Related papers: A Duality Theorem for Classical-Quantum States wit…
A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include…
A number of recent studies have focused on novel features in game theory when the games are played using quantum mechanical toolbox (entanglement, unitary operators, measurement). Researchers have concentrated in two-player-two strategy,…
The interplay between the algebraic structure (operator algebras) for the quantum observables and the convex structure of the state space has been explored for a long time and most advanced results are due to Alfsen and Shultz. Here we…
The emergence of classical world from underlying quantum mechanics is characterized by not only vanishing quantum correlations but also an unfolding of objectivity also known as quantum Darwinism. We show that the absence of this…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer…
Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical,…
The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…
We introduce and study a notion of duality for two classes of optimization problems commonly occurring in probability theory. That is, on an abstract measurable space $(\Omega,\mathcal{F})$, we consider pairs $(E,\mathcal{G})$ where $E$ is…
We consider two-stage hybrid protocols that combine quantum resource and classical resource to generate classical correlations shared by two separated players. Our motivation is twofold. First, in the near future the scale of quantum…
The classical simulation of quantum systems typically requires exponential resources. Recently, the introduction of a machine learning-based wavefunction ansatz has led to the ability to solve the quantum many-body problem in regimes that…
We present quantitative separation logic ($\mathsf{QSL}$). In contrast to classical separation logic, $\mathsf{QSL}$ employs quantities which evaluate to real numbers instead of predicates which evaluate to Boolean values. The connectives…
This thesis will be focused on the classical capacity of quantum channels, one of the first areas treated by quantum information theorists. The problem is fairly solved since some years. Nevertheless, this work will give me a reason to…
Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…
A conic program is the problem of optimizing a linear function over a closed convex cone intersected with an affine preimage of another cone. We analyse three constraint qualifications, namely a Closedness CQ, Slater CQ, and Boundedness CQ…
Mixed state quantum computation can perform certain tasks which are believed to be efficiently intractable on a classical computer. For a specific model of mixed state quantum computation, namely, {\it deterministic quantum computation with…
While recent work suggests that quantum computers can speed up the solution of semidefinite programs, little is known about the quantum complexity of more general convex optimization. We present a quantum algorithm that can optimize a…
Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…
We reconstruct finite-dimensional quantum theory with superselection rules, which can describe hybrid quantum-classical systems, from four purely operational postulates: symmetric sharpness, complete mixing, filtering, and local equality.…
We focus on a family of quantum coin-flipping protocols based on bit-commitment. We discuss how the semidefinite programming formulations of cheating strategies can be reduced to optimizing a linear combination of fidelity functions over a…