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We investigate the idea that decoherence is connected with the storage ofinformation about the decohering system somewhere in the universe. The knownconnection between decoherence of histories and the existence of records isextended from the case of pure initial states to mixed states. Records maystill exist but are necessarily imperfect. We formulate aninformation-theoretic conjecture about decoherence due to an environment: thenumber of bits required to describe a set of decoherent histories isapproximately equal to the number of bits of information thrown away to theenvironment in the coarse-graining process. This idea is verified in a simplemodel consisting of a particle coupled to an environment that can store onlyone bit of information. We explore the decoherence and information storage inthe quantum Brownian motion model. It is shown that the variables that theenvironment naturally measures and stores information about are the Fouriercomponents of the function $x(t)$ (describing the particle trajectory). Therecords storing the information about the Fourier modes are the positions andmomenta of the environmental oscillators at the final time. Decoherence ispossible even if there is only one oscillator in the environment. Theinformation count of the histories and records in the environment add upaccording to our conjecture. These results give quantitative content to theidea that decoherence is related to ``information lost''.Comment: 48 pages, plain Tex. Second revisio

Somewhere in the universe: Where is the information stored when histories decohere?