Maximum and Minimum Causal Effects of Physical Processes
Bibliographic record
Abstract
We introduce two quantitative measures of the strength of causal relations in quantum theory and more general physical theories. These two measures, called the maximum and minimum causal effect, quantify the maximum and minimum changes in the output of a quantum process induced by changes in its input. The maximum and minimum causal effect possesses useful properties, such as continuity and data-processing inequality. In quantum theory, they have close connections with quantum information tasks. The maximum quantum causal effect can be used to detect quantum channels with nonzero capacity for transmitting classical information. The minimum causal effect can be used to guarantee the recoverability of quantum information: every quantum process with a high value of the minimum quantum causal effect can be approximately inverted. Moreover, we show that the quantum causal effects satisfy a duality relation: if the minimum causal effect of a quantum system A on another quantum system B is high, then A must have a low value of the maximum causal effect on any other quantum system B ′ that is spacelike separated with B . This duality implies a monogamy relation for quantum causal effects, and represents a fundamental difference between quantum and classical causal relations. We illustrate the application of the maximum causal effect to the analysis of two paradigmatic examples, the first involving a coherent superposition of direct cause and common cause, and the second involving a coherent superposition of multiple quantum processes.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.022 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".