New theoretical framework sets limits for the realization of quantum processes in spacetime

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

Researchers at Inria, Université Grenoble Alpes and ETH Zurich recently set out to investigate whether similar types of limits also apply to quantum processes. Their paper, published in Physical Review Letters (PRL), introduces new theorems that outline fundamental limits that could constrain the realization of quantum experiments in classical background spacetimes.

“Causality is central to how we make sense of the world, but it takes on different forms within two of our key physical theories: quantum theory and general relativity,” V. Vilasini, co-author of the paper, told Phys.org.

“In quantum theory, causality concerns how information flows between systems and operations, while in general relativity, it’s tied to the structure of spacetime itself. Surprisingly, quantum theory permits 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 a causal relationship between sequential events does not exist, can physically occur, researchers first need to connect these processes to the well-established relativistic notion of causality in spacetime. This was the primary motivation behind the recent paper by Vilasini and her colleague Renato Renner.

“We developed a theoretical framework that links the two concepts of causality in a clear and consistent way, aiming to use minimal physical assumptions,” said Vilasini. “This allowed us to derive general no-go theorems for any quantum experiment performed in classical spacetime.

“Interestingly, several sophisticated experiments have already been performed, that suggest an ICO process, the ‘quantum switch’ in Minkowski spacetime. The physical interpretation of these experiments has been a subject of longstanding discussions.

“Our framework and no-go results apply to these experiments as well, and yield a new fine-grained perspective on their interpretation, and how quantum and relativistic causality can be reconciled in these experiments.”

Along with their recent paper in PRL, Vilasini and Renner published a longer manuscript in Physical Review A. In this longer paper, they outline their formalism in greater detail, including additional results they collected.

“Our PRL paper introduces two no-go theorems that outline fundamental limits on spacetime configurations and possible causal explanations for quantum experiments in classical spacetimes, which respect relativistic causality (implying no faster-than-light signaling),” explained Vilasini.

The first theorem presented by the researchers essentially shows that any experiment aimed at successfully realizing ICO processes in classical spacetime would require that input and output agent systems be non-localized or ”spread out” in spacetime.

Their second theorem, on the other hand, theoretically demonstrates that even if an ICO process is realized under the conditions outlined by the first theorem, “zooming in” at a finer level would unveil a well-defined and acyclic causal order.

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

“Similarly, in quantum experiments in classical spacetimes, while ICO might appear at a ‘coarse’ level, a closer examination would reveal a quantum process with a definite information-theoretic causal order that fits within spacetime causality.”

Typically, experimental physics research builds on previously introduced theories and are aimed at testing their predictions. In contrast, the aforementioned quantum switch experiments were already performed years ago, and have fueled the search for better theoretical frameworks to fully interpret and understand them.

“Despite our no-go results, the ICO experiments already performed remain fascinating,” said Vilasini. “Even though these experiments can unravel into a definite causal order, there’s hope that they involve a distinct quantum resource not present in classical scenarios, where spatial and temporal degrees of freedom both play a role.”

The recent papers by this team of researchers propose a unified framework that could be used to relate different notions of causality across quantum and relativistic theories, potentially enabling a reconciliation between these distinct physical theories.

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

“The idea of fine-graining causal structures introduced in our work is versatile—it can be applied whether or not there is a classical background spacetime—this 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 spacetime geometry is subject to quantum uncertainty,” said Vilasini.

In their next studies, Vilasini and her collaborators plan to continue building on their framework. First, they hope to tackle the open question of which classes of ICO processes can be physically realized in spacetime.

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

“In our next studies, it would be intriguing to investigate whether our no-go theorems still hold in these new (possibly quantum gravitational) regimes, and to determine whether a broader class of ICO processes can be realized there. For instance, is there a way to operationally certify the non-classicality of spacetime geometry, similar to how violations of Bell inequalities certify non-classicality in correlations?

“Even more fundamentally, is there a way to understand how spacetime or familiar aspects of it may emerge from basic properties of quantum information-theoretic causal structures?”

In the future, Vilasini also plans to investigate the possible applications of her framework with Renner, for realizing information processing within a fixed spacetime. In other words, she would like to determine if the “quantumness” in the localization of systems could be leveraged to realize or enhance quantum communication, computation and cryptography.

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