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Physics 498-QOI: Topics in Quantum Optics and Quantum Information
Problem set #7a [7]
{Distributed 3/6; due 3/13}
This problem set will quicken our discussions of quantum teleportation. I’m sure you will
find it very easy, and not at all long.
1. [4] Bell-state analysis. For each of the four Bell states
|y±Ò = (|HÒ1|VÒ2±|VÒ1|HÒ2)/sqrt(2); |j± Ò = (|HÒ1|HÒ2±|VÒ1|VÒ2)/sqrt(2)
write down the state after the two spatial modes are combined on a 50-50 (non-polarizing)
beamsplitter (i.e., like in the Hong-Ou-Mandel interferometer). There are several ways to do
this. One is to simply write the Bell state in terms of creation operators
(e.g., |j+ Ò = (a†H,1 a†H,2 + a†V,1 a†V,2)/sqrt(2)|0>), and then propagate each operator through the
beamsplitter.
2. [3] Teleportation. Consider a qubit |c>C in an arbitrary (pure) polarization state (as in PS
#2, 6b), and an entangled pair shared by Alice and Bob, in the maximally entangled state
|j+ ÒA,B, where the subscripts indicate that Alice has one photon and Bob the other.
Write the joint state |c>C|j+ ÒA,B in terms of the four Bell states |y±ÒA,C and |j±ÒA,C.
