Poisson Quantum Information

TL;DR

This paper develops a formalism for Poisson quantum states, deriving simple formulas for key information measures using an intensity operator, and explores classical analogs and channel effects.

Contribution

Introduces a Poisson limit approach for quantum states, defining the intensity operator and deriving formulas for quantum information measures and classical analogs.

Findings

Derived formulas for fidelity, Chernoff quantity, relative entropy, and Helstrom information in the Poisson quantum framework.

Introduced the intensity operator as a central unnormalized density-like object for Poisson states.

Showed how certain channels act simply on the intensity operators of Poisson states.

Abstract

By taking a Poisson limit for a sequence of rare quantum objects, I derive simple formulas for the Uhlmann fidelity, the quantum Chernoff quantity, the relative entropy, and the Helstrom information. I also present analogous formulas in classical information theory for a Poisson model. An operator called the intensity operator emerges as the central quantity in the formalism to describe Poisson states. It behaves like a density operator but is unnormalized. The formulas in terms of the intensity operators not only resemble the general formulas in terms of the density operators, but also coincide with some existing definitions of divergences between unnormalized positive-semidefinite matrices. Furthermore, I show that the effects of certain channels on Poisson states can be described by simple maps for the intensity operators.