A few days ago we posted a new paper.
General Bound on the Rate of Decoherence [arXiv:10045405]
Cesar A. Rodriguez-Rosario, Gen Kimura, Hideki Imai, Alan Aspuru-Guzik
We establish the necessary and sufficient conditions for a quantum system to be stable under any general system-environment interaction. Quantum systems are stable when the time-derivative of their purity is zero. This stability provides a dynamical explanation of the classicality of measurement apparatus. We also propose a protocol to detect global quantum correlations using only local dynamical information. We show how quantum correlations to the environment provide bounds to the purity rate, which in turn can be used to estimate dissipation rates for general non-Markovian open quantum systems.
[SciRate]
The paper could have been alternatively titled: “Necessary and Sufficient Conditions for System Stability Under Any Coupling to the Environment”. In this post, I want to discuss briefly our first result of the paper:
$$left[ frac{d}{dt}mathbf{P}^mathcal{S}_tright]_{t=tau} = 0; Leftrightarrow ; left[rho^mathcal{S}_tauotimes I^mathcal{E},rho^mathcal{SE}_tauright] =0$$.
We were interested in finding universal decoherence stability criteria that depended on the structure of the system-environment state, but was independent of the particular Hamiltonian dynamics. We focused on the measure of decoherence called “Purity”, in particular the rate of change of purity. We found that there exist system-environment states that preserve the purity of the system independent of the details of the interaction Hamiltonian. These states are given by the commutator in the equation above vanishing, and we call them “Stable System States” or SSS for lack of a better name.
SSS states are sparse topologically and not-dense: they are quite rare. But, at the same time, they include states whose system part looks very classical. On first sight, since they are rare, this would raise the question of why does the world looks classical to us. However, the equation above also implies that these states are stable under decoherence, and thus can be long-lived.
In other words, we can prove how classical states emerge naturally in the world without any assumptions of the dynamics! This provides a non-equilibrium thermodynamical explanation to why our universe looks classical.
Minus Two Fish 