Oughton Natasha, Timpson Christopher G
Somerville College, University of Oxford, Oxford OX2 6HD, UK.
Faculty of Philosophy, Brasenose College, University of Oxford, Oxford OX1 4AJ, UK.
Entropy (Basel). 2024 Jun 29;26(7):562. doi: 10.3390/e26070562.
The Information Causality principle was proposed to re-derive the Tsirelson bound, an upper limit on the strength of quantum correlations, and has been suggested as a candidate law of nature. The principle states that the Shannon information about Alice's distant database gained by Bob after receiving an bit message cannot exceed bits, even when Alice and Bob share non-local resources. As originally formulated, it can be shown that the principle is violated exactly when the strength of the shared correlations exceeds the Tsirelson bound. However, we demonstrate here that when an alternative measure of information, one of the Renyi measures, is chosen, the Information Causality principle no longer arrives at the correct value for the Tsirelson bound. We argue that neither the assumption of particular 'intuitive' properties of uncertainties measures, nor pragmatic choices about how to optimise costs associated with communication, are sufficient to motivate uniquely the choice of the Shannon measure from amongst the more general Renyi measures. We conclude that the dependence of the success of Information Causality on mere convention undermines its claimed significance as a foundational principle.
信息因果律原理被提出用于重新推导量子关联强度的上限——Tsirelson 界，并且已被视为一条自然定律的候选者。该原理指出，即使爱丽丝和鲍勃共享非局域资源，鲍勃在接收到一个 n 比特消息后从爱丽丝的远程数据库中获得的香农信息也不能超过 n 比特。按照最初的表述，可以证明当共享关联强度超过 Tsirelson 界时，该原理会被精确违反。然而，我们在此证明，当选择一种替代的信息度量，即 Renyi 度量之一时，信息因果律原理就不再能得出 Tsirelson 界的正确值。我们认为，无论是关于不确定性度量的特定“直观”属性的假设，还是关于如何优化与通信相关成本的务实选择，都不足以唯一地促使从更一般的 Renyi 度量中选择香农度量。我们得出结论，信息因果律的成功仅依赖于惯例，这削弱了它作为一个基本原理所宣称的重要性。
