A peculiarly quantum measurement

It is often said that quantum theory introduces an inevitable, minimum,
disturbance into any measurement. This is true, but here I want to
describe something which at first sight appears to show exactly the
opposite effect, namely, how quantum theory enables us to make a
totally non-disturbing measurement of a type that is impossible in
classical physics.
We consider a two-state system which, in order to have a simple
picture, we regard as a box that can be either EMP?"Y (not contain a
particle) or FULL (contain a particle). From a large sample of such
boxes we are given the task of selecting one that we know is FULL.
The way to do this is to 'look' and see if the box contains a particle.
However, it turns out that one photon falling on the box will either pass
right through, if the box is EMPTY, or be absorbed and destroy the
particle, if the box is FULL. Since we require to use at least one photon
in order to look at the box it follows that, after we have looked, we
either confirm that the box is EMPTY, or we know that it was FULL,
but is so no longer. Clearly, it seems, we cannot select a box that
is certainly FULL. The act of verifying that it is Fuu would simply
destroy the particle.
Here, amazingly, quantum mechanics provides a way to accomplish
our task. We first construct a photon interferometer, as shown in
figure 30. The photons enter at A and reach a beam-splitter (halfsilvered
mirror) at B, where the wave separates into two parts of equal
magnitude travelling on the paths denoted by 1 and 2. They recombine
at a second beam splitter, C, where, by suitable choice of path lengths,
it is arranged that the two contributions to the output towards the D detector destructively interfere, so that D never records a photon. In
other words, the photons always take the E path. Next we suppose
that at a certain place on, say, path 1 we can place one of our boxes
in such a way that if it is FULL the photon will be absorbed, and the
particle in the box destroyed, whereas if it is EMPTY it will have no
effect. We then place each box in turn in the interferometer, and send
in one photon. If the photon does not appear in the detector D then we
discard the box and choose another. When we have a box for which
the detector does record a photon, then we know that we have a box
that is FULL.
It is easy to see why: if the box had been EMPTY, then it would
have no effect, and by construction of the interferometer, the photon
could not go to the detector at D. Thus if a photon is seen at D, the
box is necessarily FULL. Note, also, that a FULL box just acts as
another detector, so with beam splitters having equal probabilities of
transmission and reflection, half of the experiments with a FULL box
will result in the photon destroying the particle in the box. In the
other half, the photon will reach the second beam-splitter, at C, and
one-half of the time will pass through and reach the D detector. Thus
one-quarter of the FULL boxes will lead to a photon being seen at D,
and therefore will actually be selected as FULL. What we have here is is a perfect ‘non-disturbing’ measurement, because we can see that the
photon has actually gone on the other path (path 2); nevertheless, if it
appears at the detector, it has verified that the box is FULL.
The basic ideas behind the arguments of this section are due
to A.C.Elitzw and L.Vaidman in an unpublished article from the
University of Tel Aviv (1991). Other applications of similar ideas
are given by L. Hardy Physics Letters 167A 11 (1992) and Physical
Review Letters 68 2981 (1992).