In quantum mechanics, a density matrix (or density operator) is a matrix that describes an ensemble of physical systems as quantum states (even if the...

The density matrix renormalization group (DMRG) is a numerical variational technique devised to obtain the low-energy physics of quantum many-body systems...

density matrix of ρ on subsystem A. Colloquially, we "trace out" system B to obtain the reduced density matrix on A. For example, the reduced density...

agnostic about interpretation, focusing instead on specific problems of density-matrix dynamics. Zurek's interest in decoherence stemmed from furthering Bohr's...

Another instance of explicit time dependence may occur when AS(t) is a density matrix (see below). For the operator H 0 {\displaystyle H_{0}} itself, the...

density matrix describing knowledge of the state of a subsystem. The entropy of entanglement is the Von Neumann entropy of the reduced density matrix...

density matrix), quantum master equations are differential equations for the entire density matrix, including off-diagonal elements. A density matrix...

energy state and anti-parallel in the lower one. A density matrix, ρ {\displaystyle \rho } , is a matrix that describes a quantum system in a mixed state...

statistical mechanics. For a quantum-mechanical system described by a density matrix ρ, the von Neumann entropy is S = − tr ⁡ ( ρ ln ⁡ ρ ) , {\displaystyle...

density matrix is normalized so that the trace of ρ is 1, as it is for the standard definition given in this section. Occasionally a density matrix will...

components ϱ k {\displaystyle \varrho _{k}} in any decomposition of the density matrix given as ϱ = ∑ k p k ϱ k . {\displaystyle \varrho =\sum _{k}p_{k}\varrho...

The density matrix embedding theory (DMET) is a numerical technique to solve strongly correlated electronic structure problems. By mapping the system to...

quantum system with its environment. One of these is the use of the density matrix, and its associated master equation. While in principle this approach...

quantum-mechanical wavefunction ψ(x). Thus, it maps on the quantum density matrix in the map between real phase-space functions and Hermitian operators...

In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows...

H_{A}\otimes H_{B}} of Hilbert spaces. A mixed state is described by a density matrix ρ, that is a non-negative trace-class operator of trace 1 on the tensor...

will have to be performed, many times each. To fully reconstruct the density matrix for a mixed state in a finite-dimensional Hilbert space, the following...

{\displaystyle 2^{2N}-1} real parameters are needed to describe the density matrix of a mixed state. Quantum state tomography is a method to determine...

{\displaystyle \vert k\rangle } are the eigenvalues and eigenvectors of the density matrix ϱ , {\displaystyle \varrho ,} respectively, and the summation goes over...

whole, density matrices may be used instead.: 74  A density matrix is a positive semi-definite operator whose trace is equal to 1. (The term "density operator"...

terms of the identity matrix and the Pauli matrices also leads to the Bloch sphere representation of 2 × 2 mixed states’ density matrix, (positive semidefinite...

&0&0\\{\frac {1}{\sqrt {2}}}\left|\uparrow \right\rangle &0&0\end{bmatrix}}.} Density matrix renormalization group Variational method (quantum mechanics) Renormalization...

This was first discussed as a general stochastic transformation for a density matrix by George Sudarshan. The quantum operation formalism describes not only...

}}} is a density matrix, t r {\displaystyle \mathrm {tr} } is a trace operator and ln {\displaystyle \ln } is a matrix logarithm. Density matrix formalism...

\operatorname {tr} (\rho ^{2})} where ρ {\displaystyle \rho \,} is the density matrix of the state and tr {\displaystyle \operatorname {tr} } is the trace...

Markovian master equation that describes the time evolution of the reduced density matrix ρ of a strongly coupled quantum system that is weakly coupled to an...

density matrix), quantum master equations are differential equations for the entire density matrix, including off-diagonal elements. A density matrix...

some important substitutions: the initial state is to be replaced by a density matrix, and the projection operators are to be replaced by positive operator...

Given a statistical ensemble of quantum mechanical systems with the density matrix ρ {\displaystyle \rho } , it is given by S ( ρ ) = − Tr ⁡ ( ρ ln ⁡ ρ...

\langle \beta |} . Density matrix Physically, the density matrix is a way to represent pure states and mixed states. The density matrix of pure state whose...