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We investigate how much information about a quantum system can besimultaneously communicated to independent observers, by establishingquantitative limits to bipartite quantum correlations in many-body systems. Asrecently reported in Phys. Rev. Lett. 129, 010401 (2022), bounds on quantumdiscord and entanglement of formation between a single quantum system and itsenvironment, e.g., a large number of photons, dictate that independentobservers which monitor environment fragments inevitably acquire only classicalinformation about the system. Here, we corroborate and generalize thosefindings. First, we calculate continuity bounds of quantum discord, which sethow much states with a small amount of quantum correlations deviate from beingembeddings of classical probability distributions. Also, we demonstrate auniversally valid upper bound to the bipartite entanglement of formationbetween an arbitrary pair of components of a many-body quantum system. Theresults confirm that proliferation of classical information in the Universesuppresses quantum correlations.

Quantitative bounds to propagation of quantum correlations in many-body systems