# Non-locality

## Why is the universe the way it is?

Classical Newtonian physics gives the rules governing the motion of large bodies, but we know this it is only an approximation. For microscopic and/or fast moving systems quantum mechanics and special relativity with their counter-intuitive (but experimentally tested) predictions hold sway.

We are constantly learning about the systems at the quantum level and, with each new observation or calculation, our perception of quantum mechanics changes. A major gap in our knowledge, however, is an intuitive understanding of why quantum mechanics should be the way it is.

Recently, however, research in Bristol, with collaborators in Canada and Holland, has taken a substantial step towards unravelling some of quantum mechanics’ mysteries. The work sheds light on quantum mechanics deepest and most fundamental feature: quantum entanglement.

Imagine two particles emerging from a common source, one travelling to an observer, Alice on Earth, and another to Bob who is on a distant galaxy. If Alice and Bob perform simultaneous measurements on these particles, there will be correlations between the outcomes of the measurements. While it is not surprising that there could be some correlation, what is remarkable is the degree to which the measurements are correlated. This is known as quantum non-locality and is a manifestation of the particles’ entanglement. Einstein called this non-locality “spooky”!

It appears as though the two particles are communicating with one another instantaneously. Quantum particles achieve their instantaneous correlation over whatever distance you choose to separate them, thus appearing to violate special relativity by communicating at superluminal speed.

The fact that relativity is not truly violated can be traced to the fact that results of measurements on quantum particles are probabilistic. Thus the results of Alice’s and Bob’s measurements on the entangled particles are random. There are, however, correlations between the outcomes: if Alice gets a certain outcome, Bob’s measurement is more likely to yield one of the possible outcomes. For most pairs of measurements, quantum mechanics predicts that there will be correlation, but not perfect correlation. So non-locality is related to the fundamental non-deterministic nature of quantum mechanics.

But why can’t these correlations be stronger? After all, mathematically, special relativity and quantum mechanics allow for stronger non-local correlations.

By way of explaining, let us return now to earthling Alice and extra-terrestrial Bob, who decide one day to meet for the first time. They are so busy that finding a common free date is going to be very tricky. So first they decide to work out something simpler: whether their number of common free dates is even or odd. The result of this non-local task is one bit (a 0 or a 1; 0 for even, say and 1 for odd). Despite the simplicity of the answer, it turns out that they cannot learn this single bit without one of them sending their entire diary to the other. The amount of communication needed to perform a distributed task such as this is known as its communication complexity.

Perhaps, you might think, if Alice and Bob shared entangled particles, they could solve this even-versus-odd problem with less communication. Sadly we know that quantum mechanics cannot help.

In fact this even-versus-odd task is much less contrived than it looks. It turns out that if this task could be solved with one bit (in other words, we would say that its communication complexity is trivial), every other communication task with a one-bit result, however complex, could also be solved with a one-bit transaction.

So now we return to quantum mechanics, and the question of why quantum correlations cannot be stronger than they are. Well, one answer, as discovered by this recent work, is that if quantum correlations were stronger, we would live in a world in which communication complexity is trivial.

A world in which all such communication tasks, however complicated, could be solved with one bit would be a very strange one indeed.

## Publications

Limit on Nonlocality in Any World in Which Communication Complexity Is Not Trivial (2006) Gilles Brassard, Harry Buhrman, Noah Linden, Andre Allan Methot, Alain Tapp and Falk Unger Phys. Rev. Lett., vol: 96, Page: 250401