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- Density_matrix abstract "A density matrix is a matrix that describes a quantum system in a mixed state, a statistical ensemble of several quantum states. This should be contrasted with a single state vector that describes a quantum system in 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. Explicitly, suppose a quantum system may be found in state with probability p1, or it may be found in state with probability p2, or it may be found in state with probability p3, and so on. The density operator for this system is By choosing a basis (which need not be orthogonal), one may resolve the density operator into the density matrix, whose elements are For an operator (which describes an observable of the system), the expectation value is given by In words, the expectation value of A for the mixed state is the sum of the expectation values of A for each of the pure states weighted by the probabilities pi and can be computed as the trace of the product of the density operator and .Mixed states arise in situations where the experimenter does not know which particular states are being manipulated. Examples include a system in thermal equilibrium (or additionally chemical equilibrium) or a system with an uncertain or randomly varying preparation history (so one does not know which pure state the system is in). Also, if a quantum system has two or more subsystems that are entangled, then each subsystem must be treated as a mixed state even if the complete system is in a pure state. The density matrix is also a crucial tool in quantum decoherence theory.The density matrix is a representation of a linear operator called the density operator. The close relationship between matrices and operators is a basic concept in linear algebra. In practice, the terms density matrix and density operator are often used interchangeably. Both matrix and operator are self-adjoint (or Hermitian), positive semi-definite, of trace one, and maybe infinite-dimensional. The formalism was introduced by John von Neumann in 1927 and independently, but less systematically by Lev Landau and Felix Bloch in 1927 and 1946 respectively.".
- Density_matrix thumbnail Vertical_polarization.svg?width=300.
- Density_matrix wikiPageID "62844".
- Density_matrix wikiPageRevisionID "605221374".
- Density_matrix hasPhotoCollection Density_matrix.
- Density_matrix subject Category:Functional_analysis.
- Density_matrix subject Category:Quantum_information_science.
- Density_matrix subject Category:Quantum_mechanics.
- Density_matrix subject Category:Statistical_mechanics.
- Density_matrix comment "A density matrix is a matrix that describes a quantum system in a mixed state, a statistical ensemble of several quantum states. This should be contrasted with a single state vector that describes a quantum system in 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.".
- Density_matrix label "Density matrix".
- Density_matrix label "Dichteoperator".
- Density_matrix label "Dichtheidsmatrix".
- Density_matrix label "Estado mixto".
- Density_matrix label "Macierz gęstości".
- Density_matrix label "Matrice densité".
- Density_matrix label "Matriz densidade".
- Density_matrix label "Operatore densità".
- Density_matrix label "Матрица плотности".
- Density_matrix label "密度矩陣".
- Density_matrix label "密度行列".
- Density_matrix sameAs Operátor_hustoty.
- Density_matrix sameAs Dichteoperator.
- Density_matrix sameAs Estado_mixto.
- Density_matrix sameAs Matriz_dentsitate.
- Density_matrix sameAs Matrice_densité.
- Density_matrix sameAs Operatore_densità.
- Density_matrix sameAs 密度行列.
- Density_matrix sameAs 밀도_행렬.
- Density_matrix sameAs Dichtheidsmatrix.
- Density_matrix sameAs Macierz_gęstości.
- Density_matrix sameAs Matriz_densidade.
- Density_matrix sameAs m.0gyzn.
- Density_matrix sameAs Q831774.
- Density_matrix sameAs Q831774.
- Density_matrix wasDerivedFrom Density_matrix?oldid=605221374.
- Density_matrix depiction Vertical_polarization.svg.
- Density_matrix isPrimaryTopicOf Density_matrix.
