Abstract
A state selected at random from the Hilbert space of a many-body system is overwhelmingly likely to exhibit highly non-classical correlations. For these typical states, half of the environment must be measured by an observer to determine the state of a given subsystem. The objectivity of classical reality—the fact that multiple observers can agree on the state of a subsystem after measuring just a small fraction of its environment—implies that the correlations found in nature between macroscopic systems and their environments are exceptional. Building on previous studies of quantum Darwinism showing that highly redundant branching states are produced ubiquitously during pure decoherence, we examine the conditions needed for the creation of branching states and study their demise through many-body interactions. We show that even constrained dynamics can suppress redundancy to the values typical of random states on relaxation timescales, and prove that these results hold exactly in the thermodynamic limit.
Highlights
The Hilbert space of macroscopic systems is dominated by states that have no classical counterparts
The world observed by macroscopic observers exhibits powerful regularities that make it amenable to classical interpretations on a broad range of scales
Darwinism [1, 2] is a framework for describing and quantifying what distinguishes quasiclassical states awash in the enormous sea of Hilbert space
Summary
We know that observers can find out quite a bit about a system by interacting with much less than half of its environment. Our key assumption to produce a high-redundancy state will be that S is coupled to the Ei more strongly than the Ei are coupled to each other (σd σm) This is an excellent approximations for many environments (e.g. a photon bath [15, 16], where effectively σm = 0) but not all (e.g. a gas of frequently colliding molecules). Once enough time passes for the mixing to become significant, t ∼ τm, this structure is destroyed and the plot takes the form characteristic of typical non-redundant states. In figure 3c, the eigenvalues for the corresponding state ρF are likewise plotted in both regimes This shows the formation and destruction of branches characteristic of quantum Darwinism [1, 2, 3, 4], and is suggestive of Everett’s relative states [17, 18].
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