The principle of information symmetry constrains the state-space in any physical theory

Abstract

Symmetry shares an entwined history with the structure of physical theory. We propose a consequence of symmetry towards the axiomatic derivation of Hilbert space quantum theory. We introduce the notion of information symmetry (IS) and show that it constraints the state-space structure in any physical theory. To this end, we study the minimal error binary state discrimination problem in the framework of generalized probabilistic theories. A theory is said to satisfy IS if the probability of incorrectly identifying each of two randomly prepared states is same for both the states. It is found that this simple principle rules out several classes of theories while being perfectly compatible with quantum theory.

arXiv commentAccepted in Physical Review A (Rapid Communications); Close to accepted version

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• General probabilistic theories: An introduction
• Nonlocality Without Entanglement: Quantum Theory and Beyond
• Mutually Unbiased Balanced Functions & Generalized Random Access Codes
• Local Quantum State Marking
• Classical analogue of quantum superdense coding and communication advantage of a single quantum system
• Timelike correlations and quantum tensor product structure
• Quantum Advantage: A Single Qubit's Experimental Edge in Classical Data Storage
• Optimal CHSH values for regular polygon theories in generalized probabilistic theories
• Bipartite polygon models: entanglement classes and their nonlocal behaviour