The density matrix is a representation of a linear operator called the density operator. The density matrix is obtained from the density operator by a choice … 展开

A pure quantum state is a state that can not be written as a probabilistic mixture, or convex combination, of other quantum states. There are several … 展开

A given density operator does not uniquely determine which ensemble of pure states gives rise to it; in general there are infinitely many different ensembles generating the same density matrix. Those cannot be distinguished by any measurement. The … 展开

Let $${\displaystyle A}$$ be an observable of the system, and suppose the ensemble is in a mixed state such that each of the pure states $${\displaystyle \textstyle |\psi _{j}\rangle }$$ occurs with probability $${\displaystyle p_{j}}$$. Then the corresponding density … 展开

The von Neumann entropy $${\displaystyle S}$$ of a mixture can be expressed in terms of the eigenvalues of $${\displaystyle \rho }$$ or in terms of the trace and logarithm of the density operator $${\displaystyle \rho }$$. Since $${\displaystyle \rho }$$ is … 展开

The density matrix operator may also be realized in phase space. Under the Wigner map, the density matrix transforms into the equivalent Wigner function,
The equation for the time evolution of the Wigner function, known as 展开

Density matrices are a basic tool of quantum mechanics, and appear at least occasionally in almost any type of quantum-mechanical calculation. Some specific examples where density matrices are especially helpful and common are as follows: 展开