The fundamental problem of the transition from quantum to classical physics
is usually explained by decoherence, and viewed as a gradual process. The study
of entanglement, or quantum correlations, in noisy quantum computers implies
that in some cases the transition from quantum to classical is actually a phase
transition. We define the notion of entanglement length in d-dimensional
noisy quantum computers, and show that a phase transition in entanglement
occurs at a critical noise rate, where the entanglement length transforms from
infinite to finite. Above the critical noise rate, macroscopic classical
behavior is expected, whereas below the critical noise rate, subsystems which
are macroscopically distant one from another can be entangled.
The macroscopic classical behavior in the super-critical phase is shown to
hold not only for quantum computers, but for any quantum system composed of
macroscopically many finite state particles, with local interactions and local
decoherence, subjected to some additional conditions.
This phenomenon provides a possible explanation to the emergence of classical
behavior in such systems. A simple formula for an upper bound on the
entanglement length of any such system in the super-critical phase is given,
which can be tested experimentally.Comment: 15 pages. Latex2e plus one figure in eps fil
