Properties
Some properties of the von Neumann entropy:
- S(ρ) is only zero for pure states. The same holds for the linear entropy which approximates it.
- S(ρ) is maximal and equal to for a maximally mixed state, being the dimension of the Hilbert space.
- S(ρ) is invariant under changes in the basis of, that is, with U a unitary transformation.
- S(ρ) is concave, that is, given a collection of positive numbers which sum to unity and density operators, we have
- S(ρ) is additive for independent systems. Given two density matrices describing independent systems A and B, we have .
- S(ρ) strongly subadditive for any three systems A, B, and C:
-
- .
- This automatically means that S(ρ) is subadditive:
Below, the concept of subadditivity is discussed, followed by its generalization to strong subadditivity.
Read more about this topic: Von Neumann Entropy
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