I am interested in the POVM example Nielsen and Chuang give in the discussion about indistinguishability. They define the POVM

$E_1 = \frac{\sqrt{2}}{1+\sqrt{2}} |1\rangle \langle 1|$,

$E_2 = \frac{\sqrt{2}}{2(1+\sqrt{2})} (|0\rangle - |1\rangle)( \langle 0| - \langle 1|)$,

$E_3 = I - E_1 - E_2$

Now based on Naimarks theorem I can represent this POVM in an enlarged Hilbert space, entangling the ancilla space with the physical space and then apply a projective measurement on the ancilla space.

My questions:

1. How large does the ancilla Hilbert space need to be? I guess in this case it needs to be at least a qutrit to include the 3 possible measurement outcomes, but does it need to be even larger?
2. How does the entangling $U$ need to look like to implement above POVM in this concrete example?