Information causality

Information causality is a physical principle suggested in 2009.^[1] Information causality states that the information gain a receiver (Bob) can reach about data, previously unknown to him, from a sender (Alice), by using all his local resources and $n$ classical bits communicated by the sender, is at most $n$ bits; and that this limitation should hold even in the case where Alice and Bob pre-share a physical non-signaling resource, such as an entangled quantum state.

The principle assumes classical communication: if quantum bits were allowed to be transmitted, the information gain could be higher (for example if Alice and Bob pre-share some entangled qubits) as demonstrated in the quantum superdense coding protocol.^[2]

The principle is respected by all correlations accessible with quantum physics, while it excludes all correlations which violate the quantum Tsirelson bound for the CHSH inequality. However, it does not exclude beyond-quantum correlations in multipartite situations.^[3] The principle has also been related to a principle called thermodynamic sufficiency ^[4].

References

^ Pawłowski, Marcin; Paterek, Tomasz; Kaszlikowski, Dagomir; Scarani, Valerio; Winter, Andreas; Żukowski, Marek (2009). "Information causality as a physical principle". Nature. 461 (7267): 1101–1104. arXiv:0905.2292. Bibcode:2009Natur.461.1101P. doi:10.1038/nature08400. ISSN 0028-0836. PMID 19847260. S2CID 4428663.
^ Chaves, Rafael; Majenz, Christian; Gross, David (2015). "Information-Theoretic Implications of Quantum Causal Structures". Nature Communications. 6 (1): 5766. arXiv:1407.3800. doi:10.1038/ncomms6766. ISSN 2041-1723.
^ Gallego, Rodrigo; Würflinger, Lars Erik; Acín, Antonio; Navascués, Miguel (2011-11-15). "Quantum Correlations Require Multipartite Information Principles". Physical Review Letters. 107 (21): 210403. arXiv:1107.3738. Bibcode:2011PhRvL.107u0403G. doi:10.1103/physrevlett.107.210403. ISSN 0031-9007. PMID 22181861. S2CID 31107416.
^ Harremoës, Peter (2020-02-24). "From thermodynamic sufficiency to information causality". Quantum Stud. Math. 7: 255-268. arXiv:2002.02895. doi:10.1007/s40509-020-00222-w.

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