Manuscript En01-A@1 · En01-A.tex · proposition · 558b972b

Proposition: Closed forms

Frauchiger–Renner probabilities and parameter geometry › Complex amplitudes and the order-two stratum · lines 2282–2302 · proof included or linked

En01-A@1#prop:frcomplex

For the same effect $M$ ,

η_{M} ({1}) η_{M} ({2}) η_{M} ({1, 2}) = \frac{1}{2} (x y cos α - x z cos β), = \frac{1}{2} (y z cos (α - β) - x z cos β), = \frac{1}{2} x z cos β .

Proof. The three cross contributions are

- \frac{1}{2} x y cos α, - \frac{1}{2} y z cos (α - β), + \frac{1}{2} x z cos β .

Apply the scalar localization identities used above.

Displayed formulas in this passage

unlabeled · line 2284
$η_{M} ({1}) η_{M} ({2}) η_{M} ({1, 2}) = \frac{1}{2} (x y cos α - x z cos β), = \frac{1}{2} (y z cos (α - β) - x z cos β), = \frac{1}{2} x z cos β .$
unlabeled · line 2296
$- \frac{1}{2} x y cos α, - \frac{1}{2} y z cos (α - β), + \frac{1}{2} x z cos β .$