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The Uncertainty Principle Determines the Nonlocality of Quantum Mechanics

Why is quantum behaviour as weird as it is but no weirder?

joint work with Stephanie Wehner

The paper is available from Science here. The additional materials can be found here. A free pdf of the arxiv version is available here

As weird as quantum theory is, it doesn't allow two separated individuals to send messages to each other faster than light. It doesn't allow us to act instantaneously over large distances. Nonetheless, it does contain a subtle form of nonlocality that Einstein famously (and misleadingly), derided as "spooky action at a distance".

Quantum nonlocality continues to perplex us, but there's no action at a distance going on -- it just looks like there is if you think of things in a classical way. Nonlocality is the phenomena that measurement results made on two distant systems defy any local classical description. It allows two individuals to coordinate their actions better than they could by purely classical means by making measurements on some shared quantum system. We'll explain it in more detail soon, as it is the essence of quantum mechanics -- it's the bit which tells us that there is no hidden classical theory which underlies quantum theory.

But the thing is, quantum mechanics could be even spookier, in the sense that it could be more nonlocalDon't worry, we'll explain what we mean by more nonlocality soon! than it already is while still not allowing action at a distance. So, why isn't it? What restricts quantum theory from being more nonlocal? What we've shown is that Heisenberg's uncertainty principle prevents quantum mechanics from being any spookier. What's more, there's a general relation which holds between nonlocality and uncertainty and something called "steering".

The uncertainty principle says that our knowledge of nature is limited -- there are properties of nature, such as a particle’s position and momentum, which you can never predict exactly. For example, if you learn the particle's position, then you will be completely uncertain as to the particle's momentum (or visa versa). This has traditionally been captured by the equation ΔxΔp≥ℏ/2, which is by now so famous you could safely wear it on a tshirt without getting beaten up. However, information theory has given us more sophisticated ways to describe uncertainty, and these are important if we want to understand the link between uncertainty and nonlocality.

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