Information causality from an entropic and a probabilistic perspective

Abstract

The information causality principle is a generalisation of the no-signalling principle which implies some of the known restrictions on quantum correlations. But despite its clear physical motivation, information causality is formulated in terms of a rather specialised game and figure of merit. We explore different perspectives on information causality, discussing the probability of success as the figure of merit, a relation between information causality and the non-local `inner-product game', and the derivation of a quadratic bound for these games. We then examine an entropic formulation of information causality with which one can obtain the same results, arguably in a simpler fashion.

7 pages, v2: some references added and minor improvements

References in corpus (8)

• Probabilistic theories with purification
• Guess your neighbour's input: a multipartite non-local game with no quantum advantage
• Recovering part of the quantum boundary from information causality
• Entropy and Information Causality in General Probabilistic Theories
• Entropy in general physical theories
• Distinguishability Measures and Entropies for General Probabilistic Theories
• Implausible Consequences of Superstrong Nonlocality
• Strong nonlocality: A trade-off between states and measurements

Cited by in corpus (20)

• Information-Theoretic Implications of Quantum Causal Structures
• A graph-separation theorem for quantum causal models
• Simulating all non-signalling correlations via classical or quantum theory with negative probabilities
• Classical theories with entanglement
• Tsirelson's bound from a Generalised Data Processing Inequality
• Indistinguishability of causal relations from limited marginals
• Mutually Unbiased Balanced Functions & Generalized Random Access Codes
• Quantum information causality
• Information Content of Systems as a Physical Principle
• Analysing causal structures in generalised probabilistic theories
• Nonlinear Schrödinger equations and generalized Heisenberg uncertainty principle violating the principle of estimation independence
• Information Causality in the Quantum and Post-Quantum Regime
• The chain rule implies Tsirelson's bound: an approach from generalized mutual information
• Cryptographic Quantum Bound on Nonlocality
• Measurement entropy in Generalized Non-Signalling Theory cannot detect bipartite non-locality
• Estimation independence as an axiom for quantum uncertainty
• Qubit from the classical collision entropy
• Tsirelson's Bound and the Quantum Monogamy Bound from Global Determinism
• Testing Information Causality for General Quantum Communication Protocols
• Information causality beyond the random access code model