interaction free measurement

One of the defining characteristicts of Quantum mechanics is that the effect of an observer on an experment cannot be made vanishingly small -- an assumption which classical physics had assumed. However, interaction free measurements have almost provided a way around that.

Consider the simplest possible experement -- we wish to determine whether there is an object on the table in front of us. Classically, we can shine a flashlight on the table, and look for reflected light. The heating effect of the light can be made arbitrarily small, within the limits of our flashlight and detector, by dimming the light until the total power is as small as we like. Quantum mechanically, however, we cannot use less than one photon -- which could be a problem for a sensitive photographic plate or a single atom in a delicate state, perhaps a qubit in a quantum computer.

Now consider a Mach-Zehnder Inteferometer as shown:

                  2
                  ^
                  |
     M/ - - - - - / -> 1
                H  
      |           |
      
      |           |
        H
in--> / - - - - - / M

The /s marked M are mirrors, and those marked H are half-silvered mirrors. An incoming photon at the location marked "in" will have its amplitude split between taking the top path and the bottom path. If properly set up, the intereference effects of photons wave function will cause destructive interference at the (2) port, and constructive interference at the (1) port. Thus, every photon will exit the apparatus at the (1) port, and none at (2).

Now, imagine that you block the upper path, by putting your hand, or a photodetector there. With the upper path blocked, there is only one path to the final mirror, and no interference is possible. These are the possiblities:

1. 50% probability the photon takes the upper path, and is absorbed by our blockade. Since we don't see the photon exit, we know the object is there, but we have also hit our atom, or photodetector, or whatever. So far, things don't look good.
2. 50% probability the photon takes the lower path, then:
   1. 50% probability the photon exits through detector 1, in which case we learn nothing, and repeat the experement.
   2. 50% probability the photon exits through detector 2. This could not have happened if the upper path were not blocked, yet since we collected our photon, it did not hit the block.

So, we lose about twice as often as we win, for 33% efficiency. By making the first half-silvered mirror with very low reflectivity, and the final mirror with correspondingly low transmissivity, we can raise the efficiency to 50%, though the number of trials we have to do before we know (and hence the time it takes to do the experement) goes up.

There are a number of variations on this principle that a devious experementor can make. By using a variation of the Quantum Zeno Effect, we can increase the efficiency arbitrarily close to 100%, though again, usually at the cost of the time needed to perform a sucessful measurement