Untangling Quantum Causation

Some have the motto "Follow the money" or "Cherchez la femme." For theoretical physicist Robert Spekkens, it’s "Causarum Investigatio"—investigate the causes. The words are written on the ornate ceiling of the Austrian Academy of Sciences and Spekkens often uses a photo of it in his talks.

In the everyday world it’s obvious that one thing can cause another, but it can still be heinously difficult to untangle the paths of causation. Cigarettes cause cancer. But are clusters of cancer in people living under power lines due to the power lines themselves, or because poor people, who may be more inclined to smoke, tend to live under them? Statisticians have devised all sorts of rules, equations, and experimental designs to untangle these problems in the classical world, especially in the field of medicine and drug trials.

Spekkens and his colleagues at Ontario’s Perimeter Institute for Theoretical Physics are now trying to come up with a proper account of causality in the quantum world, which Spekkens argues, "is critical to the progress of modern physics." It could also help those trying to build speedy quantum computers. "We’re basically doing the analog of a randomized drug trial in a quantum photon experiment," says Spekkens.

The quantum world, as usual, doesn’t behave exactly like the classical one. In the everyday world, if you have a situation where either A causes B (living under power lines cause cancer) or some common cause (like poverty) is triggering both, you can’t tell from a simple dataset of observations of A and B what’s going on. You need more information.

In the quantum realm this isn’t necessarily true. Say you’re looking at the polarization of photons along a bunch of different directions. If A causes B you can have perfect positive correlations of the polarizations for all those directions (where the polarization of A is always the same as that of B), but you can’t have perfect anti-correlations of the polarizations for all directions (where the polarization of A is always the opposite of that of B). If there is a common cause for A and B, however, then the opposite is true: you can have a set of perfect anti-correlations, but never a set of perfect positive correlations. Nobody really knows why that is so. "It’s interesting to think of the deeper significance of that fact, and I think we don’t quite have a handle on that," says Spekkens. But Spekkens’ team has shown this at work in a quantum photon setup, built by their lead experimentalist Kevin Resch at the University of Waterloo, Ontario (Nature Physics 11, 414–420 (2015)).

Now, with the help of an FQXi grant of almost $100,000, they have gone a step further.

To understand what they have done, consider the odd phenomenon called Berkson’s paradox. Imagine a world where a scientist’s research ability both puts them in the running for faculty positions and gets them more citations. Their teaching skills also help them to get a faculty position. In this imaginary population, teaching and citations are unconnected. Nevertheless, if you look at just the subset of scientists who won faculty positions—where those who are both bad at teaching and have poor citations have been excluded—you’ll see a strange inverse relationship: on average, faculty with high citations are poor teachers and vice versa. Such information, though just an artefact resulting from squinting at the data in a certain way, can be useful in untangling causal relationships: the induced relationship between citations and teaching tells us that both were somehow relevant to hiring decisions.

Quantum Mix

This is the scenario that Spekkens’ team has been investigating in the quantum world. They created some photons and sent them through a circuit and a logic gate, checking on their status at various points. Then they looked just at a subset of their data—say where the final photon has horizontal rather than vertical polarization (the equivalent of looking at ’just faculty’)—and checked for polarization correlations between two points in the experiment that aren’t causally related (like teaching and citations). They found them. Moreover they found that these polarizations were quantumly entangled. Not only did the experiment show that both a direct and common cause were at work, but also that these causes were mixed in a characteristically quantum kind of way (arXiv:1606.04523v1 (2016)).

"’Correlation does not imply causation’ is a mantra of all statisticians to which Rob Spekkens and his colleagues added a quantum twist," says Artur Ekert, director of the Centre for Quantum Technologies in Singapore. "It turns out that in the quantum world certain types of correlation do imply causation. This is a nice surprise."

Other teams are similarly exploring quantum causality. FQXi member Caslav Brukner at the University of Vienna, Austria, and Ognyan Oreshkov at the Université Libre de Bruxelles, Belgium, have devised an experiment that could be interpreted as showing how you can have a weird, quantum, space-time mashup where A causes B, and B causes A, says Spekkens. (See "Blurring Causal Lines.")

Oreshkov is similarly appreciative of Spekkens’ investigation. "Spekkens’ perspective is original and important," he says. "It is no doubt one of the forefront directions in this growing new field."

It’s also possible that such entangled causality could be used in quantum technologies, such as for building superfast computers. "People are using quantum weirdness as a resource," says Spekkens. "I wouldn’t be at all surprised if quantum causation leads to something too."