Download The quantum eraser, persistence of information and the

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The quantum eraser, persistence of information and the delayed choice
experiments
Shantena Augusto Sabbadini
The quantum eraser is a clever experimental design, in which first a
quantum system, prepared to be in a superposition of states corresponding
to various values of an observable O, undergoes a "measurement" by
getting entangled with another microscopic system playing the role of
"measuring apparatus," so that the value of O gets correlated with the value
of an observable M of the "apparatus." Then this correlation gets destroyed
by performing on the "apparatus" the measurement of an observable
incompatible with M.
A concrete example is a Mach-Zehnder interferometer in which a photon
can travel along two different paths and interfere with itself. If we place on
each path a device that generates a secondary photon when the primary
photon crosses it, the detection of the secondary photons provides which
path information about the primary photon and the interference pattern
disappears. But the trajectories of the two secondary photons can be mixed
in such a way that information about which is which is lost: consequently
information about the primary photon's path is also lost, and the
interference pattern reappears.
The experiment shows that persistence of information is the crucial factor
allowing the replacement of the entangled superposition that is the outcome
of a measurement process with a classical alternative (the so-called
"collapse of the state vector"). The replacement holds, in other words the
outcome of a measurement process can be seen in objective either/or terms,
so long as some kind of record or trace of the measurement results persist.
When all that information is erased, the replacement is no longer possible
and only the full entangled superposition correctly predicts the results of
future observations. The collapse of the state vector is therefore merely an
apparent phenomenon. The outcome of a measurement process is always
an entangled superposition. But for predicting the outcome of an
observation that conserves information about the measurement process, the
entangled superposition is exactly equivalent to a classical alternative. 1
The quantum eraser can be performed as a delayed choice experiment.
E.g., in the case of the Mach-Zehnder interferometer mentioned above, the
mixing of the trajectories of the secondary photons can be applied when the
primary photon is already on its way and even when it has already
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Shantena A. Sabbadini, Persistence of Information in the Quantum Measurement
Problem, Physics Essays, March 2006, Vol. 19 No. 1, pp. 135-150.
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interacted with the devices generating the secondary photons, so that the
decision to move along one path or the other, or both at once, should have
been already taken.
This aspect of the experiment looks like a retroactive effect in time, and it
has been the object of much discussion. A particularly striking version of
delayed choice are some thought-experiments proposed by John Archibald
Wheeler (1911-2008) that stretch the time delay to cosmic proportions.
Here is one such experiment. Light coming towards the Earth from a
distant star is deflected by a massive celestial object, e.g. a galaxy or a
giant black hole, acting as a gravitational lens. Then (looking at the
incoming photons trajectories in only two dimensions for simplicity), just
like in the case of the quantum eraser, each photon travels along two paths
around obstacle, paths that finally converge in our lab here on Earth (see
Figure 4.5).
Figure 4.5. Cosmic delayed choice
Now the incoming beams can be brought together, producing an
interference pattern, or can be separately analysed, revealing only the
photons coming from one or the other direction. So our choice of
experimental apparatus seems to force the photon to choose between its
wave nature, passing simultaneously on both sides of the obstacle, and its
particle nature, passing either on one side or on the other. This in itself is
not surprising: it is a well-known feature of quantum physics that
incompatible experimental arrangements bring to light complementary
aspects of the observed phenomenon (e.g., particle or wave behaviour).
What is rather extraordinary, though, is that the galaxy causing the
deflection of the light beams may be millions of light-years away, so that a
photon passing just on one side of it or on both sides at once is an event
that supposedly took place millions of years ago. It would seem that our
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choice of experimental setup today influences the past millions of years
ago.
Wheeler understood this backward influence in time in the context of his
participatory universe. He said:
The thing that causes people to argue about when and how the
photon learns that the experimental apparatus is in a certain
configuration and then changes from wave to particle to fit the
demands of the experiment's configuration is the assumption that a
photon had some physical form before the astronomers observed it.
Either it was a wave or a particle; either it went both ways around the
galaxy or only one way. Actually, quantum phenomena are neither
waves nor particles but are intrinsically undefined until the moment
they are measured [emphasis mine]. In a sense, the British
philosopher Bishop Berkeley was right when he asserted two
centuries ago "to be is to be perceived."2
And also:
We are participators in bringing into being not only the near and here
but the far away and long ago. We are in this sense participators in
bringing about something of the universe in the distant past..."3
The persistence of information approach fits well with the notion of a
participatory universe, but this participation does not need to be understood
in the sense that we "bring about something of the universe in the distant
past". The apparent retroactive effect in time is merely a reflection of the
inadequacy of our representations of matter (which are imbued with
classical prejudice). In particular, the notions of particle and wave are both
inadequate: they are just our last attempt to extend to the micro world
familiar notions of our macro world.
The only consistent description of the micro world is in terms of the
quantum state of the system together with the laws that give the
probabilities of specific results for specific measurements that can be
performed on the system. The photon, interacting with the far away galaxy,
ends up in a quantum state which is a superposition of travel on both sides
of the galaxy. Whether in our observations on Earth we see that
superposition (in the form of an interference pattern) or we see a classical
alternative (separate counts of photons in each beam) depends on whether
our specific setup is such as to erase or keep which path information. E.g.,
if we catch each beam in a properly oriented telescope, which path
information is conserved and we have no interference. If we have the two
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Scientific American, July 1992, p. 75.
"The Anthropic Universe", radio interview in Science Show, 18 February 2006.
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beams converge on a photographic plate, which path information is lost and
we have an interference pattern.
Our choice of the apparatus setup in the cosmic delayed choice experiment
therefore does not change anything in the distant past. What happened in
the distant past is the creation of an entangled state in which the photon is
travelling on both sides of the galaxy. What happens here now is that we
can choose to perform on that state an observation conserving or destroying
which path information. In the first case the entagled superposition is
equivalent to a classical alternative. The photon appears to have travelled
either one path or the other: good particle behaviour. In the second case
there is no such equivalence, and the entangled superposition is the only
correct description. The photon appears to have travelled along both paths
at once: good wave behaviour.
But there is no retroactive change, since all results, whether they do or do
not conserve which path information, can be derived from the full
entangled superposition representing the present state of the system. Our
choice of the experimental setup determines what we see today: it does not
affect what happened millions of years ago to the photon and the galaxy.