A new theoretical framework sets the limits for realizing quantum processes in space-time

Bell’s theorem, the well-known theoretical framework introduced by John Bell several decades ago, demarcates the limits of classical physical processes arising from relativistic causal principles. These are principles rooted in Einstein’s theory of relativity, which dictate how cause and effect work in the universe.

Researchers from Inria, Université Grenoble Alpes and ETH Zurich recently set out to determine whether similar types of limits also apply to quantum processes. Their article, published in Physical Examination Letters (PRL), introduces new theorems that highlight fundamental limits that could constrain the performance of quantum experiments in classical background spacetimes.

“Causality is at the heart of how we make sense of the world, but it takes different forms in two of our key physical theories: quantum theory and general relativity,” said V. Vilasini, co-author of the article, at Phys.org.

“In quantum theory, causality concerns how information flows between systems and operations, whereas in general relativity it relates to the structure of space-time itself. Surprisingly, the theory quantum allows processes with “indefinite causal order” (ICO) where the sequence of events can exist in a superposition.

To understand whether ICO processes, quantum processes in which there is no causal relationship between sequential events, can occur physically, researchers must first relate these processes to the well-established relativistic notion of causality in space-time. This is the main motivation behind the recent paper by Vilasini and his colleague Renato Renner.

“We developed a theoretical framework that connects the two concepts of causality in a clear and coherent way, with the aim of using minimal physical assumptions,” Vilasini said. “This allowed us to derive general theorems that are forbidden for any quantum experiment carried out in classical space-time.

“Interestingly, several sophisticated experiments have already been carried out, suggesting an ICO process, the ‘quantum switch’ in Minkowski space-time. The physical interpretation of these experiments has been a subject of long-standing discussion .

“Our forbidden framework and results also apply to these experiments and provide a new, finer-grained perspective on their interpretation and how quantum and relativistic causality can be reconciled in these experiments.”

With their recent article in PRLVilasini and Renner published a longer manuscript in Physical examination A. In this longer article, they describe their formalism in more detail, including additional results they collected.

“OUR PRL “The paper presents two forbidden theorems that describe the fundamental limits of space-time configurations and possible causal explanations of quantum experiments in classical space-time, which respect relativistic causality (implying faster signaling than light),” Vilasini explained.

The first theorem presented by the researchers essentially shows that any experiment to successfully carry out ICO processes in classical space-time would require the input and output agent systems to be non-localized or “spread out” across the space-time.

Their second theorem, on the other hand, theoretically demonstrates that even if an ICO process is carried out under the conditions described by the first theorem, “zooming in” to a finer level would reveal a well-defined and acyclical causal order.

“To make an analogy: Imagine a situation in which the demand and price of a product seem to influence each other in a loop,” Vilasini said. “On closer inspection, we would realize that demand at one point in time influences price at a later point in time, which then affects demand at an even later point in time, and so on.

“Similarly, in quantum experiments in classical spacetime, while ICO might appear at a ‘gross’ level, closer examination would reveal a quantum process with precise information-theoretic causal ordering which is part of the causality of space-time.”

Typically, research in experimental physics builds on previously introduced theories and aims to test their predictions. In contrast, the aforementioned quantum switching experiments were already carried out years ago and fueled the search for better theoretical frameworks to fully interpret and understand them.

“Despite our unsuccessful results, the ICO experiments already carried out remain fascinating,” Vilasini said. “Even though these experiments may proceed in a defined causal order, it is hoped that they will involve a distinct quantum resource not present in classical scenarios, in which spatial and temporal degrees of freedom both play a role.”

Recent papers from this team of researchers propose a unified framework that could be used to link different notions of causality across quantum and relativistic theories, potentially allowing reconciliation between these distinct physical theories.

Vilasini and Renner hope their theoretical framework will foster new causally-focused interdisciplinary collaborations between physicists specializing in the study of quantum mechanics and general relativity.

“The idea of ​​fine-grained causal structures introduced in our work is versatile – it can be applied whether or not there is a classical background spacetime – and could offer new techniques for exploring the physical realization of quantum processes in more exotic scenarios, such as when quantum clocks or rods are involved, or in quantum gravitational regimes where the geometry of space-time is subject to quantum uncertainty,” Vilasini said.

In their next studies, Vilasini and colleagues plan to continue developing their framework. First, they hope to address the open question of which classes of ICO processes can be physically realized in space-time.

“In a follow-up project with Matthias Salzger (now based at the International Center for the Theory of Quantum Technologies, Gdansk), we extended our framework to provide a characterization of these processes, suggesting that more counterintuitive ICO processes, such as those that violate causal inequalities cannot be faithfully realized in classical spacetimes,” Vilasini said.

“In our next studies, it would be interesting to determine whether our forbidden theorems are still valid in these new (possibly quantum gravitational) regimes, and to determine whether a broader class of ICO processes can be realized there. For example, there are- Is there a way to operationally certify the non-classicality of space-time geometry, in the same way that violations of Bell’s inequalities certify the non-classicality of correlations?

“Even more fundamentally, is there a way to understand how spacetime or its familiar aspects can emerge from the fundamental properties of the causal structures of quantum information theory?”

In the future, Vilasini also plans to study possible applications of his framework with Renner, to achieve information processing in a fixed space-time. In other words, she would like to determine whether the “quantum nature” of systems localization could be exploited to achieve or improve quantum communication, computing and cryptography.

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