Quantum Darwinism and the spreading of classical information in non-classical theories

Roberto D. Baldijao1,2, Marius Krumm2,3, Andrew J. P. Garner2, and Markus P. Mueller2,4,5

1Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Campinas, SP 13083-859, Brazil
2Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
3Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
4Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria
5Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada

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Quantum Darwinism posits that the emergence of a classical reality relies on the spreading of classical information from a quantum system to many parts of its environment. But what are the essential physical principles of quantum theory that make this mechanism possible? We address this question by formulating the simplest instance of Darwinism – CNOT-like $fan$-$out$ interactions – in a class of probabilistic theories that contain classical and quantum theory as special cases. We determine necessary and sufficient conditions for any theory to admit such interactions. We find that every theory with non-classical features that admits this idealized spreading of classical information must have both entangled states and entangled measurements. Furthermore, we show that Spekkens' toy theory admits this form of Darwinism, and so do all probabilistic theories that satisfy principles like strong symmetry, or contain a certain type of decoherence processes. Our result suggests the counter-intuitive general principle that in the presence of local non-classicality, a classical world can only emerge if this non-classicality can be "amplified" to a form of entanglement.

Quantum mechanics predicts that physical objects can have several contradictory properties at once – a phenomenon called superposition. For example, a single electron can travel along several distinct paths at the same time. Why, then, do we never see a single car take both lanes on a highway at once, and moreover always agree with other observers about the single lane that the car is in? To explain objective reality in a quantum world, physicists have proposed "Quantum Darwinism" – essentially, a mechanism that carries information from one system to many observers. In our work, we investigate the physical principles behind this, using a more general formalism that drops many details specific to quantum mechanics. We discuss the sufficient structure needed to enable such Darwinism in physical theories, and also present a non-quantum example. Furthermore, we show that a physical theory only allows for Darwinism if it also admits entanglement. That is, quite surprisingly, to tame superpositions and present an ordinary classical world, physics must necessarily invoke an even more extraordinary phenomenon.

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