Dimension of physical systems, information processing, and thermodynamics

Abstract

We ask how quantum theory compares to more general physical theories from the point of view of dimension. To do so, we first give two model independent definition of the dimension of physical systems, based on measurements and on the capacity of storing information. While both definitions are equivalent in classical and quantum mechanics, they are in general different in generalized probabilistic theories. We discuss in detail the case of a theory known as 'boxworld', and show that such a theory features systems with a dimension mismatch. This dimension mismatch can be made arbitrarily large by using an amplification procedure. Furthermore, we show that the dimension mismatch of boxworld has strong consequences on its power for performing information-theoretic tasks, leading to the collapse of communication complexity and to the violation of information causality. Finally, we discuss the consequences of a dimension mismatch from the perspective of thermodynamics, and ask whether this effect could break Landauer's erasure principle and thus the second law.

17 pages, 2 figures

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Cited by in corpus (27)

• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• Quasi-quantization: classical statistical theories with an epistemic restriction
• Quantum from principles
• General probabilistic theories: An introduction
• No-hypersignaling principle
• Device-Independent Tests of Entropy
• Entanglement and thermodynamics in general probabilistic theories
• Thermodynamics and the structure of quantum theory
• Testing dimension and non-classicality in communication networks
• Dimension of physical systems, information processing, and thermodynamics
• Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality
• Classical theories with entanglement
• Information and communication in polygon theories
• Born's rule as a quantum extension of Bayesian coherence
• Information Content of Systems as a Physical Principle
• Hyperdense coding and superadditivity of classical capacities in hypersphere theories
• Classical analogue of quantum superdense coding and communication advantage of a single quantum system
• How dynamics constrains probabilities in general probabilistic theories
• Timelike correlations and quantum tensor product structure
• On the origin of nonclassicality in single systems
• A no-go theorem for theories that decohere to quantum mechanics
• Quantum Advantage: A Single Qubit's Experimental Edge in Classical Data Storage
• Programming of channels in generalized probabilistic theories
• The signaling dimension in generalized probabilistic theories
• Limitations imposed by complementarity
• Bipartite polygon models: entanglement classes and their nonlocal behaviour
• Quantum dimension test using the uncertainty principle