The Elitzur-Vaidman bomb test

So I’ve been quite busy which I why I haven’t yet responded to the comments on my previous post, but now it’s Saturday!  Realizing that not everyone knows the Elitzur-Vaidman bomb test, I’ll give a full description to further discussion along!

Imagine a simplified Mach-Zender interferometer in which a beam of light passes through a beamsplitter (usually some kind of crystal) becoming two beams of light.  The two beams bounce off a couple of mirrors and meet again at a second beamsplitter, each splitting again with some from each merging.  Thus, in the diagram below, the yellow beams are each a mixture of the green and red beams (sort of).

If you set up the beamsplitter’s properly, you can create interference such that detector D0 always registers photons and D1 never does.  In other words, the probability that D0 detects a photon is 1 and the probability that D1 does is 0.  This is because we have set it up such that we have constructive interference leading to D0 and destructive interference leading to D1.

Suppose now that we stick our hand in the path of the green beam such that the photons are absorbed by our hand.  This destroys any interference effects.  Any single photon entering the device at the beginning, then, has a 50-50 chance of hitting our hand.  If it doesn’t, it goes through the red beam and then has an equal chance of hitting D0 or D1.  So the probabilities are

• Photon reaches D0 = 1/4
• Photon reaches D1 = 1/4
• Photon reaches hand = 1/2

Notice that by blocking the green beam with a hand, we have actually increased the probability that the photon reaches D1.

Now suppose there is a factory that produces bombs triggered by a single photon of light.  Because of manufacturing defects, though, some come off the assembly line without working triggers.  Photons passing through these wouldn’t do anything and the bombs would be labeled as duds.  How do the factory managers, however, tell if some of the bombs are in working order without triggering them?  They want at least some working bombs when they’re done otherwise the Army won’t be too pleased.

They do it using the above Mach-Zender interferometer that is preset to always produce constructive interference at D0 and destructive at D1.  Instead of placing a hand in the green beam, a bomb (actually its trigger) is placed there.  The trigger acts like a photon detector and the results will be

Bomb is a dud

• Photon reaches D0 = 1
• Photon reaches D1 = 0
• Bomb explodes = 0

Bomb is working

• Photon reaches D0 = 1/4
• Photon reaches D1 = 1/4
• Bomb explodes = 1/2

Now put a bomb fresh off the assembly line into the device (and back away – far, far away).  If the bomb explodes, it was in working order but has now been wasted (the cost of quality control under such conditions is losing a few bombs).  If the photon is detected by D0, the test is inconclusive and can be run again (if, after many repeated trials, the photon keeps showing up at D0, the bomb is probably a dud).  But if the photon ever reaches D1 – which is should do 25% of the time – then the managers know that the unexploded bomb is in working order even though the bomb never detects the passage of the photon!

Presumably someone out there has done a calculation to figure out the maximum percentage of usable bombs one can hope to get out of this by repeating the D0 tests.  I don’t know what the answer is but it’s not quite as simple as it looks since it is not clear exactly what percentage of total photons is detected at D0 (remember, it’s only 1/4 if the bombs are all working!).

Best homework problem ever

Exercise 2.16 in Quantum Processes, Systems, and Information by Ben Schumacher and Mike Westmoreland refers to the Elitzur-Vaidman bomb test and reads, “If you do not find the previous paragraph strange and disturbing, re-read it.”

Random observations (vacation filler)

Been on vacation, so I haven’t posted recently.  But here are some interesting tidbits I’ve come across recently:

• Sikorsky will be coming out with an electric helicopter later this year – and I don’t mean and R/C heli either!  Very cool.
• I can’t say it better than the headline: Extreme Hobbyists Put Satellites Into Orbit With $8,000 Kits.  I see a departmental project in our future…
• Now is a great time to be a quantum chemist.

Continuous or discrete?

Just a few of the questions running through my head today as I head out to buy propane, gas for the tractor, and to go fishing:

At the most fundamental level, is the universe continuous or discrete?  Or maybe it’s continuous but looks discrete to us?  Could we ever even know for sure?  (And, on a related note, what the hell is spacetime anyway?  Is it just a convenient way to keep track of the location of ‘events’ or does it have some real, physical nature, i.e. is it ontological?)

New position at the University of Nottingham

My friend Ivette sent me this announcement of a new position working with her at the U. of Nottingham.  Note the deadline:

Please note that applications should be made online through the University’s recruitment website
http://jobs.nottingham.ac.uk/

School of Mathematical Sciences – Division of Applied Mathematics
Research Fellow
Reference : SCI870
Closing Date : 05 August 2010
Salary : £27,319 to £35,646 per annum, depending on skills and experience
This post is available immediately and will be offered on a fixed-term contract for a period of one year

Applications are invited for the above post to work with Dr Ivette Fuentes on an EPSRC funded project on the overlap of quantum information theory and relativity. The research is aiming at exploiting relativistic effects to improve quantum information tasks and finding applications of quantum information to foundational questions in gravity. For information about the School of Mathematical Sciences, one of the most active in the UK, see:http://www.maths.nottingham.ac.uk/.

Candidates should have a PhD in mathematics or physics and experience with quantum theory and relativity. Knowledge of quantum information theory, quantum optics and/or quantum field theory is also desirable. They must be confident, organised, have good communication skills and enjoy working with a variety of different people across discipline boundaries.

Informal enquiries may be addressed to Dr I Fuentes, Email:ivette.fuentes@nottingham.ac.uk. Please note that applications sent directly to this Email address will not be accepted.

Revisiting Aspect’s third experiment

I often wonder how many people who work in quantum foundations have actually read Aspect’s papers describing his famous experiments, particularly his third.  In the ensuing years it seems to me that we have tried to bury the implications of non-locality in this paper beneath layers and layers of often impenetrable mathematics and philosophical hyperbole.  As Aspect says in the paper,

In this experiment, switching between the two channels occurs about each 10 ns. Since this delay, as well as the lifetime of the intermediate level of the cascade (5 ns), is small compared to L/c (40 ns), a detection event on one side and the corresponding change of orientation on the other side are separated by a spacelike interval.

The italics are mine. The key word here, to me, is corresponding. If the detection event on the one side and the change in orientation on the other are connected in some way and they are spacelike separated, I fail to see how we can so blithely rule out a violation of Einstein causality.  While you may beg to differ that it is not “blithe,” it appears as such to an empiricist.  If you insist on talking about abstractions like C*-algebras, then you’re opening another can of worms and asking me to believe in the physical existence of these algebras.  In other words, the more abstract we get, the more we really need to decide whether these mathematical “objects” truly are real or not.  Otherwise, it just looks like a lot of overblown rhetoric to me.