Related papers: Defining quantum divergences via convex optimizati…
Quantum relative entropy, a quantum generalization of the renowned Kullback-Leibler divergence, serves as a fundamental measure of the distinguishability between quantum states and plays a pivotal role in quantum information science.…
In classical information theory, the Doeblin coefficient of a classical channel provides an efficiently computable upper bound on the total-variation contraction coefficient of the channel, leading to what is known as a strong…
This paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations,…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
This paper introduces the induced divergence, a new quantum divergence measure that replaces the hypothesis testing divergence in position-based decoding, simplifying the analysis of quantum communication and state redistribution while…
Quantum memories are a crucial precondition in many protocols for processing quantum information. A fundamental problem that illustrates this statement is given by the task of channel discrimination, in which an unknown channel drawn from a…
Quantum coherence is one of the fundamental properties of quantum mechanics and also acts as a valuable resource for a variety of practical applications, which includes quantum computing and quantum information processing. Evaluating the…
We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite…
A quantum generalized divergence by definition satisfies the data-processing inequality; as such, the relative decrease in such a divergence under the action of a quantum channel is at most one. This relative decrease is formally known as…
R\'enyi divergences play a pivotal role in information theory, statistics, and machine learning. While several estimators of these divergences have been proposed in the literature with their consistency properties established and minimax…
When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approximation is made by neural networks, the underlying problem…
This paper argues that DNNs implement a computational Occam's razor -- finding the `simplest' algorithm that fits the data -- and that this could explain their incredible and wide-ranging success over more traditional statistical methods.…
A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output $p$-norm can be…
Machine learning algorithms have been increasingly deployed in critical automated decision-making systems that directly affect human lives. When these algorithms are only trained to minimize the training/test error, they could suffer from…
In this paper we introduce a new partial order on quantum states that considers which states can be achieved from others by updating on `agreeing' Bayesian evidence. We prove that this order can also be interpreted in terms of minimising…
Estimating the unitarity of an unknown quantum channel $\mathcal{E}$ provides information on how much it is unitary, which is a basic and important problem in quantum device certification and benchmarking. Unitarity estimation can be…
We provide a unifying framework for distributed convex optimization over time-varying networks, in the presence of constraints and uncertainty, features that are typically treated separately in the literature. We adopt a proximal…
We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any…
This paper presents a counterexample to the optimality conjecture in convex quantum channel optimization proposed by Coutts et al. The conjecture posits that for nuclear norm minimization problems in quantum channel optimization, the dual…
Fidelity is crucial for characterizing transformations of quantum states under various quantum channels, which can be served as a fundamental tool in resource theories. Firstly, we define an $\alpha$-$z$-fidelity as a significant quantity…