Measuring without measuring

One of the weirdest things about quantum mechanics (perhaps the weirdest thing) is how it reacts to measurement.  A quantum mechanical system contains more information than can be measured, and when a measurement is made, the extra information is destroyed and replaced with the result of the measurement.

Together with the “no cloning” theorem, which says that a quantum system cannot be duplicated, this means that one can never learn the actual state of a system.  You are limited to a single measurement, and that one measurement cannot reveal everything.

Or so it’s been thought.  But new research might suggest that it is possible to learn something about a quantum system without measuring it:

[Two teams of researchers] managed to do what had previously been thought impossible: they probed reality without disturbing it. Not disturbing it is the quantum-mechanical equivalent of not really looking. So they were able to show that the universe does indeed exist when it is not being observed.

The reality in question—admittedly rather a small part of the universe—was the polarisation of pairs of photons, the particles of which light is made. The state of one of these photons was inextricably linked with that of the other through a process known as quantum entanglement.

The polarised photons were able to take the place of the particle and the antiparticle in Dr Hardy’s thought experiment because they obey the same quantum-mechanical rules. Dr Yokota (and also Drs Lundeen and Steinberg) managed to observe them without looking, as it were, by not gathering enough information from any one interaction to draw a conclusion, and then pooling these partial results so that the total became meaningful.

This result is so surprising that it seems likely the Economist is garbling the story, or that I’m misunderstanding its significance.  I am reminded, however, of a counterintuitive result in computer science theory that shows how information can be extracted from a complete lack of information.  If this story is right, I wonder if they used anything like it.

The construction goes like this: Consider a room containing an odd number of people, each of whom has a bit (zero or one) imprinted on his forehead.  No one can see his own bit, and they are not allowed to communicate.  The people in the room want to determine the overall parity of the room (whether the bits’ sum is even or odd), but with no way to learn their own bits, no one can do any better than flip a coin.

No one individually has any information about the parity, and yet there exists a strategy whereby they can usually determine it by voting. Each person looks at the room and sees which bit is in the majority for the people he can see.  He then determines what the parity would be if he had the same bit as the majority, and votes for that answer.

Individually, each person is just as likely to be wrong as right, but collectively, the majority of people belong to the majority.  Thus, the people who are voting for the correct answer will outvote those who are voting incorrectly.

The only time the result fails is when the room is nearly evenly balanced.  If the room contains n zero bits, and n-1 one bits then when the people in the majority look at the room, they see a room that is evenly divided.  They have to flip a coin to decide how to vote, and half of them on average will vote incorrectly.  In the minority, everyone will vote incorrectly, so the incorrect result will win.

In all other cases, the majority remains the majority even with the loss of one person, so the strategy succeeds in generating information where none existed individually.

Leave a Reply

Please log in using one of these methods to post your comment: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: