Von Neumann entropy

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Summary

In physics, the von Neumann entropy, named after John von Neumann, is a measure of the statistical uncertainty within a description of a quantum system.

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eponymous creator
The entropy measure is named after John von Neumann, who formulated the density matrix approach to quantum mechanics.
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mathematical foundation for calculation
The von Neumann entropy is defined using the trace of the density matrix, specifically as S = -Tr(ρ ln ρ).
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classical information theory counterpart
Von Neumann entropy is the quantum mechanical generalization of the classical Shannon entropy, which measures the uncertainty of a classical probability distribution.
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mathematical object required for definition
The von Neumann entropy is a function of the density matrix, which represents the state of a quantum system.
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measure of subsystem uncertainty
The von Neumann entropy of a reduced density matrix is used to quantify the entanglement between two parts of a bipartite quantum system.
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fundamental metric in the field
Von Neumann entropy is a central quantity in quantum information theory, analogous to Shannon entropy in classical information theory.
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physical system described by entropy
Von Neumann entropy provides a quantitative measure of the statistical uncertainty inherent in a given quantum state.
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computational requirement for entropy
Calculating von Neumann entropy requires computing the matrix logarithm of the density matrix, which is typically done via spectral decomposition.
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application in statistical mechanics
In quantum statistical mechanics, the von Neumann entropy of a system in thermal equilibrium is related to its thermodynamic entropy.
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