A density matrix is a positive semidefinite matrix of trace 1. It represents a quantum state
on a finite -dimensional Hilbert
space . Its eigenvalues are nonnegative
and sum to 1, so they can be interpreted as probabilities in a decomposition into
orthogonal pure states.
A pure state has a rank-one density matrix unit vector tensor product can be separable or entangled.
See also Hermitian Matrix ,
Matrix Trace ,
Partial Trace ,
Positive
Operator ,
Positive Semidefinite Matrix ,
Quantum Entanglement ,
Quantum
Relative Entropy ,
Quantum State ,
Superposition
Principle ,
von Neumann Entropy
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References Watrous, J. The Theory of Quantum Information. Cambridge,
England: Cambridge University Press, 2018. https://doi.org/10.1017/9781316848142 .
Cite this as:
Weisstein, Eric W. "Density Matrix." From
MathWorld https://mathworld.wolfram.com/DensityMatrix.html
Subject classifications
for a unit vector 
, and satisfies 
. A mixed state is not pure. Joint density matrices
on a tensor product can be separable or entangled.
