A coordinate-invariant phase-space entropy for quantum states on Riemannian manifolds is defined and computed for oscillator states in flat and AdS2 spacetimes.
If an argument more closely paralleling the classical one is possible in the quantum phase space, it would likely involve a non-commutative version of the Radon-Nikodym theorem
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Quantum information in Riemannian spaces
A coordinate-invariant phase-space entropy for quantum states on Riemannian manifolds is defined and computed for oscillator states in flat and AdS2 spacetimes.