John von Neumann established a rigorous mathematical framework for quantum mechanics in his 1932 work Mathematical Foundations of Quantum Mechanics. In it, he provided a theory of … 展开

Some properties of the von Neumann entropy:
• S(ρ) is zero if and only if ρ represents a pure state.
• S(ρ) is … 展开

Given the density matrix ρ, von Neumann defined the entropy as
$${\displaystyle S(\rho )=-\operatorname {tr} (\rho \ln \rho ),}$$
which is a proper … 展开

Since, for a pure state, the density matrix is idempotent, ρ = ρ , the entropy S(ρ) for it vanishes. Thus, if the system is finite (finite-dimensional matrix … 展开

• Entropy (information theory)
• Linear entropy
• Partition function (mathematics)
• Quantum conditional entropy
• Quantum relative entropy 展开