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Elitzur-Vaidman bomb tester

  1. Jan 4, 2010 #1
    Hey, I'm trying to understand the Elitzur-Vaidman bomb tester since it is an essentially quantum mechanic effect, but I haven't been able to find a technical quantum mechanical treatment of the subject though I've found plenty of non-technical treatments and a few pseudo-classical treatments.

    The way I understand the setup is that we start with a photon prepared in an entangled state between going on the top and bottom arms of the bomb tester. (Let's call this state |T> + |B>) The bottom photon then encounters a bomb that is live or dead. I suppose I could treat this bomb as an operator, either being a projection operator (live bomb, projects onto |T>) or identity operator (dead bomb), but this would operate on the entire state at once, and that doesn't seem quite right. Then I really don't understand what's going on with the half-silvered mirror at the end. It seems to make the top and bottom arms of the bomb tester recombine and interfere, but I can't figure out what that means in terms of operators.

    Can someone help me out?
  2. jcsd
  3. Jan 5, 2010 #2


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    The bomb is not an operator of the kind you suggest. It is better to think of bomb as a specific classical potential V(x) playing a role in the Schrodinger equation. More precisely, the bomb is nothing but a mirror that reflects the wave function.
  4. Jan 5, 2010 #3
    Ok, then what about 2nd half silvered mirror? Should I treat the mirror as an operator?

    I want to know the proper quantum mechanical treatment of this setup because I want to design an extension to it that I think should be possible where the bottom arm, instead of testing one bomb, tests and reports information about a set of boolean values.
  5. Jan 5, 2010 #4


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    Just so we know we're talking about the same thing ...
    The bomb-tester works on the principle that if there is any chance of getting 'which-path' information, the interference at the last mirror is destroyed. A live bomb acts like a photon-detector, but a dud bomb is just a mirror. However if the bomb is live, there's a probability of 1/2 that the photon will not trigger a live bomb, but there will be no interference, telling us the bomb is live. Of course, half of the live bombs will explode, making this a rather expensive practice.

    There are two set-ups here, one with a live bomb and one with a dud. You can't combine the two unless you have a probability for selecting a dud. In that case you'd have 3 possible outcomes. The state space would be a sort of tensor product of the two-state vector a|dud>+b|live> and c|boom> + d|T>. Shouldn't you write the state space out first then the operators ?
  6. Jan 5, 2010 #5
    These papers may be helpful:

    "[URL [Broken] Photon quantum mechanics and beam splitters
    C. H. Holbrow,a) E. Galvez, and M. E. Parks[/URL]

    "[URL [Broken] Interaction-Free Measurements
    Lev Vaidman[/URL]

    3) A quantum mechanical description of electromagnetic and atom Mach-Zehnder interferometers
    Y Ben-Aryeh et al 2001 J. Opt. B: Quantum Semiclass. Opt. 3 138-145

    4) A quantum description of the beam splitter
    A Luis et al 1995 Quantum Semiclass. Opt. 7 153-160
    Last edited by a moderator: May 4, 2017
  7. Jan 5, 2010 #6


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    Thank you, Edgardo.

    What I've described is the Penrose machine, not the EV bomb-tester. Whoops.
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