arXiv subjects

Verinder S. Rana

Publications and source records attributed to Verinder S. Rana.

3 recordsLinked to original sources

arXiv2019

Geometric Measures of Information for Quantum State Characterization

We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information distance formula of Rokhlin and Rajski. We then define an analogous information area. We motivate this definition and discuss its properties. We extend this definition to higher-dimensional volumes. We briefly discuss the potential utility for these geometric measures in quantum information processing.

quant-ph↗

arXiv2019

Properties of Quantum Reactivity for a Multipartite State

We discuss the properties of quantum state reactivity as a measure for quantum correlation. This information geometry-based definition is a generalization of the two qubit construction of Schumacher to multipartite quantum states. It requires a generalization of information distance to information areas as well as to higher-dimensional volumes. The reactivity is defined in the usual chemistry way as a ratio of surface area to volume. The reactivity is an average over all detector settings. We show that this measure posses the key features required for a measure of quantum correlation. We show that it is invariant under local unitary transformations, non-increasing under local operations and classical communication, and monotonic. Its maximum bound can't be obtained using only classical correlation. Furthermore, reactivity is an analytic function of measurement probabilities and easily extendable to higher multipartite states.

quant-ph↗

arXiv2019

Quantum Reactivity: A Measure of Quantum Correlation

Defining a robust measure of quantum correlation for multipartite states is an unresolved and challenging problem. Existing measures of quantum correlation are either not scalable or do not satisfy all the accepted properties of a measure of quantum correlation. We introduce a novel geometric measure of quantum correlation that we refer to as quantum reactivity. This measure is extendable to an arbitrary large number of qubits and satisfies the required properties of monotonicity and invariance under unitary operations. Our approach is based on generalization of Schumacher's singlet state triangle inequality that used an information geometry--based entropic distance. We define quantum reactivity as the familiar ratio of surface area to volume. To accomplish this, we use a generalization of information distance to area, volume and higher--dimensional volumes. We examine a spectrum of multipartite states (Werner, W, GHZ etc.) and demonstrate that the quantum reactivity measure is a monotonic function for quantum correlation which satisfies all the properties of a measure for quantum correlation, and provides an ordering of these quantum states as to their degree of correlation.

quant-ph↗