Homework 8 ex 5

Homework 8 ex 5

by Cécile Tangwendi Michel -
Number of replies: 1

Hello,


I have difficulties to express the projector P. 

I know that there is a local measurement for particules 1,3 and 5 and therefore the particules 2,4 and 6 don't do any operation (we can express this as a unitary matrix). 

However I don't know how to express the projector ?

In reply to Cécile Tangwendi Michel

Re: Homework 8 ex 5

by Nicolas Macris -
Hi,
The measurement projects the particles of 1,3,5 on the state | GHZ >_135 and since there is no measurement for 1,2,4 the global projector is

P = | GHZ >_135 < GHZ |_135 x Id_246

(here x is the tensor product and Id the identity matrix for 124. This is a 8x8 identity matrix since the Hilbert space of 246 is C^2 x C^2 xC^2 ie., it is 8 dimensional. Note that P^2 = P so it is indeed a projector in the total Hilbert space of 123456.

N.M