Quantum and classical correlations in Bell three and four qubits, related to Hilbert-Schmidt decomposition

The present work studies quantum and classical correlations in 3-qubits and 4-qubits general Bell states, produced by operating with n B Braid operators on the computational basis of states. The analogies between the general 3qubits and 4-qubits Bell states and that of 2-qubits Bell states are discussed. The general Bell states are shown to be maximal entangled, i.e., with quantum correlations which are lost by tracing these states over one qubit, remaining only with classical correlations. The Hilbert–Schmidt (HS) decompositions for 3-qubits general Bell states are explored by using 63 parameters. The results are in agreement with concurrence and Peres-Horodecki criterion for the special cases of bipartite system. We show that by tracing 4-qubits general Bell state, which has quantum correlations, over one qubit we get a mixed state with only classical correlations. OCIS codes: (270.0270) Quantum Optics; 270.5585; Quantum information; 270.5565 (Quantum communications)