Entanglement of quantum circular states of light

TL;DR

This paper introduces a method to calculate the entanglement of superpositions of two-mode coherent states arranged on a circle in phase space, providing analytical expressions for rotationally-invariant states and exploring their properties.

Contribution

It presents a general approach for entanglement calculation and derives analytical formulas for rotationally-invariant circular states, enhancing understanding of their structure and applications.

Findings

Analytical expressions for entanglement of rotationally-invariant circular states.

Dependence of entanglement on circle radius and number of superposition components.

Rotationally-invariant circular states form an orthonormal basis for harmonic oscillator states.

Abstract

We present a general approach to calculating the entanglement of formation for superpositions of two-mode coherent states, placed equidistantly on a circle in the phase space. We show that in the particular case of rotationally-invariant circular states the Schmidt decomposition of two modes, and therefore the value of their entanglement, are given by analytical expressions. We analyse the dependence of the entanglement on the radius of the circle and number of components in the superposition. We also show that the set of rotationally-invariant circular states creates an orthonormal basis in the state space of the harmonic oscillator, and this basis is advantageous for representation of other circular states of light.