Suppose I have a state in qiskit which is a product of states, for example:
$| \psi \rangle = \left(\frac{ \sqrt{2} | 000 \rangle + |111 \rangle} {\sqrt 3}\right) \left( \frac{ |00 \rangle + |11 \rangle}{\sqrt 2} \right) \left( |01 \rangle \right) $
I want to write a code which will return the state of qubit 4 and 5, i.e. $\frac{|00 \rangle + |11 \rangle}{\sqrt 2}$. One way to do this would be to use save_density_matrix(qubits = [4, 5]), and covert that to a statevector. However, that takes too much time if I am doing this many times. Given that I know that the qubits 4 and 5 are unentangled from the rest of the system, is there a way to extract their state directly?
Even if I take the partial trace, the output is still a density matrix.
