They say that all good stories have a conflict, and on this team there was conflict for a while. The two economists were convinced that the "**agreement theorem,**" a central result in economics, had to hold in the quantum world as well. But for his three colleagues in quantum technologies it was impossible to do so. They did not want to get involved in a project destined for failure.

The agreement theorem, which Robert Aumann (2005 Nobel Laureate in Economics) proved , dictates that if two rational people start from the same prior knowledge, they cannot agree about their disagreement.

More precisely: each person can estimate the probability of an event based on the information they know. This information will always be partial, therefore the estimates may be different. That is, people can disagree. But if the estimates become common knowledge, this disagreement cannot be sustained. Putting all the information together, people necessarily reach the same conclusion. That is, they agree.

This result supports the coherence of economic markets, which is why economists were so convinced that quantum theory had to respect it. But, as their quantum colleagues reminded them, in this theory it is impossible to know two incompatible properties on the same object with the maximum precision. If you know one, the other eludes you. Says Heisenberg's uncertainty principle (another Nobel Prize, this time in Physics in 1932).

__The economy, in danger because of the quantum world__

It seemed that the agreement theorem was in direct conflict with the uncertainty principle. Two people could try to estimate the probability of an event based on the information they already knew. But even gathering all the information, the only possible conclusion would be that this event could not be known. Both estimates would be valid, and the disagreement would hold.

Beyond optimism, however, economists had a good case for starting this research. If the agreement theorem also applied to the quantum world, they would be demonstrating that the theory that best describes the world has an internal coherence until now unknown.

If, on the other hand, it turned out that quantum theory did not fulfill the theorem, the implications could be dramatic. It would not be unusual for quantum technologies to be used to do finance in the near future. In this case, it might become impossible to agree on the price of things. The world economy could be in jeopardy.

Whether quantum theory fulfilled the agreement theorem or not, the repercussions would go far beyond physics. The economists had convinced their colleagues of quantum: you had to know the answer. Another proof that the more at stake, the better conflicts work.

The road was not easy. The language of quantum theory and that of economics had nothing to do with each other. Translating between them was very difficult. But, little by little, examples began to emerge of situations where the agreement theorem was not fulfilled.

Of course, none seemed to have a representation in quantum theory.

__Rescuing coherence__

Until, suddenly, they found out why. Neither example could have quantum representation, and the key was in a fundamental theorem in this physical theory. The theorem Tsirelson, simple but profound. It seemed to simplify the calculations. The entire team went to work to tie up the missing ends. Finally, the mathematics confirmed it: quantum theory respected the agreement theorem.

The conflict had been resolved. Indeed, quantum theory is consistent. The world economy can breathe easy, and although it sometimes resists our intuition, quantum theory is not as rare as we thought.

Our main team, now reconciled, has published its results this week in Nature Communications.

A good story would end here. Conflict resolved, happy ending, mission accomplished. But reality doesn't always live up to the standards of storytelling, and our story has a surprising epilogue.

__New physical theories?__

That quantum theory fulfills the agreement theorem has implications that go beyond the theory itself. It could happen that, in the future, we develop a new theory that surpasses the quantum one in terms of the ability to explain the world in which we live. If this theory does not satisfy the agreement theorem, what should we think?

According to the research team, we should rule it out. They propose to consider the agreement theorem as a physical principle. What's more, they propose a test for new theories: only those that fulfill the agreement theorem pass it. Thus, it is easy to ensure that any new theory has internal coherence.

The agreement theorem adds to the long list of physical principles that have already been proposed. The objective is to discard any theory that does not respect them. As the list grows, we will reject more and more theories and, perhaps, we will find that quantum is the only theory that fulfills all the principles. Only then can we stop looking, because we will know that quantum theory is the best possible description of nature.

About the authors: Patricia Contreras Tejada is a researcher in mathematics and quantum information at the Institute of Mathematical Sciences (ICMAT-CSIC) and Giannicola Scarpa is an assistant professor at the Higher Technical School of Computer Systems Engineering of the Polytechnic University of Madrid (UPM )

This article was originally published on The Conversation.

## No comments