Superdecoherence of spin states

We present a detailed study of the depolarization dynamics of an indi-
vidual spin with an arbitrary spin quantum number 𝑗, or, equivalently,
of a system of 𝑁 = 2𝑗 constituent spin-1/2 initially in a symmetric
state undergoing collective depolarization. In particular, we identify
the most superdecoherent states. In the case of isotropic depolariza-
tion, we show that a class of maximally entangled pure states distinct
from GHZ and W states, a.k.a. spin anticoherent states, display
the highest decoherence rate for any number of spins. Moreover, we
find that these states become absolutely separable after a time which
does not depend on the number of spins. We also prove that entangle-
ment is a necessary and sufficient condition, both for pure and mixed
states, for superdecoherence to take place. Finally, for anisotropic
depolarization, we identify not only the states with the highest initial
decoherence rate, but also the states that lose their purity most rapidly
over any finite time for a few spins.