Entangling capabilities of Symmetric two qubit gates

TL;DR

This paper explores how symmetric two-qubit gates, modeled via Hamiltonians like NMR and Lipkin-Meshkov-Glick, can generate maximally entangled states, analyzing their properties and entangling power within a symmetric subspace.

Contribution

It introduces a method using SU(3) generators to analyze entangling capabilities of symmetric two-qubit gates and characterizes perfect entanglers in this context.

Findings

Hamiltonian decomposition using SU(3) generators enables analysis of entangling power.

Identification of perfect entanglers capable of generating maximally entangled states.

Application of the framework to symmetric two-qubit systems in quantum processing.

Abstract

Our work addresses the problem of generating maximally entangled two spin-1/2 (qubit) symmetric states using NMR, NQR, Lipkin-Meshkov-Glick Hamiltonians. Time evolution of such Hamiltonians provides various logic gates which can be used for quantum processing tasks. Pairs of spin-1/2's have modeled a wide range of problems in physics. Here we are interested in two spin-1/2 symmetric states which belong to a subspace spanned by the angular momentum basis {|j = 1, {\mu}>; {\mu} = +1, 0,-1}. Our technique relies on the decomposition of a Hamiltonian in terms of SU(3) generators. In this context, we define a set of linearly independent, traceless, Hermitian operators which provides an alternate set of SU(n) generators. These matrices are constructed out of angular momentum operators Jx,Jy,Jz. We construct and study the properties of perfect entanglers acting on a symmetric subspace i.e., spin-1 operators that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power.