Related papers: Trumping and Power Majorization
Uncertainty relation is not only of fundamental importance to quantum mechanics, but also crucial to the quantum information technology. Recently, majorization formulation of uncertainty relations (MURs) have been widely studied, ranging…
Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered.…
Abstract Like electoral systems, decision-making methods are also vulnerable to manipulation by decision-makers. The ability to effectively defend against such threats can only come from thoroughly understanding the manipulation mechanisms.…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `matrix properties'. In this paper we extend this algorithm to…
We investigate the question which communication tasks can be accomplished within a given operational theory. The concrete task is to find out which communication matrices have a prepare-and-measure implementation with states and measurement…
Multipartite entanglement holds great importance in quantum information processing. The distribution of entanglement among subsystems can be characterized by monogamy relations. Based on the $\beta$th power of concurrence and negativity, we…
We introduce and consider a certain probability question involving elementary number theory and the likelihood that a fixed prime will appear in a certain recursively defined factorization of an integer. We derive several convergent…
In reinforcement learning, state representations are used to tractably deal with large problem spaces. State representations serve both to approximate the value function with few parameters, but also to generalize to newly encountered…
In field theory, one can consider a variety of states. Within the framework of factorization algebras, one typically works with the natural augmentation state $\langle-\rangle_{\rm aug}$. In physics, however, other states arise naturally,…
The theorem like Pontryagin's maximum principle for multiple integrals is proved. Unlike the usual maximum principle, the maximum should be taken not over all matrices, but only on matrices of rank one. Examples are given.
This paper reviews the main network analysis methods used to measure structural power, which refers to the ability to shape outcomes through network position and influence, and the ability to affect others through network connections. These…
We study how iterated convolutions of probability measures compare under stochastic domination. We give necessary and sufficient conditions for the existence of an integer $n$ such that $\mu^{*n}$ is stochastically dominated by $\nu^{*n}$…
Rao-Blackwellization is a notion often occurring in the MCMC literature, with possibly different meanings and connections with the original Rao--Blackwell theorem (Rao, 1945 and Blackwell,1947), including a reduction of the variance of the…
From the perspective of majorization theory, we study how to enhance the entanglement of a two-mode squeezed vacuum (TMSV) state by using local filtration operations. We present several schemes achieving entanglement enhancement with photon…
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…
Based on the theory of Matrix Product States, we give precise statements and complete analytical proofs of the following claim: a large fractionalization in the magnetization or the need of long-range interactions imply large entanglement…
In topics such as the thermodynamic formalism of linear cocycles, the dimension theory of self-affine sets, and the theory of random matrix products, it has often been found useful to assume positivity of the matrix entries in order to…
The concept of power among players can be expressed as a combination of their utilities. A player who obeys another takes into account the utility of the dominant one. Technically it is a matter of superimposing some weighted sum or product…
Entanglement in high energy and and nuclear reactions is receiving great attention. A proper description of these reactions uses density matrices, and the express of entanglement in terms of {\it separability}. Quantum tomography bypasses…