Quantum entropy and polarization measurements of the two-photon system

TL;DR

This paper derives an exact formula for the von Neumann entropy of a two-photon polarization system with a five-parameter density matrix, exploring entropy behavior and quantum conditional entropy in various states.

Contribution

It provides a novel analytical expression for the entropy of a bipartite two-photon system and analyzes its dependence on polarization parameters, revealing exotic state transitions.

Findings

Exact entropy expression for five-parameter polarization states

Identification of exotic and non-exotic states with negative quantum conditional entropy

Visualization of entropy dependence and state transitions

Abstract

We consider the bipartite state of a two-photon polarization system and obtain the exact analytical expression for the von Neumann entropy in the particular case of a 5-parameter polarization density matrix. We investigate and graphically illustrate the dependence of the entropy on these five parameters, in particular, the existence of exotic, transition from exotic to non-exotic, and non-exotic states, where the quantum conditional entropy is negative, both positive and negative, and positive, respectively. We study the "cooling" or "heating" effect that follows from the reduced density of photon 2 when a measurement is performed on photon 1.