing inequality, which tells us that if…
We introduce a new framework for quantifying the complexity of quantum channels, grounded in a suitably chosen resource set. This class of convex functions is designed to analyze the complexity of both open and closed quantum systems. By…
Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…
We find optimality conditions for testers in discrimination of quantum channels. These conditions are obtained using semidefinite programming and are similar to optimality conditions for POVMs obtained by Holevo for ensembles of quantum…
Optimizing quantum circuits is critical for enhancing computational speed and mitigating errors caused by quantum noise. Effective optimization must be achieved without compromising the correctness of the computations. This survey explores…
The complete positivity vs positivity correspondence in the Choi-Jamio{\l}kowski-Kraus-Sudarshan quantum channel-state isomorphism depends on the choice of basis. Instead of the "canonical" basis, if we use, e.g., the Pauli spin matrices…
Recently Shor proved equivalence of several open (sub)additivity problems related to the Holevo capacity and the entanglement of formation [15]. In our previous note [6] equivalence of these to the additivity of the Holevo capacity for…
There are a few obstacles, which bring about imperfect quantum teleportation of a continuous variable state, such as unavailability of maximally entangled two-mode squeezed states, inefficient detection and imperfect unitary transformation…
This paper presents a novel approach to solving convex optimization problems by leveraging the fact that, under certain regularity conditions, any set of primal or dual variables satisfying the Karush-Kuhn-Tucker (KKT) conditions is…
We consider the problem of quantum channel certification to unitary, where one is given access to an unknown $d$-dimensional channel $\mathcal{E}$, and wants to test whether $\mathcal{E}$ is equal to a target unitary channel or is…
Violation of modified Wigner inequality by means binary bipartite quantum system allows the discrimination between the quantum world and the classical local-realistic one, and also ensures the security of Ekert-like quantum key distribution…