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Is non-local communication really impossible?

Pierre Uzan

Published Jan 19, 2026• 0 citations
OpenAlex

Abstract

This paper shows the possibility of non-local communication between two entangled, spacelike separated sub-systems. More specifically, it is shown that if there exist (at least) two non-commuting observables respectively defined on these two sub-systems then, for some entangled state of the global system, the probability distribution of the outcomes of measurements performed in one of its parts is changed by the actions that have been performed in the other one. This causal dependency, which includes that of the settings, makes possible a nonlocal exchange of information between the parties.

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This paper shows the possibility of non-local communication between two entangled, spacelike separated sub-systems. More specifically, it is shown that if there exist (at least) two non-commuting observables respectively defined on these two sub-systems then, for some entangled state of the global system, the probability distribution of the outcomes of measurements performed in one of its parts is changed by the actions that have been performed in the other one. This causal dependency, which includes that of the settings, makes possible a nonlocal exchange of information between the parties.
Bell proved that quantum entanglement enables two spacelike separated parties to exhibit classically impossible correlations. Even though these correlations are stronger than anything classically achievable, they cannot be harnessed to make instantaneous (faster than light) communication possible. Yet, Popescu and Rohrlich have shown that even stronger correlations can be defined, under which instantaneous communication remains impossible. This raises the question: Why are the correlations achievable by quantum mechanics not maximal among those that preserve causality? We give a partial answer to this question by showing that slightly stronger correlations would result in a world in which communication complexity becomes trivial.
This work aims at exploring whether the nonlocal correlations due to quantum entanglement could exist without nonlocal causation. This is done with the aid of a toy model which is based on a simple but decidedly unorthodox physical hypothesis: the nonlocally correlated outcomes of the wavefunction collapse of two entangled particles is driven by an exchange of information between them. Of course exchange of information between spacelike separated entities is forbidden in 3+1 space-time, thus we can wonder whether or not a way out could be found by invoking the existence of some hidden field propagating in an extra time dimension to make the mentioned exchange of information occurring at finite velocity through this extra dimension. Only the description of the wavefunction collapse would be affected by the existence of this extra-time dimension. The model proposed here is defined by borrowing Bohm-Bub’s proposal to describe the wavefunction collapse by means of nonlinear (non-unitary) dynamical equations and then elaborating this approach for an entangled system. The model so obtained is just speculative without any claim of being robust against any criticism, nevertheless, it satisfies the purpose of giving the possibility to the hypotheses formulated above to be verified experimentally; in fact, it makes the proposal of an experiment potentially interesting which would otherwise be immediately dismissed as manifestly trivial. The proposed experiment would consist of checking the possible violation of Bell’s inequality between two identical but independent systems under appropriate conditions. Beyond its theoretical interest, entanglement is a key topic in quantum computing and quantum technologies, so any attempt to gain a deeper understanding of it could be useful.
A central aspect of quantum information is that correlations between spacelike separated observers sharing entangled states cannot be reproduced by local hidden variable (LHV) models, a phenomenon known as Bell nonlocality. If one wishes to explain such correlations by classical means, a natural possibility is to allow communication between the parties. In particular, LHV models augmented with two bits of classical communication can explain the correlations of any two-qubit state. Would this still hold if communication is restricted to measurement outcomes? While in certain scenarios with a finite number of inputs the answer is yes, we prove that if a model must reproduce all projective measurements, then for any qubit-qudit state the answer is no. In fact, a qubit-qudit under projective measurements admits an LHV model with outcome communication if and only if it already admits an LHV model without communication. On the other hand, we also show that when restricted sets of measurements are considered (for instance, when the qubit measurements are in the upper hemisphere of the Bloch ball), outcome communication does offer an advantage. This exemplifies that trivial properties in standard LHV scenarios, such as deterministic measurements and outcome-relabelling, play a crucial role in the outcome communication scenario.
It is well known that entangled quantum states are nonlocal: the corrrelations between local measurements carried out on these states cannot be reproduced by local hidden variable models. Svetlichny, followed by others, showed that multipartite quantum states are more nonlocal than bipartite ones in the sense that even some nonlocal classical models with (super-luminal) communication between some of the parties cannot reproduce the quantum correlations. Here we study in detail the kinds of nonlocality present in quantum states. More precisely, we enquire what kinds of classical communication patterns cannot reproduce quantum correlations. By studying the extremal points of the space of all multiparty probability distributions, in which all parties can make one of a pair of measurements each with two possible outcomes, we find a necessary condition for classical nonlocal models to reproduce the statistics of all quantum states. This condition extends and generalizes work of Svetlichny and others in which it was showed that a particular class of classical nonlocal models, the ``separable'' models, cannot reproduce the statistics of all multiparticle quantum states. Our condition shows that the nonlocality present in some entangled multiparticle quantum states is much stronger than previously thought. We also study the sufficiency of our condition.
The paper is divided in two parts. In the first one a summary of the main issues about quantum non–locality is provided. In the second part, the connections with information and causality are considered. In particular, it is shown that a principle of information causality implies that hyper–correlations among experimental settings are not possible but only correlations among possible outcomes. Since a setting is for measuring a particular observable and the eigenbasis of this observable can be considered a code, this means that information codification is a local procedure.
Quantum entanglement cannot be used as a communication channel without an auxiliary light speed limited classical key to unlock the message at the receiver? Hermitian observables guarantee orthogonal sender base states that erase any nonlocal influence of the sender settings on the detection probabilities at the receiver. However, this is no longer true when the entangled whole has different macro-quantum coherent Glauber sender states. Glauber states are non-orthogonal eigenstates of the non-Hermitian photon destruction operator. The Born probability interpretation breaks down because of phase rigidity (P.W. Anderson's More is different). This is a new regime that is to orthodox quantum theory what general relativity is to special relativity. Antony Valentini has argued that the breakdown of the Born probability rule entails signal non locality (aka entanglement signals). The space-time interval between the sending and the receiving irreversible measurements is irrelevant depending only on the free will of the local observers. That is, this is a pre-metrical topological information effect. There is asymmetry between the sending and the receiving. Therefore, there is no ambiguity between active (retro) cause and passive effect. In particular a message can be decoded back from the future before it is sent, but only if it will be sent in a globally self-consistent Novikov time loop.