Quantum correlations with no causal order

Causality is one of the oldest and most important concepts of Physics. Even recently, at the beginning of the XX century, with the invention of Special Relativity, this concept was in some sense rediscovered. As in a relativistic framework the events can change their temporal order a great effort was made in order to preserve causality in the theory.

There is a general consensus in the scientific community about this concept: For all scientific theories, even for all the theories that will come in the future, causality should be preserved. If causal relations are broken an important number of paradoxes and counter-intuitive results arise. You could even go back in time and kill your grandgrandfather!

In quantum mechanics the discovery of entangled states, that are states with correlations than can act immediately even in they are separated by a distance of millions of light years, challenged this concept. The solution for preserving causality was to accept that quantum systems are intrinsically random and no theory can give a complete description of them.

Very recently, in Reference ¹, a paper published in Nature Communications by Ognyan Oreshkov and coworkers, from the University of Vienna, the concept of causality itself is discussed. Just by assuming that quantum mechanics is valid only locally, they show that it is difficult to talk about ‘causal order’. As it has been made before in order to analyze the effects of quantum mechanics the authors decided to illustrate their result with a thought experiment.

The rules of this experiment are:

• There are two parties, Alice and Bob. They are in labs that are far away from each other.
• They both receive one random bit, either 0 or 1.
• They can send information out between their labs.
• They have to guess the bit of each other. This decision should be made at the same time they send their information out.

Obviously, the experiment should be repeated several times, and the goal is to guess the bit of the other party as much times as possible. The ‘figure of merit’ that measures how well we are performing the game is the probability of guessing for both Alice and Bob together, that is a number between 0 and 1.

Let see what can we do in a classical, and causal, framework. It is clear that the success probability will depend in this case on the time order of the events. If Alice sends her information first, she can use it in order to communicate Bob what her bit was. Indeed, Bob will succeed all the time. The problem now is that Alice has no clue about Bob’s bit, so the best she can do is just say something at random. The same problem arises if it is Bob the first in sending the information. So, in the best possible scenario, the probability of success is 1 for one of them, the one that acts second, and ½ for the other one, the one that acts first. That means that the best possible probability in a classical causal framework is ¾.

So, is there any difference in a quantum mechanics framework? Not really, quantum mechanics is also a theory with a definite causal background and has to fulfill the same constrains. But, what happens if we slightly modify quantum mechanics in order to remove the space-time background, making it only valid locally, but not globally? That is the problem analyzed in Ref. ¹ by Oreshkov et al. There, the authors performed a similar experiment, where it is assumed that Alice and Bob can make any kind of quantum operation in their labs. In these labs quantum mechanics holds, but there is not any assumption of a preexisting background time, or global causal structure. In this scenario, that differs from normal quantum mechanics, they show that the limit of the probability of success can be enhanced beyond the causal limit.

The rules for the non-causal quantum game are:

• Each laboratory is isolated.
• Quantum mechanics can be applied locally in the labs, but there is no assumption of what happens globally.
• There is also no assumptions about the spatio-temporal location of the experiments. That means that it is not define who makes the measurement before.
• They don’t need to communicate in this case. This is a necessary assumption in this case, because in this case there is not a definite spatio-temporal order, so it is not defined who acts first and can communicate and who is second and can not.

Based on these assumptions the authors create a new framework based on local quantum mechanics for analyzing the possible options of Alice and Bob. The results are surprising, they find a possibility of reaching a success probability of 0,853, that is higher than the ¾ probability of the best causal scenario. Even, without communication between them.

And what does it mean? Is causality broken in this new theory and we can communicate now with our dead grandgrandfather? That could be very interesting for science fiction writers, but it is not like that. The authors claim in their paper that, as quantum mechanics can be applied locally to Alice and Bob’s labs, causality should be preserved. This is due to the noise in the evolution ‘backward in time’ and it is compatible with the Novikov principle.

So, if causality itself is not broken, why is this result interesting? First, the analysis of new possible frameworks is always useful. In general relativity, for instance, when one imposes only local constrains new and interesting features arise, as exotic causal structures. It looks like that something similar happens in the quantum regime. Also, this results imply that if quantum mechanics only works locally new kind of correlations appear, stronger than the ones that are usual in normal quantum mechanics, like entanglement. Even, if these correlations can not break the causal order, as is expectable, the potential implications are huge. We should not forget that entanglement leads to interesting applications as quantum computing, quantum teleportation or cryptography. We can not know which applications these new correlations may have.

Finally, there is a more important question: Are these correlations something real or just a mathematical trick? About this question, the authors mention in the discussion of their paper that maybe these correlations can be found in regimes where the actual theories are untested, such as, for example, those in which quantum mechanics and general relativity become relevant.

So, in my opinion, for the moment this result is purely theoretical, but very interesting in any case. This kind of studies, even if they are just theory, usually open a door to new ways of thinking. Also new theories and potential applications can be realized from it. Only time can show how useful it will be.