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
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
