The phrase "a quantum description of" is correct and usable in written English.
It can be used in contexts related to physics, particularly when discussing theories or models that describe quantum phenomena.
Example: "The researchers provided a quantum description of the particle's behavior at the subatomic level."
Alternatives: "a quantum representation of" or "a quantum model of".
Modern attempts to make a quantum description of gravity predict small deviations from the predictions of general relativity.
Quantum theory explains electromagnetism and the strong and weak forces, but a quantum description of the remaining fundamental force of gravity has not been achieved.
All potential problems cancel out, despite the fact that the theory requires a massless particle of spin 2 in other words, the gauge boson of gravity, the graviton and thus automatically contains a quantum description of gravity.
And so a quantum description of cosmology is required for a complete and consistent worldview.
Numerical simulations of an evaporating black hole are consistent with a quantum description of gravity [Also see Perspective by Maldacena].
Nowadays states which are superpositions of the ground state and an excited state of an atom are produced routinely in quantum optics experiments, and thus analogs of $\EC_c$ can be quite relevant for a quantum description of what goes on in the laboratory.
The consistency of the two views is understood using the double-adiabatic approximation in a fully quantum description of the system.
In such circumstances the $[w^j]$ are what in Ch. 14 of Griffiths (2002a) are referred to as dependent or contextual ("conditional" would be equally good) properties: they must be understood in conjunction with other properties, which in this case are the pointer positions $[M^j]$, when forming part of a quantum description or history.
In the past few years insights from black hole physics and string theory have lead to a new theoretical framework in which the gravitational laws are derived an underlying microscopic quantum description of spacetime.
Finally, while wave function collapse is a legitimate calculational procedure when describing a preparation in quantum mechanical terms, it amounts to nothing more than a convenient way of calculating conditional probabilities useful in the quantum description of a preparation.
In one of his regular letters to a colleague, Wolfgang Pauli, he presented the inklings of an idea that has since became a fundamental part of the quantum description of the world.
