相关论文: Accelerated optimization of measured relative entr…
We present a method for improving measurements of the entanglement R\'enyi entropies in quantum Monte Carlo simulations by relating them with measurements of participation R\'enyi entropies. Exploiting the capability of building improved…
We provide the sandwiched R\'enyi divergence of order $\alpha\in(\frac{1}{2},1)$, as well as its induced quantum information quantities, with an operational interpretation in the characterization of the exact strong converse exponents of…
Quantum key distribution requires tight and reliable bounds on the secret key rate to ensure robust security. This is particularly so for the regime of finite block sizes, where the optimization of generalized R\'enyi entropic quantities is…
Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…
Quantifying entanglement for multipartite quantum state is a crucial task in many aspects of quantum information theory. Among all the entanglement measures, relative entropy of entanglement $E_{R}$ is an outstanding quantity due to its…
We propose a series of quantum algorithms for computing a wide range of quantum entropies and distances, including the von Neumann entropy, quantum R\'{e}nyi entropy, trace distance, and fidelity. The proposed algorithms significantly…
We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the…
Two typical fixed-length random number generation problems in information theory are considered for general sources. One is the source resolvability problem and the other is the intrinsic randomness problem. In each of these problems, the…
We introduce variants of relative entropy of entanglement based on the optimal distinguishability from unentangled states by means of restricted measurements. In this way, we are able to prove that the standard regularized entropy of…
Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…
By generalizing the density matrix to a transition matrix between two states, represented as $|\phi\rangle$ and $|\psi\rangle$, one can define the pseudoentropy analogous to the entanglement entropy. In this paper, we establish an operator…
The operational characterization of quantum coherence is the corner stone in the development of resource theory of coherence. We introduce a new coherence quantifier based on max-relative entropy. We prove that max-relative entropy of…
We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. R\'enyi entropy is used as uncertainty measure associated with the distribution…
Classical analysis of convex and non-convex optimization methods often requires the Lipshitzness of the gradient, which limits the analysis to functions bounded by quadratics. Recent work relaxed this requirement to a non-uniform smoothness…
In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. This point of view covers the stochastic gradient…
RMSProp and ADAM continue to be extremely popular algorithms for training neural nets but their theoretical convergence properties have remained unclear. Further, recent work has seemed to suggest that these algorithms have worse…
Gradient compression is of growing interests for solving constrained optimization problems including compressed sensing, noisy recovery and matrix completion under limited communication resources and storage costs. Convergence analysis of…
We study the error introduced by entropy regularization in infinite-horizon discrete discounted Markov decision processes. We show that this error decreases exponentially in the inverse regularization strength, both in a weighted…
R\'enyi entropies are conceptually valuable and experimentally relevant generalisations of the celebrated von Neumann entanglement entropy. After a quantum quench in a clean quantum many-body system they generically display a universal…
Optimization theory has been widely studied in academia and finds a large variety of applications in industry. The different optimization models in their discrete and/or continuous settings have catered to a rich source of research…