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I have a state $|p\rangle$ that has an extractable Bell state and I want to write it as a Bell state, $|b\rangle$, with a local unitary acting on one side. Basically I am trying to find a local unitary $U$ that satisfies:

$$ |p\rangle = (U \otimes 1)|b\rangle $$

$|b\rangle$ is a Bell state $|p\rangle$ is a known state with an extractable Bell state

Does anyone know how to do this?

My initial guess was $U \otimes 1 = |p \rangle \langle b|$ but this isn't a unitary operator.

The known state $|p\rangle$ is in state vector form. I am using Python an NumPy for reference.