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

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

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

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...

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

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...

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...

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

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...

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

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

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...

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"...

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

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

{\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...

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...

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...

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...

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

note that any density operator S can be diagonalized, that it can be represented in some orthonormal basis by a (possibly infinite) matrix of the form [...

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