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Information Causality

A proposed principle limiting Bob's information gain about Alice's unknown data to the n classical bits she sends, even with pre-shared nonsignalling correlations.

Version
v1 · 2026-09-28 · History
Domain-specific #
10052
Domain group
Natural Sciences
Origin domain
Physics
Subdomains
Quantum Information Science, Quantum Foundations, Physical Principles for Correlations → Physics

Core Idea

Information causality is a proposed bound on a communication-assisted information task. Alice may share a nonsignalling resource with Bob, but if she sends only n classical bits, Bob's total gain about data previously unknown to him cannot exceed that n-bit budget under the principle's definition.

This is stronger than no-signalling alone and is useful for testing hypothetical post-quantum correlations. The claim is not a general law that all information must have a physical sender; it is a particular classical-message task, and its bipartite success does not settle every multipartite case.

Structural Signature

Sig role-phrases:

  • Sender's unknown data — Provides the information Bob is trying to learn rather than pre-known shared content. It is necessary. Counterfactual: Already-known data do not measure new information gain.
  • Receiver's local resources — Includes Bob's local computation and pre-shared correlations available before communication. It is necessary to scope. Counterfactual: Ignoring pre-shared resources misses the claimed strength of the principle.
  • Classical message budget — Caps Alice-to-Bob communication at n classical bits. It is defining input. Counterfactual: Replacing it with quantum transmission changes the principle's domain.
  • Information-gain measure — Quantifies Bob's new information about Alice's data across the specified retrieval task. It is defining readout. Counterfactual: A single guessed answer alone may not capture the total-information bound.
  • Nonsignalling correlation class — Tests whether a physical or hypothetical shared resource obeys the message-limited gain rule. It is diagnostic domain. Counterfactual: Some beyond-quantum correlations fail the bound despite no-signalling.
  • Scenario boundary — Separates bipartite CHSH conclusions from stronger claims about all multipartite correlations. It is limit. Counterfactual: A bipartite pass cannot prove complete characterization of quantum theory.

What It Is Not

  • Not the everyday notion of causation. The name refers to a formal information-gain limit in quantum foundations.
  • Not no-signalling alone. A nonsignalling resource can still violate the stronger information-causality bound in a communication task.
  • Not a quantum-message bound. Sending qubits alters the allowed communication resource.
  • Not a complete axiomatization of quantum correlations. Multipartite scenarios require additional principles.
  • Closest near-miss. No-signalling merely forbids communication through a shared resource alone; information causality adds a bound on information gained when a limited classical message is sent.

Scope of Application

  • Quantum foundations. Tests whether candidate correlation theories satisfy a proposed physical information principle.
  • Communication-task analysis. Relates classical message length to information gain when parties have pre-shared resources.
  • Bell-correlation boundaries. Excludes specified post-quantum CHSH-strength correlations despite no-signalling.
  • Multipartite limitations. Marks why a bipartite information principle does not by itself identify the whole quantum set.

Clarity

Specify who holds which data, what Bob initially knows, the task distribution and gain measure, the n-bit classical message, pre-shared correlation class, and whether the result is bipartite or multipartite. A claim that a 'correlation transmits information' is not well formed until the local resource and actual communication channel are separated.

Manages Complexity

Nonlocal correlations, transmitted messages, prior knowledge, and information gain interact. The principle compresses that scenario to an inequality tied to communicated classical bits, yet its interpretation still depends on the exact task and correlation class; a broad slogan loses the mathematical boundary.

Abstract Reasoning

  1. Define Alice's unknown data and Bob's retrieval objective.
  2. Fix the permitted classical communication budget and pre-shared nonsignalling resource.
  3. Calculate or bound Bob's total new information under the task definition.
  4. Compare that gain with the message budget to test information causality.
  5. State which correlation regime and party count the result covers, and withhold wider conclusions.

Knowledge Transfer

The message-budget reasoning transfers to other bipartite information-causality games that preserve classical communication and the same gain definition. It does not transfer unchanged to qubit transmission, ordinary causal inference, or unrestricted multipartite theories; a more general parent idea about resource bounds is not the named physical principle.

Examples

Canonical

Alice possesses data Bob does not know and sends a one-bit classical message. Even if they share quantum entanglement beforehand, the information-causality principle limits Bob's total new information about those data to that one-bit budget in its prescribed task. The example names a bound, not a protocol for transmitting or extracting data.

Mapped back: Sender's unknown data → Alice's initially hidden data; Receiver's local resources → local processing plus pre-shared entanglement; Classical message budget → one bit; Information-gain measure → total new information limited to one bit; Nonsignalling correlation class → quantum entanglement; Scenario boundary → bipartite Alice–Bob task.

Applied / In Practice

In the classical limit, Alice and Bob may share randomness before the task, yet that shared resource by itself does not communicate Alice's later private data. After Alice sends a two-bit classical message, information causality bounds Bob's new information about those data by two bits. This positive case exposes why the prior shared resource and actual message must be counted separately.

Mapped back: Sender's unknown data → Alice's later private data; Receiver's local resources → prior shared randomness and local computation; Classical message budget → two bits; Information-gain measure → at most two bits of new information; Nonsignalling correlation class → classical shared randomness; Scenario boundary → bipartite classical limiting case.

Structural Tensions

T1 — No-Signalling Permissiveness versus Information-Gain Restraint. A shared resource can obey no-signalling while enabling information gains incompatible with a limited classical message; the stronger rule narrows the admissible correlation set.

Diagnostic: Does this resource let Bob exceed the communicated-bit budget in the specified task?

T2 — Simple Physical Principle versus Complete Quantum Characterization. A compact bipartite bound explains why some superquantum correlations are excluded, but elevating it to a full multipartite characterization loses cases the principle cannot rule out.

Diagnostic: Which scenario and quantum boundary is actually established?

Structural–Framed Character

A provisional portable skeleton is an information-gain bound set by a communication budget. The named principle requires an Alice–Bob task, n transmitted classical bits, and pre-shared nonsignalling resources; no exact DAG genus is verified.

Evaluative weight: It is a proposed physical admissibility test, not a moral rule. Human-practice-bound: Low formally, though task and gain measures are specified by researchers. Institutional origin: Quantum-foundations scholarship formulated the principle; its status depends on theory and proof. Vocabulary travels: Budget logic applies to related games, not automatically to qubits or unrestricted multipartite settings. Import versus recognize: Recognize an instance only with the same classical-bit and gain roles; generic “information is causal” talk imports a different idea.

Its character: A conditional formal bound with an explicit quantum-foundations frontier.

Structural Core vs. Domain Accent

Skeletal core. A bounded communication resource limits a receiver's information gain.

Domain-bound accent. Alice's unknown data, Bob's query, n classical bits, the gain measure, and pre-shared nonsignalling correlations specify the task.

Why not prime. A generic budget metaphor lacks this task and bound; the named result cannot be asserted for arbitrary communication models.

  • Recorded DAG status — approved unparented root. The frozen graph supplies no necessary parent for the exact quantum-information task and its bound.

  • Related — no-signalling, Tsirelson bound, superdense coding, and quantum nonlocality. The first is weaker, the second a comparison boundary, the third changes communication type, and the fourth is the broader subject; none is silently made a DAG parent.

Neighborhood in Abstraction Space

Information Causality sits in a moderately populated region (41st percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Quantum States & Computational Models (12 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08

Not to Be Confused With

  • No-signalling. Tell: Is there a bounded classical message and a total-information test, or only absence of signalling from shared resources?
  • Superdense coding. Tell: Are qubits transmitted, thereby changing the communication model?
  • Tsirelson bound. Tell: Is the statement a CHSH correlation boundary or the operational information-gain principle?
  • General causal inference. Tell: Is the object an Alice–Bob communication task rather than an observational cause–effect claim?

References

  • Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Information_causality (revision 1369616195).

  • Pawłowski et al., Information causality as a physical principle, Nature 461 (2009): https://www.nature.com/articles/nature08400

  • Gallego et al., Quantum correlations require multipartite information principles, Physical Review Letters 107 (2011): https://doi.org/10.1103/PhysRevLett.107.210403

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.