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

density matrix operator | 0.6 | 0.1 | 3933 | 36 | 23 |

density | 0.12 | 0.9 | 7936 | 24 | 7 |

matrix | 1.29 | 0.1 | 7637 | 75 | 6 |

operator | 0.99 | 0.8 | 787 | 53 | 8 |

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

We will now formally introduce the density matrix notation by looking at the how it is used to represent both pure and mixed states. 1. Pure States Pure states are those for which we can precisely define their quantum state at every point in time.

It is known as the reduced density matrix of on subsystem 1. It is easy to check that this operator has all the properties of a density operator. Conversely, the Schrödinger–HJW theorem implies that all density operators can be written as for some state .

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. [1] [2] [3] This definition can be motivated by considering a situation where a pure state is prepared with probability , known as an ensemble.