In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed...

the reduced density matrix of ρ on subsystem A. Colloquially, we "trace out" or "trace over" system B to obtain the reduced density matrix on A.: 207–212 : 133 : §22...

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

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

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...

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...

{\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...

is a non-perturbative approach developed to study the evolution of a density matrix ρ ( t ) {\displaystyle \rho (t)} of quantum dissipative systems. The...

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

in a reduced density matrix of any order. Superfluidity corresponds to a large factored component in the first-order reduced density matrix. (And, all higher...

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...

{\displaystyle \operatorname {ln} } denotes the matrix version of the natural logarithm. If the density matrix ρ is written in a basis of its eigenvectors...

It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey Markov...

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 or other mathematical objects with elements or entries arranged in...

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...

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...

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

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

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

{\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"...

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...

physicist. His accomplishments include the independent co-discovery of the density matrix method in quantum mechanics (alongside John von Neumann), the quantum...

for solving one dimensional strongly correlated quantum systems – the density matrix renormalization group (DMRG) algorithm. For a system of N {\displaystyle...

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...

{\displaystyle \operatorname {ln} } denotes the matrix version of the natural logarithm. If the density matrix ρ is written in a basis of its eigenvectors...

state) is most often represented by a density matrix, denoted by ρ ^ {\displaystyle {\hat {\rho }}} . The density matrix provides a fully general tool that...