The quantum states of a spin
(a qubit) are parametrized by the space
, the Bloch sphere. A spin
j for a generic
j (a
-state system) is represented instead by a
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The quantum states of a spin
(a qubit) are parametrized by the space
, the Bloch sphere. A spin
j for a generic
j (a
-state system) is represented instead by a point in a larger space,
. Here we study the state of a single angular momentum/spin in the limit
. A special class of states,
, with spin oriented towards definite spatial directions,
, i.e.,
, are found to behave as classical angular momenta,
, in this limit. Vice versa, general spin states in
do not become classical, even at a large
j. We study these questions by analyzing the Stern–Gerlach processes, the angular momentum composition rule, and the rotation matrix. Our observations help to better clarify how classical mechanics emerges from quantum mechanics in this context (e.g., with the unique trajectories of a particle carrying a large spin in an inhomogeneous magnetic field) and to make the widespread idea that large spins somehow become classical more precise.
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