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FQXI ARTICLE

July 3, 2015

Cheating the Causal Game

A new quantum framework that blurs cause-and-effect at a fundamental level could improve information processing and lead to a theory of quantum gravity.

FQXi Awardees: Caslav Brukner

October 16, 2012

Caslav Brukner

Fabio Costa, Ognyan Oreshkov and Caslav Brukner

University of Vienna, Austria

From an early age we take the cause and effect of events happening in time for granted; it’s how we think. Without cause and effect, where would science be? We could not attempt to predict the outcome of experiments to test ideas about the world, or try to formulate such theories of what will happen. Even the math that describes the atomic world—quantum theory—assumes that events take place in time in an ordered and connected fashion. Which makes it all the more strange that some physicists are trying to ditch this neat time-ordering.

This is by no means an obvious strategy to employ, notes Caslav Brukner, at the University of Vienna, Austria, one of the physicists behind the idea. "It’s simply new physics," he says. "We are asking whether space, time and causal order are truly fundamental ingredients of nature." The team hopes that by taking an approach that doesn’t rely on causal structure, it might provide a clue about where causal order comes from. Is it a necessary property of nature or can it be derived from more primitive concepts?

Uncertainty is inherent in quantum theory. It’s well established that the physical aspects of quantum experiments, such as a particle’s position or momentum, are not well defined before they are measured. But postulating that the ordering of events is also somewhat fuzzy takes this conception of uncertainty to a bold new level. Now Brukner and his colleagues, Ognyan Oreshkov and Fabio Costa, also at the University of Vienna, have calculated that time-ordering can become muddled in some situations. Even weirder, this is helpful rather than harmful, and if harnessed could potentially improve quantum information processing protocols, and help researchers trying to devise a theory of quantum gravity.

Playing the Game

Brukner illustrates his approach with what he calls a

But Brukner’s new findings make things a bit more complicated. "We have shown that there are certain quantum resources that would allow us to go beyond this 75 per cent if the causal relations between us are not well-defined," says Brukner. In other words, if you don’t define your time-ordering, you can win the game more often. Their work is published in

Past-Future/Future-Past

A new framework for quantum mechanics which does not assume a pre-existing

global time. It demonstrates the possibility for two agents to perform a

communication task in which it is impossible to tell with certainty who

influences whom.

Credit: University of Vienna

Brukner may not need to worry so much, however. Other independent researchers are more optimistic about creating the required conditions to replicate the team’s theoretical quantum game in the lab, in a fairly down-to-earth scenario. All that is needed is to create a situation in which two players—you and I—can send information to each other through a wire and, crucially, the causal relation of who signals to whom must be ill-defined. Physicist Matt Leifer of the Perimeter Institute (PI), in Waterloo, Ontario, who was not involved in developing the paper, says that we can imagine such a wire that is controlled by a quantum system that is in a superposition of two states. That means that in this set-up, the signal can either go from me to you or from you to me, but we don’t know which will occur.

It’s simply new physics.

We are asking whether

space, time and causal

order are truly fundamental.

We are asking whether

space, time and causal

order are truly fundamental.

- Caslav Brukner

Brukner’s team is not the first to investigate these issues. Perhaps fittingly for a theory of indefinite causality, it’s difficult to pin down exactly where and when these notions began. One of the first researchers to venture forth into what Brukner described as the "new land"—devising theories using indefinite causal relations—was Lucien Hardy, who is also based at PI (see arXiv:gr-qc/0509120v1).

Then, one afternoon over coffee at the University of Pavia, Italy, a group of quantum theorists were discussing Hardy’s ideas and wondered whether casual relations could be superposed. Just as Brukner now notes that such fuzziness can increase the chances of a win in a quantum game, they realised that in a similar manner, this uncertainty could have useful applications in quantum information. Giulio Chiribella, who was in that first discussion with Benoit Valiron, FQXI member Giacomo Mauro D’Ariano and Paolo Perinotti says: "From that afternoon discussion, we suggested a way to superpose the ordering of operations in a computation, and we argued that this effect could lead to more efficient protocols for information processing."

Quantum computers, in theory, exploit superposition to perform powerful operations on data—but the idea of indefinite causal structure brings the phenomenon of superposition into a new realm, the realm of the ordering of computational operations. "Caslav’s causal game has been a key result supporting this intuition," says Chiribella, from the Center for Quantum Information, Tsinghua University, Beijing. "This is because it has provided the first concrete example of an advantage coming from indefinite causal ordering."

He describes Brukner as "one of the leading researchers in the new school of quantum foundations," and always looks forward to meeting up with him over conference dinners to chat about quantum physics and the new directions the community is exploring. "No matter which subject we pick, these chats are always fun and inspirational," says Chiribella. "I very much like his pragmatic attitude, which combines foundational ideas with applications in quantum information, always keeping an eye on the possible experimental implementations."

Chribella has made some important contributions to the new research field: in testing the properties of two black boxes. The game is to work out the contents of the box based on how it changes numbers that are input into the box. For instance, if you input 1, 2 and 3 into the box and get out 3, 5 and 7, you could calculate that the box multiplies by 2 and adds one. Chiribella discovered that the process of working out the properties of the boxes is more efficient if, instead of examining one box first then the second, you take advantage of a superposition of the two possible orderings.

"These works clearly demonstrate that harnessing the new quantum effects that arise in the absence of a definite causal structure can offer advantages and help us to save computational resources and energy costs," says Chiribella. "I expect many new examples of this kind to appear in the next few years."

Quantum Gravitational Prize

Like many theoretial physicists, Brukner has his eyes on the bigger prize. The team hopes that their new description of cause-and-effect in the quantum world will help researchers developing a theory of quantum gravity, a grand project for theorists world-over. A successful theory of quantum gravity would merge quantum theory with Einstein’s theory of general relativity to describe every interaction in the universe that we know about, from the subatomic scale to the cosmological. One of the biggest obstacles has been that general relativity and quantum mechanics treat time very differently. In the former theory, time is another dimension alongside space and can bend and stretch, speed up and slow down, in different circumstances. Quantum theories, however, usually assume that time is set apart from space and ticks at a set rate. Theories of indefinite causality tackle this mismatch head-on, by questioning what time is at a fundamental level.

Guilio Chiribella

Teaching at a student summer camp in Tsinghua University, Beijing, China.

All the researchers hope their efforts will help them to formulate a more general quantum theory, in which our familiar causal structure—of dogs barking and families waking—is not assumed, but emerges in the right conditions. "I find this new direction promising because it challenges one of the key paradigms of quantum and classical mechanics: the paradigm of a state evolving in time," says Chiribella. "We are now pushing quantum theory to the extreme limits of what can be conceived by our imagination."

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PENTCHO VALEV wrote on May 24, 2015

The following argument is valid (although Einsteinians are unable to prove its validity):

Premise: Einstein's 1911 gravitational-time-dilation assumption is correct.

Conclusion: The acceleration of light falling to the Earth is negative, -2g (that is, the speed of falling photons DECREASES).

Clearly the Conclusion is absurd so the Premise is false (gravitational time dilation does not exist).

Here are references showing that Einstein's relativity does indeed...

The following argument is valid (although Einsteinians are unable to prove its validity):

Premise: Einstein's 1911 gravitational-time-dilation assumption is correct.

Conclusion: The acceleration of light falling to the Earth is negative, -2g (that is, the speed of falling photons DECREASES).

Clearly the Conclusion is absurd so the Premise is false (gravitational time dilation does not exist).

Here are references showing that Einstein's relativity does indeed...

PENTCHO VALEV wrote on May 22, 2015

Effect without Cause in Einstein's Relativity

Hanoch Gutfreund: "The general theory of relativity predicts that time progresses slower in a stronger gravitational field than in a weaker one."

This is a lie of course (taught by 99% of the Einsteinians) - general relativity does not predict that the ticking rate of clocks varies with the strength of the gravitational field. Rather, it predicts that gravitational time dilation occurs even in a HOMOGENEOUS gravitational field. This...

Effect without Cause in Einstein's Relativity

Hanoch Gutfreund: "The general theory of relativity predicts that time progresses slower in a stronger gravitational field than in a weaker one."

This is a lie of course (taught by 99% of the Einsteinians) - general relativity does not predict that the ticking rate of clocks varies with the strength of the gravitational field. Rather, it predicts that gravitational time dilation occurs even in a HOMOGENEOUS gravitational field. This...

VLADIMIR F. TAMARI wrote on March 24, 2013

oops sorry - here is the correct link to Eric Reiter's unquantum.net

oops sorry - here is the correct link to Eric Reiter's unquantum.net

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