# Information causality

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'''Information causality''' is a [physical principle](/source/physical_law) suggested in 2009.<ref>{{cite journal | last1=Pawłowski | first1=Marcin | last2=Paterek | first2=Tomasz | last3=Kaszlikowski | first3=Dagomir | last4=Scarani | first4=Valerio | last5=Winter | first5=Andreas |author-link5=Andreas Winter| last6=Żukowski | first6=Marek | title=Information causality as a physical principle | journal=Nature | volume=461 | issue=7267 | year=2009 | issn=0028-0836 | doi=10.1038/nature08400 | pages=1101–1104| pmid=19847260 |arxiv=0905.2292| bibcode=2009Natur.461.1101P | s2cid=4428663 }}</ref> Information causality states that the information gain a receiver ([Bob](/source/Alice_and_Bob)) can reach about data, previously unknown to him, from a sender (Alice), by using all his local resources and <math>n</math> classical bits communicated by the sender, is at most <math>n</math> bits; and that this limitation should hold even in the case where Alice and Bob pre-share a physical [non-signaling](/source/No-signaling_principle) resource, such as an entangled quantum state.

The principle assumes classical communication: if [quantum bits](/source/Qubit) 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](/source/superdense_coding) protocol.<ref>{{cite journal | last1=Chaves | first1=Rafael | last2=Majenz | first2=Christian | last3=Gross | first3=David | title=Information-Theoretic Implications of Quantum Causal Structures | journal=Nature Communications | volume=6 | issue=1 | year=2015 | issn=2041-1723 | doi=10.1038/ncomms6766 | page=5766 | pmid=25562600 | arxiv=1407.3800 | bibcode=2015NatCo...6.5766C }}</ref>

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](/source/Tsirelson's_bound). However, it does not exclude beyond-quantum correlations in multipartite situations.<ref>{{cite journal | last1=Gallego | first1=Rodrigo | last2=Würflinger | first2=Lars Erik | last3=Acín | first3=Antonio | last4=Navascués | first4=Miguel | title=Quantum Correlations Require Multipartite Information Principles | journal=Physical Review Letters | volume=107 | issue=21 | date=2011-11-15 | issn=0031-9007 | doi=10.1103/physrevlett.107.210403 | article-number=210403| pmid=22181861 | arxiv=1107.3738 | bibcode=2011PhRvL.107u0403G | s2cid=31107416 }}</ref> The principle has also been related to a principle called thermodynamic sufficiency.<ref>{{cite journal | last1=Harremoës | first1=Peter | title=From thermodynamic sufficiency to information causality | journal=Quantum Stud. Math. | volume=7 | page=255-268 | date=2020-02-24 | issue=2 | doi=10.1007/s40509-020-00222-w  | arxiv=2002.02895 | bibcode=2020QSMF....7..255H }}</ref> 

== See also ==
* [Tsirelson's bound](/source/Tsirelson's_bound)
* [Quantum nonlocality](/source/Quantum_nonlocality)

== References ==
{{Reflist}}

{{DEFAULTSORT:Information causality}}
Category:Quantum information science

{{Quantum-stub}}

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Adapted from the Wikipedia article [Information causality](https://en.wikipedia.org/wiki/Information_causality) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Information_causality?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.