Information and communication in polygon theories

Abstract

Generalized probabilistic theories (GPT) provide a framework in which one can formulate physical theories that includes classical and quantum theories, but also many other alternative theories. In order to compare different GPTs, we advocate an approach in which one views a state in a GPT as a resource, and quantifies the cost of interconverting between different such resources. We illustrate this approach on polygon theories (Janotta et al. New J. Phys 13, 063024, 2011) that interpolate (as the number n of edges of the polygon increases) between a classical trit (when n=3) and a real quantum bit (when n=infinity). Our main results are that simulating the transmission of a single n-gon state requires more than one qubit, or more than log(log(n)) bits, and that n-gon states with n odd cannot be simulated by n'-gon states with n' even (for all n,n'). These results are obtained by showing that the classical capacity of a single n-gon state with n even is 1 bit, whereas it is larger than 1 bit when n is odd; by showing that transmitting a single n-gon state with n even violates information causality; and by showing studying the communication complexity cost of the nondeterministic not equal function using n-gon states.

arXiv comment18 pages

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• The principle of information symmetry constrains the state-space in any physical theory
• Hyperdense coding and superadditivity of classical capacities in hypersphere theories
• The Information Content of Systems in General Physical Theories
• Classical analogue of quantum superdense coding and communication advantage of a single quantum system
• Bell measurement rules out supraquantum correlations
• Quantum Darwinism and the spreading of classical information in non-classical theories
• A Post-Quantum Associative Memory
• Proceedings of the 7th International Workshop on Physics and Computation
• Optimal CHSH values for regular polygon theories in generalized probabilistic theories
• Spacetime symmetries and the qubit Bloch ball: a physical derivation of finite dimensional quantum theory and the number of spatial dimensions
• Randomness-free Detection of Non-projective Measurements: Qubits & beyond
• Bipartite polygon models: entanglement classes and their nonlocal behaviour