Related papers: Noninformative Quantum q-Priors
Information causality was initially proposed as a physical principle aimed at deriving the predictions of quantum mechanics on the type of correlations observed in the Bell experiment. In the same work, information causality was famously…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
It is known that mutually unbiased bases, whenever they exist, are optimal in an information theoretic sense for the determination of unknown state of a quantum ensemble. These bases may not exist in most dimensions and some suboptimal…
Identifying governing partial differential equations (PDEs) from noisy spatiotemporal data remains challenging due to differentiation-induced noise amplification and ambiguity from overcomplete libraries. We propose a prior-informed…
We analyze the quantum query complexity of sorting under partial information. In this problem, we are given a partially ordered set $P$ and are asked to identify a linear extension of $P$ using pairwise comparisons. For the standard sorting…
Quantum metrology is a rapidly developing branch of quantum technologies. While various theories have been established on quantum metrology for Markovian processes, i.e., quantum channel estimation, quantum metrology for non-Markovian…
In this paper, our prime objective is to apply the techniques of parameter estimation theory and the concept of Quantum Metrology in the form of Fisher Information to investigate the role of certain physical quantities in the open quantum…
An analytical solution for the posterior estimate in Bayesian tomography of the unknown quantum state of an arbitrary quantum system (with a finite-dimensional Hilbert space) is found. First, we derive the Bayesian estimate for a pure…
Local information objectivity, that local, independent observers can infer the same information about a model upon exchange of independently acquired experimental data, is fundamental to science. It is mathematically encoded via Cencov's…
Inference from limited data requires a notion of measure on parameter space, most explicit in the Bayesian framework as a prior. Here we demonstrate that Jeffreys prior, the best-known uninformative choice, introduces enormous bias when…
We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical…
We propose a two-sample mean test based on the Bayes factor with non-informative priors, specifically designed for scenarios where the dimension $p$ grows with the sample size $n$ with a linear rate $p/n \to c_1 \in (0, \infty)$. We…
Fermionic (atomic nuclei) and bosonic (correlated atoms in a trap) systems are studied from an information-theoretic point of view. Shannon and Onicescu information measures are calculated for the above systems comparing correlated and…
The quantum geometric tensor and quantum Fisher information have recently been shown to provide a unified geometric description of the linear response of many-body systems. However, a similar geometric description of higher-order…
The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be…
Performing a quantum measurement yields two different results: a classical outcome drawn from a probability distribution, according to Born's rule, and a quantum outcome corresponding to the post-measurement state. Quantum devices that…
Quantum learning (in metrology and machine learning) involves estimating unknown parameters from measurements of quantum states. The quantum Fisher information matrix can bound the average amount of information learnt about the unknown…
A concept of measuring the quantum distance between two different quantum states which is called quantum information metric is presented. The holographic principle (AdS/CFT) suggests that the quantum information metric $G_{\lambda\lambda}$…
Realist, no-collapse interpretations of quantum mechanics, such as Everett's, face the probability problem: how to justify the norm-squared (Born) rule from the wavefunction alone. While any basis-independent measure can only be…
Bohr's complementarity principle is of fundamental historic and conceptual importance for Quantum Mechanics (QM), and states that, with a given experimental apparatus configuration, one can observe either the wave-like or the particle-like…