### Quantum Statistics From Outside Space And Time

**[From left to right]**

**Front row: Yeong-Cherng Liang (Geneva), Jean-Daniel Bancal (then Geneva, now Singapore);**

**Middle row: Antonio Acin (Barcelona), Nicolas Gisin (Geneva);**

**Back row: Valerio Scarani (Singapore), Stefano Pironio (Brussels).**

**Authors:**

**Jean-Daniel Bancal**

^{1,5}, Stefano Pironio^{2}, Antonio Acin^{3,4}, Yeong-Cherng Liang^{1}, Valerio Scarani^{5}, Nicolas Gisin^{1}

**Affiliations:**

^{1}Group of Applied Physics, University of Geneva, Switzerland

^{2}Laboratoire d’Information Quantique, Université Libre de Bruxelles, Belgium

^{3}ICFO-Institut de Ciències Fotòniques, Castelldefels (Barcelona), Spain

^{4}ICREA-Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain

^{5}Centre for Quantum Technologies and Department of Physics, National University of Singapore, SingaporeQuantum theory predicts

*what nature does*with unparalleled scope and accuracy. In the new perspective of quantum information, one can add that quantum theory predicts

*what nature can do for you*. But the theory is silent about

*how nature does it*. This silence is at the heart of the uneasiness that some scientists and most laypersons have felt, and continue feeling, when confronted with quantum physics.

Einstein, for one, believed that this silence was only a temporary feature of the then-newly born formalism. He was confident that, with time, someone would find an explanation for quantum phenomena in terms of

*mechanisms in space-time*. However, the passing of time brought physics further from Einstein’s wishes: in 1964, John Bell proved that quantum theory is incompatible with pre-established agreement. Indeed, some predictions of the theory violate a criterion called Bell inequality. Whenever this happens, we are certain that the results of measurements were certainly not pre-recorded in the physical systems. This violation has been clearly observed in several experiments, since Aspect’s pioneering one in 1982.

**Past 2Physics article by Antonio Acín:**

August 19, 2012: "Testing the Dimension of Classical and Quantum Systems" by Martin Hendrych, Rodrigo Gallego, Michal Mičuda, Nicolas Brunner, Antonio Acín, Juan P. Torres

The violation of Bell inequalities puts severe constraints on Einstein’s hope: any mechanism in space-time that reproduces quantum predictions must involve

*superluminal influences*– exactly what Einstein wanted to avoid at all cost! The faster-than-light character comes from the fact that the predictions of quantum theory, as well as the observed experimental results, are unchanged if the measurement events are space-like separated.

For many physicists, once the obscene word “superluminal” is uttered, all speech must cease. Others, less definite at the moment of telling nature how to behave, were ready to give some credit to a mechanistic explanation, but under one condition: it must not be possible for us to use these influences to send actual messages faster than light. In other words, to be acceptable by the physics community, the hypothetical influences must at least be “hidden”. Abner Shimony coined the expression “peaceful coexistence” between relativity and the violation of Bell inequalities. There did not seem to be much more to be said on the topic, apart from noticing that the Bohmian presentation of quantum theory uses precisely hidden influences in the updating of its “quantum potential”.

In our recent work, we show that

*the constraint can be strengthened to the extreme:*any finite-speed influence would lead to the possibility of sending messages faster than light, in blatant violation of relativity. The price to pay for peaceful coexistence is to accept influences that propagate at infinite speed, making the quantum universe fully connected, while conspiring to remain hidden from us.

In order to understand the generality of our result, let us first stress one point: if the goal would be to reproduce all the predictions of quantum theory as we know it, it is already obvious that the speed must be infinite. Indeed, finite-speed influences would certainly lead to deviations from quantum predictions, depending on the space-time configuration: for instance, if the measurement events cannot be connected by the influence, one should never observe a violation of Bell inequalities. In this work, we decided not to erect quantum theory to the rank of untouchable truth: we accepted finite-speed influences as working assumption, together with the required deviations from the predictions of our present-day formalism. We only assumed that, if the influences have the time to propagate from one measurement event to the next, quantum statistics are produced (because this is what is observed). Even in such a flexible scenario, we were able to prove that ultimately finite-speed influences cannot be hidden. Further, the conclusion can be reached using only observable statistics: it is not only theory-independent, but also “device-independent”.

**Illustration of how to obtain a constraint on finite-speed models with three particles**

The trick consists in devising a suitable multi-partite configuration, because no conclusion can be reached in the more familiar bipartite scenario. The idea of the argument can be sketched with three parties (see figure). The diagrams are drawn in the preferred frame in which the hypothetical influences propagate. Configuration (a) is such that the influences propagate from A to B, then from B to C: in this case, we request that quantum statistics are recovered. In configuration (b), A and B do not receive each other’s influence, while C receives the influences from both A and B. Now:

- On the one hand, according to the role of influences in this model, a possible violation of Bell inequalities by A and B in configuration (a) should cease if the observers change to configuration (b) e.g. by advancing B’s measurement.
- On the other hand, for the influences to be hidden, the statistics AC and BC must be the same in both configurations.

In conclusion: assuming that some quantum statistics can be observed, a classical mechanism that explains them must not only use superluminal influences: either it uses infinite-speed influences, or it allows us to send messages faster than light. Both alternatives are mind-boggling? Well, there is a reason why physicists prefer to skip the issue of “how nature does it”.

**The history of an idea, with three references:**

- The idea is already ten years old, but at that time we did not have the mathematical tools to find a complete proof: Valerio Scarani, Nicolas Gisin, "Superluminal influences, hidden variables, and signaling", Physics Letters A, 295, 167 (2002). Abstract.
- We resumed working on this project in February 2011. Two weeks later appeared in the arXiv a nice breakthrough: Sandro Coretti, Esther Hänggi, Stefan Wolf, "Nonlocality is transitive", Physical Review Letters, 107, 100402 (2011). Abstract. Wolf and coworkers had found a proof for “no-signaling statistics”. Those statistics cannot be obtained with quantum physics, so the final challenge remained open; nevertheless, this work showed that there is real hope of finding a proof.
- Our proof for quantum statistics is: J-D. Bancal, S. Pironio, A. Acín, Y-C. Liang, V. Scarani, N. Gisin, "Quantum non-locality based on finite-speed causal influences leads to superluminal signaling", Nature Physics, 8, 867 (2012). Abstract.

Labels: Complex System 2, Quantum Computation and Communication 8

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