Keyword | CPC | PCC | Volume | Score | Length of keyword |
---|---|---|---|---|---|

density matrix formalism | 0.44 | 0.1 | 5279 | 58 | 24 |

density | 0.93 | 0.2 | 2021 | 25 | 7 |

matrix | 0.31 | 0.2 | 7695 | 72 | 6 |

formalism | 0.48 | 0.5 | 7995 | 26 | 9 |

Keyword | CPC | PCC | Volume | Score |
---|---|---|---|---|

density matrix formalism | 0.68 | 0.8 | 766 | 9 |

The formalism of density operators and matrices was introduced in 1927 by John von Neumann and independently, but less systematically, by Lev Landau and later in 1946 by Felix Bloch. Von Neumann introduced the density matrix in order to develop both quantum statistical mechanics and a theory of quantum measurements.

Example: light polarization. One of the advantages of the density matrix is that there is just one density matrix for each mixed state, whereas there are many statistical ensembles of pure states for each mixed state. Nevertheless, the density matrix contains all the information necessary to calculate any measurable property of the mixed state.

In practice, the terms density matrix and density operator are often used interchangeably. In operator language, a density operator for a system is a positive semi-definite, Hermitian operator of trace one acting on the Hilbert space of the system. This definition can be motivated by considering a situation where a pure state

The density matrix is the quantum-mechanical analogue to a phase-space probability measure (probability distribution of position and momentum) in classical statistical mechanics. Mixed states arise in situations where the experimenter does not know which particular states are being manipulated.