Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like state and nine families of 4-qubit entangled states

摘要

Three entanglement concentration protocols (ECPs) are proposed. The first ECP and a modified version of that are shown to be useful for the creation of maximally entangled cat and GHZ-like states from their non-maximally entangled counterparts. The last two ECPs are designed for the creation of maximally entangled (n + 1)-qubit state 1/root 2 (vertical bar Psi(0)>vertical bar 0 > + vertical bar Psi(1)>vertical bar 1 >) from the partially entangled (n + 1)-qubit normalized state alpha vertical bar Psi(0)>vertical bar(0)> + beta vertical bar Psi(1)>vertical bar 1 >, where = 0 and vertical bar alpha vertical bar not equal 1/root 2. It is also shown that W, GHZ, GHZ-like, Bell and cat states and specific states from the nine SLOCC-nonequivalent families of 4-qubit entangled states can be expressed as 1/root 2 (vertical bar Psi(0)>vertical bar 0 > + vertical bar Psi(1)>vertical bar 1 >), and consequently, the last two ECPs proposed here are applicable to all these states. Quantum circuits for the implementation of the proposed ECPs are provided, and it is shown that the proposed ECPs can be realized using linear optics. The efficiency of the ECPs is studied using a recently introduced quantitative measure (Sheng et al., Phys Rev A 85:012307, 2012). Limitations of the measure are also reported.