I1

Problem 1: Derive the commutation relations [oz, Ox] = 120y, ox, Oy ] = 1202, Oy, Oz] = 120x, where [oz, Ox] = 020x - OxOz Problem 2: Given the entangled Bell state |WAB) = #7 (IHA)|HB) + [VA)|VB)), use the new basis 1 1 IDA) = V2 (IHA) + IVA)), IAA) = VZ (IHA) - IVA)) for A and the same basis change for B, to show [/AB) = =, (IDA)IDB) + [AA)|AB)). Then use an arbitrary basis 10) = cos 0 |H) + sin e [V), |0) = - sin 0 [H) + cos 0 [V) To show [/AB) = (10A)10B) + 0A)|0 B))