Entangled Three-Particle State: Spin and Uncertainty

Question:
Consider the three-particle state: |+ − − > −| − −+ >
a) Is this an entangled state? Justify your answer.
b) Compute the expectation value of the z-component Sz of the spin angular momentum S =½ ℏ σ.
c) Compute the uncertainty in Sz .
d) Similarly, compute the uncertainty in Sx .
e) Show that your results from parts (c) and (d) are consistent with the uncertainty principle.

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