Concurrence as a measure of entanglement

[LagrangeEuler]

In book Quantum computing explained by David Mahon concurrence, as a measure of entanglement is defined as
C(\psi)=|\langle \psi|\tilde{\psi} \rangle |
where $|\psi\rangle=Y \otimes Y|\psi^*\rangle$
or with density matrix
$\rho(Y \otimes Y)\rho^{\dagger}(Y \otimes Y)$.
Could someone explain me what is $|\tilde{\psi}\rangle$ and $Y$?

 

[DrClaude]

where $|\psi\rangle=Y \otimes Y|\psi^*\rangle$
or with density matrix
$\rho(Y \otimes Y)\rho^{\dagger}(Y \otimes Y)$.

That's actually
$$|\tilde{\psi} \rangle=Y \otimes Y|\psi^*\rangle $$
and
$$
\tilde{\rho} = (Y \otimes Y)\rho^{\dagger}(Y \otimes Y)
$$
$Y$ is the Pauli spin matrix $\sigma_y$.