A Werner state of two qubits has singlet weight .

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Problem

A Werner state ρW=w∣Ψ−⟩⟨Ψ−∣+(1−w)I/4\rho_W=w|\Psi^-\rangle\langle\Psi^-|+(1-w)I/4 of two qubits has singlet weight w=0.9w=0.9. ((a)) Find the eigenvalues of the partial transpose ρWTB\rho_W^{T_B} and decide whether the state is entangled. ((b)) Find the largest CHSH value it can give and decide whether it violates the CHSH inequality. ((c)) Find the singlet fraction fsf_{\rm s}. ((d)) State the reduced density operator of each qubit.

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