Related papers: Maximum Quantum Entropy Method
The main goal of this paper is to extend and apply the principle of maximum entropy (MaxEnt) to incomplete quantum process estimation tasks. We will define a so-called process entropy function being the von Neumann entropy of the state…
Quantum state tomography is an integral part of quantum computation and offers the starting point for the validation of various quantum devices. One of the central tasks in the field of state tomography is to reconstruct with high fidelity,…
A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…
We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fixed observables. We point out the existence of…
We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for…
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…
Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
The phenomenon of entropy concentration provides strong support for the maximum entropy method, MaxEnt, for inferring a probability vector from information in the form of constraints. Here we extend this phenomenon, in a discrete setting,…
We develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined…
The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution $f(x|\mu)$ there is a "universal" relation among the…
A brief discussion is given of the traditional version of the Maximum Entropy Method, including a review of some of the criticism that has been made in regard to its use in statistical inference. Motivated by these questions, a modified…
Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally suitable, possibilities. Following Jaynes'…
The measured relative entropies of quantum states and channels find operational significance in quantum information theory as achievable error rates in hypothesis testing tasks. They are of interest in the near term, as they correspond to…
The maximum entropy principle, as applied to quantum systems, is a fundamental prescript positing that for a quantum system for which we only have partial knowledge, the maximum entropy state consistent with the partial knowledge is a…
A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and…
Based on the resource theory for quantifying the coherence of quantum channels, we introduce a new coherence quantifier for quantum channels via maximum relative entropy. We prove that the maximum relative entropy for coherence of quantum…
We study the continuity of the maximum-entropy inference map for two observables in finite dimensions. We prove that the continuity is equivalent to the strong continuity of the set-valued inverse numerical range map. This gives a…
It is supposed that the exponential multiplier in the method of the non-equilibrium statistical operator (Zubarev`s approach) can be considered as a distribution density of the past lifetime of the system, and can be replaced by an…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…