Entangled SU(2) and SU(1,1) coherent states

TL;DR

This paper develops and analyzes entangled SU(2) and SU(1,1) coherent states, exploring their properties, special cases, and methods for generation, with applications to multiparticle systems and quantum information.

Contribution

It introduces new entangled coherent states, including binomial, negative binomial, and squeezed states, and discusses their generation and entanglement properties.

Findings

Entangled binomial states enable contraction to harmonic oscillator coherent states.

Methods for generating entangled SU(2) and SU(1,1) states are proposed.

Degrees of entanglement are calculated for various entangled states.

Abstract

Entangled SU(2) and SU(1,1) coherent states are developed as superpositions of multiparticle SU(2) and SU(1,1) coherent states. In certain cases, these are coherent states with respect to generalized su(2) and su(1,1) generators, and multiparticle parity states arise as a special case. As a special example of entangled SU(2) coherent states, entangled binomial states are introduced and these entangled binomial states enable the contraction from entangled SU(2) coherent states to entangled harmonic oscillator coherent states. Entangled SU(2) coherent states are discussed in the context of pairs of qubits. We also introduce the entangled negative binomial states and entangled squeezed states as examples of entangled SU(1,1) coherent states. A method for generating the entangled SU(2) and SU(1,1) coherent states is discussed and degrees of entanglement calculated. Two types of SU(1,1) coherent states are discussed in each case: Perelomov coherent states and Barut-Girardello coherent states.