Information AboutDensity Matrix |
| CATEGORIES ABOUT DENSITY MATRIX | |
| quantum mechanics | |
| functional analysis | |
| quantum information science | |
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quantum-mechanical analogue to a Phase-space density (probability distribution of position and momentum) in classical statistical mechanics. The need for a statistical description via Density Matrices arises because it is not possible to describe a quantum mechanical system that undergoes general Quantum Operation s such as Measurement , using exclusively states represented by Ket vectors. In general a system is said to be in a Mixed State , except in the case the state is not reducible to a Convex Combination of other statistical states. In that case it is said to be in a Pure State . Typical situations in which a density matrix is needed include: a quantum system in thermal equilibrium (at finite temperatures), nonequilibrium time-evolution that starts out of a mixed equilibrium state, and Entanglement between two subsystems, where each individual system must be described by a density matrix even though the complete system may be in a pure state. See Quantum Statistical Mechanics . The density matrix (commonly designated by ρ) is an operator acting on the Hilbert Space of the system in question. For the special case of a pure state, it is given by the Projection Operator of this state. For a mixed state, where the system is in the | ||
| :<math> Ho | \sum_j p_j \psi_j
ang \lang \psi_j </math> |
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| :<math> \operatorname{tr}[ Ho A] | \sum_j p_j \lang \psi_jA\psi_j
ang </math> |
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