Density matrix information

In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation...

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...

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...

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

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...

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...

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

{\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...

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...

treatment except that it operates on the wave function rather than using a density matrix approach. The main component of this method is evolving the system's...

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

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...

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...

is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix.: 9–11  The stochastic matrix was first developed by Andrey...

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

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

s(t), or more explicitly with a time-ordered exponential integral. The density matrix can be shown to transform to the interaction picture in the same way...

is the density matrix, Tr {\displaystyle \operatorname {Tr} } is trace, and ln {\displaystyle \ln } is the matrix logarithm. This density matrix formulation...

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...

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