Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like state and 9 families of 4-qubit entangled states

Abstract

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 $\frac{1}{\sqrt{2}}\left(|{\Psi }_0⟩|0⟩+|{\Psi }_1⟩|1⟩\right)$ from the partially entangled $(n+1)$-qubit normalized state $\alpha |{\Psi }_0⟩|0⟩+\beta |{\Psi }_1⟩|1⟩$, where $⟨{\Psi }_1|{\Psi }_0⟩=0$ and $|\alpha |\ne \frac{1}{\sqrt{2}}$. It is also shown that W, GHZ, GHZ-like, Bell and cat states and specific states from the 9 SLOCC-nonequivalent families of 4-qubit entangled states can be expressed as $\frac{1}{\sqrt{2}}\left(|{\Psi }_0⟩|0⟩+|{\Psi }_1⟩|1⟩\right)$ and consequently the last two ECPs proposed here are applicable to all these states. Quantum circuits for implementation of the proposed ECPs are provided and it is shown that the proposed ECPs can be realized using linear optics. Efficiency of the ECPs are studied using a recently introduced quantitative measure (Phys. Rev. A $\text{85}$, 012307 (2012)). Limitations of the measure are also reported.

11 pages 7 figures

References in corpus (10)

• Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics
• A classification of entanglement in three-qubit systems
• Hyperentanglement concentration for two-photon four-qubit systems with linear optics
• Four-qubit entanglement from string theory
• All Maximally Entangled Four Qubits States
• Three-tangle for mixtures of generalized GHZ and generalized W states
• Experimental realization of linear-optical partial SWAP gates
• The rebit three-tangle and its relation to two-qubit entanglement
• Normal Forms and Tensor Ranks of Pure States of Four Qubits
• Teleportation and Superdense coding with Genuine quadripartite entangled states

Cited by in corpus (5)

• Self-error-rejecting photonic qubit transmission in polarization-spatial modes with linear optical elements
• Hierarchical Quantum Network using Hybrid Entanglement
• General structures of reversible and quantum gates
• Linear optics based entanglement concentration protocols for Cluster-type entangled coherent state
• Entanglement concentration protocols for GHZ-type entangled coherent state based on linear optics