Related papers: Average number is an insufficient metric for inter…

We consider the apparatus in a quantum measurement process to be in a mixed state. We propose a simple upper bound on the probability of correctly distinguishing any number of mixed states. We use this to derive fundamental bounds on the…

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…

The ratio of Bayesian evidences is a popular tool in cosmology to compare different models. There are however several issues with this method: Bayes' ratio depends on the prior even in the limit of non-informative priors, and Jeffrey's…

The possibility to study intermittency in a single event of high multiplicity is investigated in the framework of the $\alpha-$model. It is found that, for cascade long enough, the dispersion of intermittency exponents obtained from…

A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…

Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…

Quantum metrology overcomes standard precision limits by exploiting collective quantum superpositions of physical systems used for sensing, with the prominent example of non-classical multiphoton states improving interferometric techniques.…

Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it…

Inserting a lossy dielectric into one arm of an interference experiment acts in many ways like a measurement. If two entangled photons are passed through the interferometer, a certain amount of information is gained about which path they…

It is widely known that `collapse of the wave function' on a quantum system A may be brought about by an interaction with another quantum system B. We will prove that this is not just a possible, but a necessary consequence of information…

So-called average subsystem entropies are defined by first taking partial traces over some pure state to define density matrices, then calculating the subsystem entropies, and finally averaging over the pure states to define the average…

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 argued that the nature of probability is essentially informational rather than physical and that quantum mechanical predictions should be viewed as logical inferences made on the basis of the information content of a given…

Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…

Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected…

We introduce a general scheme of many-particle interferometry in which two identical sources are used and "which-way information" is eliminated by making the paths of one or more particles identical (path identity). The scheme allows us to…

The amount of information that can be accessed via measurement of a quantum system prepared in different states is limited by the Kholevo bound. We present a simple proof of this theorem and its extension to sequential measurements based on…

It is shown that the standard expression for the information entropy, originally due to Shannon, is only valid for a particular set of states. For the general case of statistical mechanics, one needs to include an additional term in the…

The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the…