Related papers: Monotone measures of statistical complexity
We demonstrate --- using the case of the two-dimensional quantum systems --- that the "natural measure on the space of density matrices describing N-dimensional quantum systems" proposed by Zyczkowski et al (quant-ph/9804024) does not…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
We present an overview of the quantitative theory of single-copy entanglement in finite-dimensional quantum systems. In particular we emphasize the point of view that different entanglement measures quantify different types of resources…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
Entropy always increases monotonically in a closed system but complexity increases at first and then decreases as equilibrium is approached. Commonsense information-related definitions for entropy and complexity demonstrate that complexity…
A number of complexity measures for Boolean functions have previously been introduced. These include (1) sensitivity, (2) block sensitivity, (3) witness complexity, (4) subcube partition complexity and (5) algorithmic complexity. Each of…
Understanding the way in which random entities interact is of key interest in numerous scientific fields. This can range from a full characterization of the joint distribution to single scalar summary statistics. In this work we identify a…
We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as…
We propose a formal resource-theoretic approach to quantify the degree of polarization of two and three-dimensional random electromagnetic fields. This endows the space of spectral polarization matrices with the orders induced by…
Quantum measurements can produce randomness arising from the uncertainty principle. When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement…
If we want to transform the quantum state of a system to another using local measurement processes, what is the probability of success? This probability is bounded by quantifying entanglement in both the states. In this paper, we construct…
We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…
We introduce new entanglement monotones which generalize, to the case of many parties, those which give rise to the majorization-based partial ordering of bipartite states' entanglement. We give some examples of restrictions they impose on…
Various well-known statistical measures like \emph{L\'opez-Ruiz, Mancini, Calbet} (LMC) and \emph{Fisher-Shannon} complexity have been explored for confined isotropic harmonic oscillator (CHO) in composite position ($r$) and momentum ($p$)…
General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the…
We introduce two infinite sequences of entanglement monotones, which are constructed from expectation values of polynomials in the modular Hamiltonian. These monotones yield infinite sequences of inequalities that must be satisfied in…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding…
This paper addresses the problem of quantifying diversity for a set of objects. First, we conduct a systematic review of existing diversity measures and explore their undesirable behavior in certain cases. Based on this review, we formulate…