Equivalent-neighbor interactions of the conduction-band electron spins of quantum dots in the model of Imamoḡlu et al. [Phys. Rev. Lett. 83, 4204 (1999)] are analyzed. An analytical solution and its Schmidt decomposition are found and applied to evaluate how much the initially excited dots can be entangled with the remaining dots if all of them are initially disentangled. It is demonstrated that perfect maximally entangled states (MES’s) can only be generated in systems of up to six dots with a single dot initially excited. It is also shown that highly entangled states, approximating the MES’s with good accuracy, can still be generated in systems of odd numbers of dots with almost half of them excited. A sudden decrease of entanglement is observed on increasing the total number of dots in a system with a fixed number of excitations.

• Received 5 March 2002

DOI:https://doi.org/10.1103/PhysRevA.65.062321