Related papers: Geometric optimization for quantum communication
We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…
The aim of this thesis is to develop a theoretical framework to study parameter estimation of quantum channels. We study the task of estimating unknown parameters encoded in a channel in the sequential setting. A sequential strategy is the…
I will investigate the capacities of noisy quantum channels through a combined analytical and numerical approach. First, I introduce novel flagged extension techniques that embed a channel into a higher-dimensional space, enabling…
We present a diffeomorphism-invariant formulation of differential entropy for Riemannian spaces, providing a fine-grained, coordinate-independent notion of quantum information for continuous variables in physical space. To this end, we…
We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish…
Basing on unified approach to {\it all} kinds of quantum capacities we show that the rate of quantum information transmission is bounded by the maximal attainable rate of coherent information. Moreover, we show that, if for any bipartite…
Under the data manifold hypothesis, high-dimensional data are concentrated near a low-dimensional manifold. We study the problem of Riemannian optimization over such manifolds when they are given only implicitly through the data…
Since optimization on Riemannian manifolds relies on the chosen metric, it is appealing to know that how the performance of a Riemannian optimization method varies with different metrics and how to exquisitely construct a metric such that a…
Designing quantum circuits for ground state preparation is a fundamental task in quantum information science. However, standard Variational Quantum Algorithms (VQAs) are often constrained by limited ansatz expressivity and difficult…
The field of quantum communications promises the faithful distribution of quantum information, quantum entanglement, and absolutely secret keys, however, the highest rates of these tasks are fundamentally limited by the transmission…
Constellation shaping is a practical and effective technique to improve the performance and the rate adaptivity of optical communication systems. In principle, it could also be used to mitigate the impact of nonlinear effects, possibly…
In probabilistic modeling, parameter estimation is commonly formulated as a minimization problem on a parameter manifold. Optimization in such spaces requires geometry-aware methods that respect the underlying information structure. While…
The common approach of designing a communication device is to maximize a well-defined objective function, e.g., the channel capacity and the cut-off rate. We propose easy-to-implement solutions for Gaussian channels that approximate the…
Basing on states and channels isomorphism we point out that semidefinite programming can be used as a quick test for nonzero one-way quantum channel capacity. This can be achieved by search of symmetric extensions of states isomorphic to a…
Machine learning techniques are increasingly being used in fundamental research to solve various challenging problems. Here we explore one such technique to address an important problem in quantum communication scenario. While transferring…
Capacities of quantum channels are fundamental quantities in the theory of quantum information. A desirable property is the additivity for a capacity. However, this cannot be achieved for a few quantities that have been established as…
Quantum communication holds the potential to revolutionize information transmission by enabling secure data exchange that exceeds the limits of classical systems. One of the key performance metrics in quantum information theory, namely the…
We give a survey of the two remarkable analytical problems of quantum information theory. The main part is a detailed report of the recent (partial) solution of the quantum Gaussian optimizers problem which establishes an optimal property…
The computational cost of quantum algorithms for physics and chemistry is closely linked to the spectrum of the Hamiltonian, a property that manifests in the necessary rescaling of its eigenvalues. The typical approach of using the 1-norm…
Information must take up space, must weigh, and its flux must be limited. Quantum limits on communication and information storage leading to these conclusions are here described. Quantum channel capacity theory is reviewed for both steady…