Broadcasting of entanglement in three-particle GHZ state via quantum copying

We introduce entanglement measures to describe entanglement in a threeparticle system and apply it to studying broadcasting of entanglement in three-particle GHZ state. We show that entanglement of three-qubit GHZ state can be partially broadcasted with the help of local or non-local copying processes. It is found that non-local cloning is much more efficient than local cloning for the broadcasting of entanglement. PACS number(s): 03.75.Fi, 03.65Bz; 32.80.Pj, 74.20.De Typeset using REVTEX 1 Quantum entanglement, first noted by Einstein-Podolsky-Rosen and Schrödinger [1], is one of the essential features of quantum mechanics. It has been well known that quntum entanglement plays a key role in many such applications like quantum teleportation [2], super-dense coding [3], quantum error correction [4], and quantum computational speedups [5]. Recently, maximally entangled states of three particles, i.e., three-particle GHZ states, have been produced experimentally [6]. Usually, it is difficult to obtain ideal entangled multi-particle state. An interesting question is: whether there are ways which can broadcast the entanglement of correlated systems? The answer is ok. Masiak and Knight [7] have shown that copies of entangled pair of qubits can be genetated through using a universal quantum cloning machine (UQCM) [8] , although the degree of entanglement of the resultant copies is substantially reduced due to a residual entanglement between the copied output and the copying machine. On the other hand, up to now there is not an appropriate measure to describe quantatively the entanglement of three and more subsystems due to the high complexity of entanglement in multi-particle system [9]. The purpose of this paper is to propose measures of entanglement in three qubit system in terms of the entanglement tensor approach [10], and use these measures to investigate broadcasting of entanglement [11] in three-particle GHZ state. Consider a system consisting of three qubits. The density operator of the system can be expanded as a sum of tensor products in terms of Puali matrices, ρ̂ = 1 8 [1̂⊗ 1̂⊗ 1̂ + 3