My (and Leonid Khalfin's) thoughts about quantum/classical correspondence culminated in two works
1992 L.A. Khalfin, B.S. Tsirelson, "Quantum/classical correspondence in the light of Bell's inequalities." Foundations of Physics 22:7, 879-948. [MR93k:81017] [download]
1994 B.S. Tsirelson, "This non-axiomatizable quantum theory: From Hilbert's sixth problem to the recent viewpoint of Gell-Mann and Hartle." Preprint IHES/M/94/2, 19 pp. [download]
Frankly, foundations of quantum theory are still as enigmatic as before. Anyway, two ideas from these works are noted a bit:
A quantum-mechamical system with few collective degrees of freedom admits a classical description, provided that quantum correlations between these degrees of freedom are destroyed (decohered by thermal fluctuations) faster than created (by dynamical interaction). Roughly speaking, instead of a limiting procedure (from quantum to classical) we have a threshold.
The classical description is a relative, empirical reality (rather than absolute, independent reality), and is consistent with the quantum description (rather than derived from it).
Quantum computers are very different from quantum-mechanical systems with few collective degrees of freedom. Nevertheless:
The threshold result might have an impact on a long standing question in quantum physics, regarding the transition from quantum to classical physics [...] Traditionally, this transition is treated by taking the limit of Planck's constant to 0, and it is viewed as a gradual transition (but see [Khalfin, Tsirelson 1992]). [...] It is interesting to consider a different point of view, in which the definition of quantum versus classical behavior is computational. [...] Then, increasing the noise, a transition from the quantum computational behavior to classical computational behavior occurs. Does this transition happen at a critical error rate? Indications for a positive answer are already shown in a previous paper of ours [...] We view this connection between quantum complexity and quantum physics as extremely interesting.
(Aharonov and Ben-Or, preprint arXiv:quant-ph/9906129, p. 60.)
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Aharonov, Ben-Or, Bush, Diosi, d'Espagnat, Kiefer, Lahti, Landsman, Luo, Mittelstaedt, Schulman, Yudin, Zhang, Zurek. (Detail)
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