Maximal Entanglement of Two-qubit States Constructed by Linearly Independent Coherent States

TL;DR

This paper derives the necessary and sufficient conditions for maximal entanglement in two-qubit states formed by linearly independent coherent states with real parameters, generalizing previous classifications of nonorthogonal states.

Contribution

It provides a new, generalized criterion for maximal entanglement in two-qubit states constructed from linearly independent coherent states with specific inner product conditions.

Findings

Derived necessary and sufficient conditions for maximal entanglement.

Extended classification of nonorthogonal states to a broader set.

Generalized previous results to states with real parameters and specific inner products.

Abstract

In this paper, we find the necessary and sufficient condition for the maximal entanglement of the state, $ |\psi>=\mu|\alpha>|\beta>+\lambda|\alpha>|\delta>+ \rho|\gamma>|\beta>+\nu|\gamma>|\delta>,$ constructed by linearly independent coherent states with \emph{real parameters} when $<\alpha|\gamma>=<\beta|\delta>$. This is a further generalization of the classified nonorthogonal states discussed in Ref. Physics Letters A {\bf{291}}, 73-76 (2001).