Related papers: A Duality Theorem for Classical-Quantum States wit…
Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that…
The capability to quantitatively distinguish quantum states is of great importance for a variety of tasks, and has recently played an important role in the study of quantum reduced dynamics and their characterization in terms of memory…
For a primal-dual pair of conic linear problems that are described by convex cones $S\subset X$, $T\subset Y$, bilinear symmetric objective functions $\langle\cdot,\cdot\rangle_X$, $\langle\cdot,\cdot\rangle_Y$ and a linear operator…
Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous…
We develop a methodology for closing duality gap and guaranteeing strong duality in infinite convex optimization. Specifically, we examine two new Lagrangian-type dual formulations involving infinitely many dual variables and infinite sums…
That superpositions of states can be useful for performing tasks in quantum systems has been known since the early days of quantum information, but only recently has quantitative theory of quantum coherence been proposed. Here we apply that…
Deploying mathematical optimization in autonomous production systems requires precise contracts for objects returned by an optimization solver. Unfortunately, conventions on dual solution and infeasibility certificates (rays) vary widely…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
We study the problem of optimization over positive valued-operator measure to extract classical correlation in a bipartite quantum system. The proposed method is applied to binary states only. Moreover, to illustrate this method, an…
A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a…
We present a procedure which allows us to recover classical and nonclassical logical structures as \emph{concrete logics} associated with physical theories expressed by means of classical languages. This procedure consists in choosing, for…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
The efficient and reliable verification of quantum states plays a crucial role in various quantum information processing tasks. We consider the task of verifying entangled states using one-way and two-way classical communication and…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of…
Schur-Weyl duality is a powerful tool in representation theory which has many applications to quantum information theory. We provide a generalization of this duality and demonstrate some of its applications. In particular, we use it to…
Combining quantum computers with classical compute power has become a standard means for developing algorithms that are eventually supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or…
Causality is one of the most fundamental notions in physics. Generalized probabilistic theories (GPTs) and the process matrix framework incorporate it in different forms. However, a direct connection between these frameworks remains…
Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring…