Von Neumann entropy
Type of entropy in quantum theory / From Wikipedia, the free encyclopedia
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In physics, the von Neumann entropy, named after John von Neumann, is an extension of the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics. For a quantum-mechanical system described by a density matrix ρ, the von Neumann entropy is[1]
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where denotes the trace and ln denotes the (natural) matrix logarithm. If the density matrix ρ is written in a basis of its eigenvectors as
then the von Neumann entropy is merely[1]
In this form, S can be seen as the information theoretic Shannon entropy.[1]
The von Neumann entropy is also used in different forms (conditional entropies, relative entropies, etc.) in the framework of quantum information theory to characterize the entropy of entanglement.[2]