⚛️ quantum physics

Theories with no superluminal signaling have greater information-processing power than theories with no superluminal causation

This paper demonstrates that physical theories permitting superluminal causation while strictly prohibiting superluminal signaling possess greater information-processing power than those forbidding both, as they can achieve specific non-classical correlation tasks that are impossible under the stricter no-superluminal-causation constraint.

Original authors: V. Vilasini, Roger Colbeck

Published 2026-04-13

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: V. Vilasini, Roger Colbeck

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, cosmic office building. In this building, there are strict rules about how information can travel. Usually, we think of two main rules:

The "No-Teleporting" Rule (No Superluminal Signaling): You cannot send a message to someone faster than the speed of light. If you shout a secret, it takes time to travel across the room. This is the rule that keeps our current physics (and our ability to send emails) from breaking down.
The "No-Telepathy" Rule (No Superluminal Causation): Not only can you not send a message, but you also cannot influence someone's reality faster than light. You can't just "will" a lightbulb in another room to turn on without a wire or a signal.

For a long time, physicists thought these two rules were the same thing. If you can't signal, you can't cause anything. But this new paper by Vilasini and Colbeck says: "Wait a minute. These are actually two different rules, and breaking the second one gives you superpowers that the first one doesn't."

Here is the breakdown of their discovery using simple analogies.

The Two Rules of the Cosmic Office

Rule A (No Superluminal Signaling - NSS): This is the rule about communication. It says, "You cannot send a text message to a colleague in a different time zone before the message has physically traveled there." If you break this, you can send a message into the past or faster than light, which creates paradoxes (like telling your past self to buy lottery tickets).
Rule B (No Superluminal Causation - NSC): This is the rule about influence. It says, "You cannot change the outcome of an event in a distant room just by flipping a switch here, unless a signal travels there first."

The authors show that you can theoretically build a universe where Rule A is still followed (no one can send a message faster than light), but Rule B is broken (you can still influence distant events instantly).

The Magic Trick: "Jamming"

To prove this, the authors use a concept called "Jamming."

Imagine three people: Alice, Charlie, and Bob.

Alice and Charlie are in two different rooms, far apart. They are trying to coordinate a secret handshake (a "non-classical correlation") without talking to each other.
In our normal world, they can't do this perfectly unless they share a secret plan beforehand.
Bob is a third person who can "jam" their connection.

The Scenario:
Alice and Charlie send their "settings" (what they are trying to do) to Bob. Bob then flips a switch that instantly changes the relationship between Alice's and Charlie's results.

The Catch: Bob cannot tell Alice or Charlie what the result is. He can't send them a message. So, Rule A (No Signaling) is safe. No one is sending a faster-than-light text.
The Twist: However, Bob did instantly change the outcome of their results. He influenced them. So, Rule B (No Causation) is broken.

The Two Impossible Tasks

The paper sets up two specific "challenges" for Alice and Charlie to solve:

Task 1: Alice and Charlie are in a normal timeline. Their inputs happen before their outputs.
- Result: If you follow Rule B (No Causation), they cannot solve the puzzle. It's impossible.
- Result: If you break Rule B but keep Rule A (using the Jamming trick), they can solve it perfectly.
Task 2 (The Time-Bender): This is the wilder scenario. Alice and Charlie set their inputs after they have already seen their results. It's like the movie Tenet or Interstellar.
- Result: If you follow Rule B, it is impossible for them to generate the correlation. The math says it's strictly forbidden.
- Result: If you break Rule B (allowing influence to go backward or instantly) but keep Rule A (no messages sent), they can solve it.

The "Retrocausality" Surprise

The most mind-bending part of the paper is about Task 2.

In a universe where you can "jam" correlations without sending messages, you can create a situation where the effect happens before the cause.

Imagine you are baking a cake.

Normal Physics: You mix the batter (Cause), then the cake bakes (Effect).
This Paper's Physics: The cake is already baked and sitting on the table. Then, you decide to mix the batter. The act of mixing the batter instantly "retroactively" ensures the cake was baked correctly.

The authors show that in a 1D universe (a straight line), you can arrange things so that the "baking" happens so far in the past that it looks like the future is changing the past. This is called certifiable retrocausality. You can prove the past changed, but you still can't send a message to your past self to win the lottery (because Rule A still holds).

Why Does This Matter?

You might ask, "Does this mean time travel is real?"
No. The authors are not saying our universe is like this. They are saying: "If we want to understand why our universe follows the strict rules it does, we need to know exactly what we are gaining by following them."

The Takeaway: By strictly forbidding "No Superluminal Causation" (Rule B), our universe loses a lot of "information processing power." We can't do these fancy coordination tricks.
The Insight: The fact that we can't do these tricks in real life suggests that Nature is very strict about Rule B. It's not just about preventing paradoxes (Rule A); it's about preventing the universe from having "too much power" to coordinate events instantly.

Summary Analogy

Think of the universe as a video game.

Rule A (No Signaling) is the rule that you can't send a cheat code to another player.
Rule B (No Causation) is the rule that you can't hack the server to change another player's score instantly.

This paper says: "If we only enforce Rule A, the game is still fair, but the players can secretly coordinate their scores in ways that seem like magic. If we enforce Rule B, the game is more limited, but it prevents these 'magic' correlations."

The authors are essentially showing us the "cheat codes" that exist if we relax the rules of causality, proving that our universe's strict adherence to "No Causation" is what keeps reality grounded, even if it limits our ability to process information in super-cool ways.

1. Problem Statement

The paper addresses a foundational question in physics: the distinction between two relativistic causality principles that are often conflated but are conceptually distinct:

No Superluminal Causation (NSC): Causal influences cannot propagate outside the future lightcone.
No Superluminal Signaling (NSS): Agents cannot communicate (signal) information faster than light.

While NSC implies NSS, the converse is not necessarily true. It is theoretically possible for a theory to violate NSC (allowing superluminal causal influence) while still satisfying NSS (preventing observable signaling). The authors aim to determine if this distinction has operational consequences. Specifically, they investigate whether theories that violate NSC but satisfy NSS possess greater information-processing power than theories strictly adhering to NSC. They focus on the task of generating non-classical correlations (violations of Bell inequalities) in specific spacetime configurations.

2. Methodology

The authors utilize a rigorous framework combining causal modeling and spacetime embeddings:

Causal Structures: They model physical theories as directed graphs where nodes represent variables (observed or unobserved) and edges represent causal mechanisms. They distinguish between classical, quantum, and post-quantum theories by the nature of the causal mechanisms (functions, quantum channels, or general maps).
Affects Relations: To formalize signaling, they use "affects relations." A variable $X$ affects $Y$ if an intervention on $X$ changes the probability distribution of $Y$ . They extend this to higher-order affects relations (e.g., $X$ affects $Y$ given interventions on $Z$ ) to capture complex signaling scenarios.
Spacetime Embedding: Causal models are embedded into a spacetime manifold (modeled as a partially ordered set $T$ $T$ ).
- NSC Definition: If $X \to Y$ is a causal edge, then the spacetime location of $X$ must be in the past lightcone of $Y$ ( $X \prec Y$ ).
- NSS Definition: An affects relation $X$ affects $Y$ (given $Z$ ) is compatible with spacetime only if the joint future of $Y$ and $Z$ is contained within the future of $X$ ( $F(Y) \cap F(Z) \subseteq F(X)$ ). This ensures no agent can access $Y$ and $Z$ before $X$ could have influenced them.
Tasks: The authors define two specific tasks involving two agents (Alice and Charlie) generating non-classical correlations $P(XZ|AC)$:
- Task 1: Inputs $A, C$ and outputs $X, Z$ are pairwise spacelike separated, except $A \prec X$ and $C \prec Z$ .
- Task 2: Inputs and outputs are such that the joint future of the outputs is contained in the joint future of the inputs ( $F(X) \cap F(Z) \subseteq F(A) \cap F(C)$ ), but no input is in the past lightcone of its corresponding output ( $A \not\prec X, C \not\prec Z$ ).

3. Key Contributions

Formal Distinction of Principles: The paper provides a rigorous operational distinction between NSC and NSS, demonstrating that they are not equivalent in terms of information-theoretic capabilities.
Impossibility Theorems for NSC:
- Task 1: Impossible to achieve non-classical correlations in any classical theory satisfying NSC (consistent with Bell's theorem).
- Task 2: Impossible to achieve any non-classical correlations (even in post-quantum theories) if NSC holds. In this configuration, NSC forces the correlation to be trivial ($P(XZ|AC) = P(XZ)$).
Feasibility under NSS (Jamming): The authors construct a protocol using "Jamming" (a concept from tripartite Bell scenarios) to show that Task 1 and Task 2 can be achieved in theories that violate NSC but satisfy NSS.
- Protocol: A third agent (Bob) receives classical inputs from Alice and Charlie. Bob chooses a setting $B$ that "jams" the correlations between Alice and Charlie's outputs ( $X$ and $Z$ ).
- Mechanism: Bob's setting $B$ influences the joint distribution $P(XZ)$ without affecting the marginals $P(X)$ or $P(Z)$ individually. This satisfies NSS (no signaling to Alice or Charlie individually) but violates NSC (causal influence from $B$ to $X/Z$ is superluminal).
Operational Certification: The paper demonstrates that in Task 2, the violation of NSC can be operationally certified without violating NSS. If an observer can predict the parity of outputs ( $X \oplus Z$ ) better than random guessing using inputs ( $A, C$ ), it proves the existence of superluminal causation, regardless of the underlying theory.
Retrocausality in (1+1)D: In (1+1)-dimensional Minkowski spacetime, the authors show that these protocols allow for certifiable retrocausality. The outputs $X$ and $Z$ can be generated at times arbitrarily earlier than the inputs $A$ and $C$ (negative time delay) while still satisfying NSS, provided the joint future of the outputs remains within the future of the jamming agent.

4. Results

Information Processing Gap: The set of theories satisfying NSS is strictly larger in terms of information-processing power than those satisfying NSC. Specifically, NSS theories can generate maximally non-classical correlations (PR-boxes) in spacetime configurations where NSC theories cannot generate any non-classical correlations.
Speed of Correlation Generation: In NSC theories, generating non-classical correlations between separated parties requires time $t \geq \Delta x / c$ . In NSS theories utilizing jamming, this time can be halved ( $t = \Delta x / 2c$ ) or, in (1+1)D, become negative (retrocausal).
Link to PR-Boxes: The protocol effectively converts the "jamming" resource into a Popescu-Rohrlich (PR) box, linking two distinct types of post-quantum resources.
Rejection of Jamming Theories: The results provide a strong argument against the physicality of theories allowing jamming (like certain non-local hidden variable theories). While they respect NSS, their ability to perform Task 2 (and the resulting certifiable retrocausality) suggests they violate fundamental relativistic principles (NSC).

5. Significance

Foundations of Physics: The work clarifies the hierarchy of relativistic principles. It suggests that NSC is a stronger and more necessary constraint than NSS for a physical theory to be considered "realistic," as violating NSC leads to counterintuitive phenomena like certifiable retrocausality.
Characterizing Quantum Theory: By exploring the boundaries of what is possible under NSC vs. NSS, the paper contributes to the program of reconstructing quantum theory from physical principles. It highlights that quantum theory sits in a specific niche: it violates NSC (in the sense of Bell non-locality) but respects NSS, yet it does not allow the extreme retrocausality or PR-box correlations achievable in general NSS theories.
Philosophical Implications: The findings challenge the viability of retrocausal models proposed to explain Bell correlations. Unlike previous retrocausal models which are indistinguishable from forward-causal models, this protocol offers a way to operationally verify retrocausality, making such theories more testable (and potentially falsifiable).
Future Directions: The paper opens avenues for studying information processing in theories with indefinite causal order and exploring the limits of device-independent cryptography in the presence of superluminal causation.

In summary, the paper proves that No Superluminal Signaling is insufficient to bound the information-processing power of a theory to that of standard physics. The additional constraint of No Superluminal Causation is required to prevent the generation of non-classical correlations in specific spacetime configurations and to rule out certifiable retrocausality.