One-shot and asymptotic classical capacity in general physical theories

Abstract

With the recent development of quantum information theory, some attempts exist to construct information theory beyond quantum theory. Here we consider hypothesis testing relative entropy and one-shot classical capacity, that is, the optimal rate of classical information transmitted by using a single channel under a constraint of a certain error probability, in general physical theories where states and measurements are operationally defined. Then we obtain the upper bound of one-shot classical capacity by generalizing the method given by Wang and Renner [Phys. Rev. Lett. 108, 200501 (2012)]. Also, we derive the lower bound of the capacity by showing the existence of a good code that can transmit classical information with a certain error probability. Applying the above two bounds, we prove the asymptotic equivalence between classical capacity and hypothesis testing relative entropy even in any general physical theory.

arXiv comment7+6 pages, 1 figure. Accepted version for publication in PRA. We fixed typos, improved some explanations, and changed the structure of Chapters 5 and 6. The first sentence on page 5 is modified, adding the references

References in corpus (30)

• Information Causality as a Physical Principle
• Informational derivation of Quantum Theory
• From Classical to Quantum Shannon Theory
• Probabilistic theories with purification
• One-Shot Classical-Quantum Capacity and Hypothesis Testing
• The quantum capacity of channels with arbitrarily correlated noise
• Generalized Probability Theories: What determines the structure of quantum theory?
• Higher-order interference and single-system postulates characterizing quantum theory
• Entropy and Information Causality in General Probabilistic Theories
• Entropy in general physical theories
• General probabilistic theories: An introduction
• Generalized Probabilistic Theories Without the No-Restriction Hypothesis
• The structure of reversible computation determines the self-duality of quantum theory
• Distilling entanglement from arbitrary resources
• Distinguishability Measures and Entropies for General Probabilistic Theories
• A smooth entropy approach to quantum hypothesis testing and the classical capacity of quantum channels
• Entanglement and thermodynamics in general probabilistic theories
• Optimal State Discrimination in General Probabilistic Theories
• Entanglement and superposition are equivalent concepts in any physical theory
• Thermodynamics and the structure of quantum theory
• Entangleability of cones
• Incompatible measurements in a class of general probabilistic theories
• Operational axioms for diagonalizing states
• Contextuality of general probabilistic theories
• Perfect Discrimination of Non-Orthogonal Separable Pure States on Bipartite System in General Probabilistic Theory
• Entropies in General Probabilistic Theories and its Application to Holevo Bound
• Optimal Observables for Minimum-Error State Discrimination in General Probabilistic Theories
• Perfect Discrimination in Approximate Quantum Theory of General Probabilistic Theories
• Von Neumann's information engine without the spectral theorem
• Assemblages and steering in general probabilistic theories