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Constructing a density matrix using a canonical ensemble gives a result of the form = / (), where is the inverse temperature () and is the system's Hamiltonian. The normalization condition that the trace of ρ {\displaystyle \rho } be equal to 1 defines the partition function to be Z ( β ) = t r exp ( − β H ) {\displaystyle Z(\beta ...
The Peres–Horodecki criterion is a necessary condition, for the joint density matrix of two quantum mechanical systems and , to be separable. It is also called the PPT criterion, for positive partial transpose. In the 2×2 and 2×3 dimensional cases the condition is also sufficient.
Download as PDF; Printable version; In other projects Wikidata item; ... This is an extended version of the energy density table from the main Energy density page:
A graphical intuition of purity may be gained by looking at the relation between the density matrix and the Bloch sphere, = (+), where is the vector representing the quantum state (on or inside the sphere), and = (,,) is the vector of the Pauli matrices.
The fidelity between two quantum states and , expressed as density matrices, is commonly defined as: [1] [2] (,) = ().The square roots in this expression are well-defined because both and are positive semidefinite matrices, and the square root of a positive semidefinite matrix is defined via the spectral theorem.
New York: The International Nickel Company, Inc., 1941: 16. — "Values ranging from 21.3 to 21.5 gm/cm 3 at 20 °C have been reported for the density of annealed platinum; the best value being about 21.45 gm/cm 3 at 20 °C." 21.46 g/cm 3 — Rose, T. Kirke. The Precious Metals, Comprising Gold, Silver and Platinum. New York: D. Van Nostrand ...
Mulliken charges arise from the Mulliken population analysis [1] [2] and provide a means of estimating partial atomic charges from calculations carried out by the methods of computational chemistry, particularly those based on the linear combination of atomic orbitals molecular orbital method, and are routinely used as variables in linear regression (QSAR [3]) procedures. [4]
In quantum mechanics, and especially quantum information and the study of open quantum systems, the trace distance is a metric on the space of density matrices and gives a measure of the distinguishability between two states.