Assignment 7, due Nov. 23, 2005

Skim or Read or Pass in Front of your Eyes:

D. P. DiVincenzo, "The Physical Implementation of Quantum Computation", April 22, 2001, quant-ph/0002077; a good review of implementation requirements for quantum computing. Quant-ph is a web archive of papers, and I put a local copy on the course page, which is posted in the usual place. As has happened before, you may not have the background for some of this paper; skip those parts and don't worry about it. Much of the paper may make sense. We started talking about "qubits" -- they're bits behind the "quantum curtain" and don't have the value 0 or 1 unless you look at them, just like the electrons in Feynman's lecture. So people write their state as a combination of |0> and |1>... more next week.

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Problems:

Try to answer these two problems by yourself, without using books, friends, or the internet. If you have trouble, then look up the answers (which are well known), and, of course, reference your sources.

1. A beam splitter, or semi-transparent mirror, reduces the intensity of a beam of particles. The "particles" are often photons, but you can imagine beam splitters for any other particles, like electrons, protons, neutrons, quarks, etc. Describe in detail what happens when a beam of very small particles (sub-atomic scale) is aimed a beam splitter as the intensity of the beam is made smaller and smaller, say down to one particle per year.

2. A Mach-Zehnder interferometer is a device in which a beam is split 50/50 by a beamsplitter, and then recombined at a second beam splitter. Here's a picture by Dennis van der Linden and Pascal van der Veeken, students in Molecular Sciences at Wageningen University in the Netherlands. (This looks like a nice site, a thesis project. As I said above, don't peek unless you give up. Then see keyword "locality" there.)



Describe in detail what happens when the beam is very low intensity, say one particle per year.

By the way, if you think this is just a made-up experiment, you can buy your own (don't peek) Mach-Zehnder interferometer for light off-the-shelf. It has practical uses.

PS: This is Ernst Mach, as in Mach 2.