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arXiv:quant-ph/9906113

Quantum superluminal communication does not result in the causal loop

Shan Gao

Published Jun 29, 1999• 1 citation
arXivHTMLPDF

Abstract

We show that the quantum superluminal communication based on the quantum nonlocal influence, if exists, will not result in the causal loop, this conclusion is essentially determined by the peculiarity of the quantum nonlocal influence itself, according to which there must exist a preferred Lorentz frame for consistently describing the quantum nonlocal process.

DOI
10.48550/arxiv.quant-ph/9906113

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We show that the quantum superluminal communication based on the quantum nonlocal influence, if exists, will not result in the causal loop, this conclusion is essentially determined by the peculiarity of the quantum nonlocal influence itself, according to which there must exist a preferred Lorentz frame for consistently describing the quantum nonlocal process.
The implications of quantum nonlocality are briefly reviewed. It is shown that the collapse of the wave function requires the existence of a preferred Lorentz frame. This opens the first door to quantum superluminal communication (QSC). A theory of QSC is deeply analyzed. We demonstrate that the combination of the collapse of the wave function and the consciousness of the observer will permit the observer to distinguish nonorthogonal states under some condition. This provides a principle for realizing QSC. A practical QSC scheme is given based upon the QSC principle. Some evidence of the existence of QSC is also discussed. Besides, a new space-time transformation for QSC is analyzed, and two ways to measure the preferred Lorentz frame are given.
It may well be that a relativistic version of the theory, while Lorentz invariant and local at the observational level, may be necessarily non-local and with a preferred frame (or aether) at the fundamental level. – John Bell [1] Introduction Bell's theorem establishes a contradiction between locality (and a few other assumptions) and certain predictions of quantum mechanics [2]. There have been two main issues surrounding the deep implications of this celebrated theorem. The first issue is basic, and it concerns whether the theorem really establishes that nonlocality is a necessary feature of any empirically viable theory and hence a feature of nature itself. One aspect of the issue concerns exactly what the underlying assumptions of Bell's theorem are. For example, some argue that these assumptions include the assumption of counterfactual definiteness [3–5], while others disagree [6–8]. The other aspect of the issue concerns which assumption should be dropped due to the resulting contradiction. Some believe that standard quantum mechanics may avoid nonlocality by denying counterfactual definiteness [3–5]. The second issue is much deeper, and it concerns how to make sense of the strange nonlocality when assuming that Bell's theorem establishes that our world is nonlocal. In particular, it has yet to be determined whether such quantum nonlocality is compatible with the theory of relativity, e.g., whether the nonlocality requires the existence of a preferred Lorentz frame [7, 9, 10]. It seems that “there is a preferred frame of reference, and in this preferred frame of reference things do go faster than light … Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant” [11]. But it also seems possible that the existence of a preferred Lorentz frame is an illusion, since it cannot be detected according to standard quantum mechanics. A more subtle issue is whether quantum nonlocality permits superluminal signaling. It is widely thought that the answers to these questions will lead to a deeper understanding of Bell's theorem and quantum nonlocality. In this paper, we will present a new analysis of quantum nonlocality and its apparent incompatibility with relativity.
Causality is fundamental to science, but it appears in several different forms. One is relativistic causality, which is tied to a spacetime structure and forbids signaling outside the future. A second is an operational notion of causation that considers the flow of information between physical systems and interventions on them. In [V. Vilasini and R. Colbeck, General framework for cyclic and fine-tuned causal models and their compatibility with space-time, Phys. Rev. A 106, 032204 (2022).PLRAAN2469-992610.1103/PhysRevA.106.032204], we propose a framework for characterizing when a causal model can coexist with relativistic principles such as no superluminal signaling, while allowing for cyclic and nonclassical causal influences and the possibility of causation without signaling. In a theory without superluminal causation, both superluminal signaling and causal loops are not possible in Minkowski spacetime. Here we demonstrate that if we only forbid superluminal signaling, superluminal causation remains possible and show the mathematical possibility of causal loops that can be embedded in a Minkowski spacetime without leading to superluminal signaling. The existence of such loops in the given spacetime could in principle be operationally verified using interventions. This establishes that the physical principle of no superluminal signaling is not by itself sufficient to rule out causal loops between Minkowski spacetime events. Interestingly, the conditions required to rule out causal loops in a spacetime depend on the dimension. Whether such loops are possible in three spatial dimensions remains an important open question.
Non-classical correlations resulting from entangled quantum systems have sparked debates about the compatibility of quantum theory and relativity, and about the right way to think about causation. Key to a causal theory is that superluminal signalling is forbidden, which holds in quantum theory. In Bell scenarios, relativistic causality principles like no superluminal signalling are often assumed to follow from the standard no-signalling constraints on correlations. We explore the connections between a range of relativistic principles, including no superluminal signalling and no causal loops, and constraints on correlations that can arise with arbitrary interventions, within multi-party Bell scenarios. This includes standard no-signalling conditions and proposed relaxations allowing phenomena like jamming, where it was suggested that superluminal signalling and causal loops remain impossible. Using our recent framework combining relativistic principles with causal modelling, we show that any theory (classical or non-classical) allowing jamming must rely on causal fine-tuning and superluminal causal influences. Additionally, we show that jamming theories can lead to superluminal signalling in certain situations, highlighting limitations for their physicality. However, we identify cases where jamming correlations avoid superluminal signalling under general interventions, demonstrating that standard no-signalling constraints are not necessary for this purpose. We also show that these constraints are insufficient to rule out superluminal signalling and are neither necessary nor sufficient for ensuring no causal loops under general interventions. Finally, we derive necessary and sufficient conditions for ruling out superluminal signalling and operationally detectable causal loops, solidifying our understanding of relativistic causality principles in information processing tasks in space-time.