Related papers: Majorization of quantum polarization distributions
There has been much discussion in the literature about rival measures of classical polarization in three dimensions. We gather and compare the various proposed measures of polarization, creating a geometric representation of the…
Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…
Majorization theory is a powerful mathematical tool to compare the disorder in distributions, with wide-ranging applications in many fields including mathematics, physics, information theory, and economics. While majorization theory…
We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results.…
We use majorization and confidence intervals as a convenient tool to compare the uncertainty in photon number for different quantum light states. To this end majorization is formulated in terms of confidence intervals. As a suitable case…
Polarization is one of light's most versatile degrees of freedom for both classical and quantum applications. The ability to measure light's state of polarization and changes therein is thus essential; this is the science of polarimetry. It…
We advocate for a simple multipole expansion of the polarization density matrix. The resulting multipoles are used to construct bona fide quasiprobability distributions that appear as a sum of successive moments of the Stokes variables; the…
Quantum descriptions of polarization show the rich degrees of freedom underlying classical light. While changes in polarization of light are well-described classically, a full quantum description of polarimetry, which characterizes…
The degree of polarization of a quantum state can be defined as its Hilbert-Schmidt distance to the set of unpolarized states. We demonstrate that the states optimizing this degree for a fixed average number of photons $\bar{N}$ present a…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
In this work we show how the concept of majorization in continuous distributions can be employed to characterize chaotic, diffusive and quantum dynamics. The key point lies in that majorization allows to define an intuitive arrow of time,…
Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to…
Majorization is a partial order on real vectors which plays an important role in a variety of subjects, ranging from algebra and combinatorics to probability and statistics. In this paper, we consider a generalized notion of majorization…
We show that majorization provides a powerful approach to the coherence conveyed by partially polarized transversal electromagnetic waves. Here we present the formalism, provide some examples and compare with standard measures of…
Many-party correlations between measurement outcomes in general probabilistic theories are given by conditional probability distributions obeying the non-signalling condition. We show that any such distribution can be obtained from…
Classical definition of degree of polarization is expressed in quantum domain by replacing intensities through quantum mechanical average values of relevant number operators and is viewed as first generalization of Intensity. This…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
The theory of majorization has seen substantial application in quantum information. Its framework predicates on the comparability between real vectors. We explore the antithesis of this premise, namely, incomparability. Specifically, we…
This paper studies majorization of high tensor powers of finitely supported probability distributions. Viewing probability distributions as a resource with majorization as a means of transformation corresponds to the resource theory of pure…
The problem of quantum state discrimination, which is a foundational aspect of quantum information theory, and its relation to the theory of majorization are discussed. The purpose of this study is to review different approaches to the…