Information Causality as a Physical Principle (0905.2292v3)

Abstract: Quantum physics exhibits remarkable distinguishing characteristics. For example, it gives only probabilistic predictions (non-determinism) and does not allow copying of unknown state (no-cloning). Quantum correlations may be stronger than any classical ones, nevertheless information cannot be transmitted faster than light (no-signaling). However, all these features do not single out quantum physics. A broad class of theories exist which share such traits with quantum mechanics, while they allow even stronger than quantum correlations. Here, we introduce the principle of Information Causality. It states that information that Bob can gain about a previously completely unknown to him data set of Alice, by using all his local resources (which may be correlated with her resources) and a classical communication from her, is bounded by the information volume of the communication. In other words, if Alice communicates m bits to Bob, the total information access that Bob gains to her data is not greater than m. For m=0, Information Causality reduces to the standard no-signaling principle. We show that this new principle is respected both in classical and quantum physics, whereas it is violated by all the no-signaling correlations which are stronger that the strongest quantum correlations. Maximally strong no-signalling correlations would allow Bob access to any m bit subset of the whole data set held by Alice. If only one bit is sent by Alice (m=1), this is tantamount to Bob being able to access the value of any single bit of Alice's data (but of course not all of them). We suggest that Information Causality, a generalization of no-signaling, might be one of the foundational properties of Nature.

• The paper introduces Information Causality as a principle limiting the information Bob can access based on the classical bits communicated by Alice.
• It rigorously demonstrates that hypothetical PR-boxes violate this limit, exceeding quantum bounds like Tsirelson's bound.
• The approach offers a new framework for understanding quantum correlations and may guide future advances in quantum information protocols.

Information Causality as a Physical Principle: An Overview

The paper "Information Causality as a Physical Principle" introduces an innovative concept called Information Causality, which serves as a potential foundational principle for distinguishing physical quantum theories from nonphysical ones. Authored by researchers Marcin Pawłowski, Tomasz Paterek, Dagomir Kaszlikowski, Valerio Scarani, Andreas Winter, and Marek Żukowski, the paper explores the necessity and implications of Information Causality in theoretical physics.

Core Concepts

At the heart of the discussion are the inherent discrepancies between classical and quantum physics, particularly in terms of nonlocal correlations — entanglement that surpasses classical definition but adheres to the no-signaling principle. Quantum mechanics is renowned for its probabilistic nature, inability to clone unknown states, and stronger-than-classical correlations. Nevertheless, these attributes are not uniquely quantum; other theoretical frameworks also exhibit such traits but allow for even stronger-than-quantum correlations, as proposed by Popescu and Rohrlich.

Information Causality posits that the information Bob can gain about a previously completely unknown dataset of Alice is bound by the volume of classical information Alice communicates to Bob. Specifically, if Alice sends $m$ bits, the information accessible to Bob cannot exceed $m$ bits. For $m=0$, it reduces to the no-signaling condition, asserting that quantum and classical physics respect this principle while other hypothetical no-signaling theories, which allow PR-box-like correlations, do not.

Framework and Results

The paper formalizes Information Causality as a principle that constrains the mutual information shared between two parties engaged in a communication task. The authors provide a comprehensive treatment of this task in which Alice aims to help Bob reconstruct bits of her data through minimal communication, utilizing previously shared correlations.

The violation of Information Causality is elegantly demonstrated using PR-boxes or nonlocal boxes, hypothetical devices that achieve what is impossible within quantum limits. These PR-boxes suggest maximal correlations beyond Tsirelson's bound, a well-known quantum limit. The central results demonstrate that all systems adhering to quantum physics respect Information Causality, whereas PR-boxes, with Maximal Algebraic Correlations, violate this principle.

The research manifests critical numerical benchmarks:

• The mutual information limit $S_C \leq 3$, where classical occurrences surpass $S_Q = 2 + \sqrt{2}$ per Tsirelson's bound for quantum mechanics.
• PR-boxes maximize at $S_{NS} = 4$, revealing a gross violation of Information Causality — a contradiction to physical realism.

Implications and Speculations

The advocated principle provides a deep conceptual insight, potentially enlightening unexplained aspects of quantum theory. It positions Information Causality as a stepping stone analogous to the no-signaling principle, suggesting it might play a crucial role in defining the allowable boundaries within physical reality.

The broader implication encompasses a reevaluation of quantum correlations, guiding future research on whether Information Causality could uniquely define quantum bounds amidst no-signaling conditions. Researchers hypothesize about its placement with regard to securing quantum protocols and optimizing information-theoretic tasks independent of explicit quantum frameworks.

Conclusion

The paper "Information Causality as a Physical Principle" unveils a potential universality inherent in quantum mechanics, potentially offering researchers a new lens to explore entanglement, signaling constraints, and the underlying calculus of quantum correlations. The principle’s alignment with known physical realities, its speculation into fundamental descriptions of nature, and the thought-provoking boundaries it delineates make it a considerable point of interest for future theoretical explorations within the quantum domain.