Question

2. [10pts) In considering the EPR experiment, we used the anti-correlation property of the spin-0 state as an essential aspect of the analysis. In this question you are going to show that this property does not depend on the choice of direction of axis of the Stern-Gerlach analyzers. Show that the entangled state: |4= (1 131] 1)2 – 1 1/)2) is physically equivalent to the general state: 4) = - (11)in1)2n - | 1)in 1)2n) where ñ is a unit direction vector in an arbitrary direction. Conclusion: the two observers record perfect anti-correlations independent of the orientation of their detectors, as long as both are aligned along the same direction.

Answer 1

Answer h Given information, The entangled state, 1993 - na CT sold >2-147, 1932) Here, f_indicaty (t) Vi-indicaty (-). Soi rewrite the above equation, tips a{f+vf->2 -*-*11+] – Iton, t-sn in terms of It>, b-x is a 14 >= cos f \t> tsin.Be181-* - l->n = sino 1+2-e1% cos oll->

Now, The general state, lø>= 1 [lt an tson-14, 2n/p> en] Heres a means ↑ meary - (+) do muans -(-) so) Tops ma Cityint->»n -1->on't>zn] - Now, Let's analyse the first tim H-m 1-2an+ſcosoja lt >, tsing e * -->] {sin ois 1+ 22 -1.605.04) >] = cose sing1+xıltmete esinę l->ift), --Cosie I+xz 1->2218 21% sinq.coso |->,

similarly, I+>10 1+ >en = sinq.cosol2. +,1zz te ipsin”012. [+>,1->2 el castell->11+>2-2 Pcosęsinel-> |* Here, using above. Belations It>n ->2n-|->init >an becomes, [<<+1k-1-4-11th love SO) 14>- de' [1+2->2-1-3, 1+ >>] When we calculata probability amplitucha, we can safely drop elit, because it cancels with complex conjugate. So, a phase does not change state. SO) 193 m (10-08-22-->11*ne]