INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL J. Phys. A: Math. Gen. 38 (2005) 9087–9103 doi:10.1088/0305-4470/38/41/017 Control of entanglement in Ising-type networks with one and two excitations J Novotn´ y 1 , M Štefa ˇ n´ ak 1 , T Kiss 2 and I Jex 1 1 Department of Physics, FJFI ˇ CVUT, Bˇ rehov´ a 7, 115 19 Praha 1, Star´ e Mˇ esto, Czech Republic 2 Department of Nonlinear and Quantum Optics, Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, Konkoly-Thege u. 29-33, H-1121 Budapest, Hungary Received 11 May 2005, in final form 6 September 2005 Published 28 September 2005 Online at stacks.iop.org/JPhysA/38/9087 Abstract We analyse the dynamics of single- and two-particle states in Ising-type networks. The mutual entanglement is quantified using the concept of concurrence. We derive explicit expressions for the concurrence for single- and two-particle initial states in arbitrary passive networks and specify the result for Ising-type networks. We show how to design a network to prepare a prescribed pattern of entanglement for one excitation and study the maximum attainable entanglement for passive optical networks in general. The effect of network randomization on the average entanglement is also studied. PACS numbers: 42.50.−p, 42.50.Ar, 03.65.Ud 1. Introduction Linear optical instruments are particularly simple and versatile. They include beam splitters [1], phase shifters and parametric amplifiers. All of them are characterized by simple (linear) relations between the input and output fields. The creation operator of the outputs are given as linear combinations of input creation and annihilation operators. The coefficients of the linear transform characterize the physical properties of the devices and determine the characteristics of the output once the input is specified. The linear elements represent interesting devices in their own right. They can be used to demonstrate striking quantum effects like destructive interference (on the beam splitter) which has quite a number of interesting applications ranging from simple beam splitting to quantum state identification and comparison [2]. The other large area of applications is connected with larger systems formed out of beam splitters and phase shifters. In this way, we obtain interferometers with a broad field of applications. Such arrangements of passive optical elements (networks) can be used for many purposes. They can serve naturally as real interferometers and can be applied to many practical applications such as many-state comparison, quantum state detection or photon number identification. 0305-4470/05/419087+17$30.00 © 2005 IOP Publishing Ltd Printed in the UK 9087