DLCZ protocol - what does the beamsplitter do?

[zje]

I might be a little out of my league, but I'm trying to work through the DLCZ protocol for quantum communication (http://arxiv.org/abs/quant-ph/0105105). I've read the paper and gone through the introductory parts of this thesis: http://thesis.library.caltech.edu/2059/, but I'm still unclear on a very fundamental point:

What does the beamsplitter in FIG 1 of the arxiv paper do? Specifically, it boils down to the following question:
Why does a click in D1 or D2 signal entanglement of the atomic ensembles?

Thanks so much for your help! I'm really curious to figure this out and I realize that this probably stems from my lack of understanding in how a beam splitter works. Every reference I've read just states that a click means entanglement was successful.

 

[vtahmoorian]

As far as I understood, since we are working with two ensemble in DLCZ,we face two modes regarding to two possible stokes photons coming from two distinct ensemble A and B, each mode is an operator which includes two different stokes photon operators, take them as d and d~...d=a*exp(-iφa)+b*exp(-iφb)/√2 and d~=a*exp(-iφa)-b*exp(-iφb)/√2 ...each of these possible photon modes can be detected at either of detectors,a detection of single photon in d for example, projects the state of two atomic ensemble in a specific entangled state .
By the way the role of beam splitter is splitting the the beams coming from two ensemble in 50%-50% and send them to detectors D and D~, so that we can sense the interfered photons there.
I suggest you also to read http://cms.unige.ch/gap/quantum/wiki/_media/publications:bib:revmodphys.83.33.pdf

 

[Zarqon]

The point of the beamsplitter is to overlap the photon modes to make their origin path indistinguishable. If there is a click in one of the detectors, then you know that one photon has come from one of the samples, but because of the beamsplitter, there is fundamentally no way of knowing from which sample it originated, and they consequently become entangled.

So, in short, the entangledment comes directly from the indistinguishability. Was that more clear?