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Mathematical tool in quantum physics
In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed
Density_matrix
Physics phenomenon
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. For example
Quantum_entanglement
Numerical variational technique
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 renormalization group
Density_matrix_renormalization_group
Loss of quantum coherence
agnostic about interpretation, focusing instead on specific problems of density-matrix dynamics. Zurek's interest in decoherence stemmed from furthering Bohr's
Quantum_decoherence
View of quantum mechanics
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
Interaction_picture
Mathematical entity to describe the probability of each possible measurement on a system
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
Quantum_state
is a non-perturbative approach developed to study the evolution of a density matrix ρ ( t ) {\displaystyle \rho (t)} of quantum dissipative systems. The
Hierarchical equations of motion
Hierarchical_equations_of_motion
Quantum state of multiple particles represented as complex matrices
A matrix product state (MPS) is a representation of a quantum many-body state. It is at the core of the density matrix renormalization group (DMRG) algorithm
Matrix_product_state
Efficient reconstruction of quantum states based on measurements
{\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
Permutationally invariant quantum state tomography
Permutationally_invariant_quantum_state_tomography
Concept in quantum mechanics
density matrix), quantum master equations are differential equations for the entire density matrix, including off-diagonal elements. A density matrix
Quantum_master_equation
Property of a thermodynamic system
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
Entropy
The density matrix embedding theory (DMET) is a numerical technique to solve strongly correlated electronic structure problems. By mapping the system to
Density matrix embedding theory
Density_matrix_embedding_theory
Type of entropy in quantum theory
{\displaystyle \operatorname {ln} } denotes the matrix version of the natural logarithm. If the density matrix ρ is written in a basis of its eigenvectors
Von_Neumann_entropy
Array of numbers
In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and
Matrix_(mathematics)
Formulations of quantum mechanics
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
Dynamical_pictures
Function over linear operators
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
Partial_trace
Quantum
{\displaystyle \vert k\rangle } are the eigenvalues and eigenvectors of the density matrix ϱ , {\displaystyle \varrho ,} respectively, and the summation goes over
Quantum_Fisher_information
Quantum feature of condensed-matter systems
macroscopic quantum phenomena. It refers to off-diagonal elements in the density matrix separated in space in a many-body quantum mechanical system. An ODLRO
Off-diagonal_long-range_order
Markovian quantum master equation for density matrices (mixed states)
quantum system with its environment. One of these is the use of the density matrix, and its associated master equation. While this approach to solving
Lindbladian
Model of magnetic susceptibility under certain conditions
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
Curie–Weiss_law
Description of a quantum-mechanical system
whole, density matrices may be used instead. A density matrix is a positive semi-definite operator whose trace is equal to 1. (The term "density operator"
Schrödinger_equation
Concept in quantum physics
density matrix describing knowledge of the state of a subsystem. The entropy of entanglement is the Von Neumann entropy of the reduced density matrix
Entropy_of_entanglement
Matrix used to describe the transitions of a Markov chain
It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey Markov
Stochastic_matrix
Equations governing time evolution of physical systems
density matrix), quantum master equations are differential equations for the entire density matrix, including off-diagonal elements. A density matrix
Master_equation
Hungarian and American mathematician and physicist (1903–1957)
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
John_von_Neumann
Markovian master equation of a quantum system weakly coupled to its environment
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
Redfield_equation
Soviet theoretical physicist (1908–1968)
physicist. His accomplishments include the independent co-discovery of the density matrix method in quantum mechanics (alongside John von Neumann), the quantum
Lev_Landau
Quantum mechanics mathematical equation
change with time. However, one can again find the time evolution of the density matrix ρ ^ ( t ) {\displaystyle {\hat {\rho }}(t)} rsp. of the partition function
Kubo_formula
Matrices important in quantum mechanics and the study of spin
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
Pauli_matrices
Wigner distribution function in physics as opposed to in signal processing
quantum-mechanical wavefunction ψ(x). Thus, it maps on the quantum density matrix in the map between real phase-space functions and Hermitian operators
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
Quantum mechanical system that interacts with a quantum-mechanical environment
\rho _{S}=\mathrm {tr} _{B}\rho } is the reduced density matrix for system S. This reduced density matrix is primary focus of study for open quantum systems
Open_quantum_system
Reconstruction of quantum states based on measurements
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
Quantum_tomography
Concept in physics of one-way time
applicable density matrix, the conventional theory's inability to predict actual measurement outcomes via non-unitary collapse remains. That is, the density matrix
Arrow_of_time
Specific quantum state of a quantum harmonic oscillator
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
Coherent_state
\operatorname {tr} (\rho ^{2})} where ρ {\displaystyle \rho \,} is the density matrix of the state and tr {\displaystyle \operatorname {tr} } is the trace
Purity_(quantum_mechanics)
Matrix-valued random variable
probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled
Random_matrix
Calculation rule in quantum mechanics
(In the more general case where one considers the time evolution of a density matrix, proper normalization is ensured by requiring that the time evolution
Born_rule
Set of values that describe the polarization state of electromagnetic radiation
Q/I=tr\left(\rho \sigma _{z}\right)} , where ρ {\displaystyle \rho } is the density matrix of the mixed state. Generally, a linear polarization at angle θ has
Stokes_parameters
Quantum mechanical waves describing matter
on the beam coherence, which at the quantum level is equivalent to a density matrix approach. As with light, transverse coherence (across the direction
Matter_wave
Foundational principle in quantum physics
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
Uncertainty_principle
Criterion in quantum information theory
The Peres–Horodecki criterion is a necessary condition, for the joint density matrix ρ {\displaystyle \rho } of two quantum mechanical systems A {\displaystyle
Peres–Horodecki_criterion
Mathematical wave functions
in applications in physics. In 1992, Steven R. White developed the density matrix renormalization group (DMRG) for quantum lattice systems. The DMRG was
Tensor_network
Computer printing process
Dot matrix printing, sometimes called impact matrix printing, is a computer printing process in which ink is applied to a surface using a relatively low-resolution
Dot_matrix_printing
Statistical mechanics of quantum-mechanical systems
{\displaystyle \operatorname {ln} } denotes the matrix version of the natural logarithm. If the density matrix ρ is written in a basis of its eigenvectors
Quantum_statistical_mechanics
Class of transformations that quantum systems and processes can undergo
This was first discussed as a general stochastic transformation for a density matrix by George Sudarshan in 1961. The quantum operation formalism describes
Quantum_operation
Interpretation of quantum mechanics
information science Quantum computing Quantum chaos Decoherence EPR paradox Density matrix Scattering theory Quantum statistical mechanics Quantum machine learning
Many-worlds_interpretation
Computational simulation method for open quantum systems
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
Quantum_jump_method
Type of state in thermal systems
complications like phase transitions or spontaneous symmetry breaking. The density matrix of a thermal state is given by ρ β , μ = e − β ( H − μ N ) T r [ e −
KMS_state
\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
Glossary of elementary quantum mechanics
Glossary_of_elementary_quantum_mechanics
Idealization of a large number of atomic-sized systems
state) is most often represented by a density matrix, denoted by ρ ^ {\displaystyle {\hat {\rho }}} . The density matrix provides a fully general tool that
Ensemble (mathematical physics)
Ensemble_(mathematical_physics)
Principle in quantum information theory
accessible to Alice and Bob. The total state of the system is described by a density matrix σ. The goal of the theorem is to prove that Bob cannot in any way distinguish
No-communication_theorem
Fact that observing a situation changes it
information science Quantum computing Quantum chaos Decoherence EPR paradox Density matrix Scattering theory Quantum statistical mechanics Quantum machine learning
Observer_effect_(physics)
Mathematical approach to quantum optics
function P ( α ) {\displaystyle P(\alpha )} with the property that the density matrix ρ ^ {\displaystyle {\hat {\rho }}} is diagonal in the basis of coherent
Glauber–Sudarshan P representation
Glauber–Sudarshan_P_representation
Model of a quantum/optical system
discussion there). However, usually one casts these equations into a density matrix form. The system we are dealing with can be described by the wave function:
Maxwell–Bloch_equations
Theoretical chemist
simulate quantum many-body systems in chemistry and physics, including density matrix renormalization group (DMRG) theory and tensor network algorithms. Chan
Garnet_K.-L._Chan
Mathematical structures that allow quantum mechanics to be explained
quantum state of the composite system is called a separable state. The density matrix of a bipartite system in a separable state can be expressed as ρ = ∑
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Statistical ensemble of particles in thermodynamic equilibrium
represented by a density matrix, denoted by ρ ^ {\displaystyle {\hat {\rho }}} . The grand canonical ensemble is the density matrix[citation needed] ρ
Grand_canonical_ensemble
Phenomenon of isolated many-body quantum systems not reaching thermal equilibrium
This question can be formalized by considering the quantum mechanical density matrix ρ of the system. If the system is divided into a subregion A (the region
Many-body_localization
Formulation of quantum mechanics
quasiprobability distribution (instead of a wave function, state vector, or density matrix) and operator multiplication is replaced by a star product. The theory
Phase-space_formulation
Quantum state
d^{2}} × d 2 {\displaystyle d^{2}} -dimensional bipartite quantum state density matrix that is invariant under all unitary operators of the form U ⊗ U {\displaystyle
Werner_state
Mapping between functions in the quantum phase space
distribution is the Wigner transform of the quantum density matrix, and, conversely, the density matrix is the Weyl transform of the Wigner function. In
Wigner–Weyl_transform
Riemannian metric on the space of mixed states of a quantum system
(named after Carl W. Helstrom) defines an infinitesimal distance between density matrix operators defining quantum states. It is a quantum generalization of
Bures_metric
Relationship of various quantum subsystems
physical system. Given a density matrix ρ 123 {\displaystyle \rho ^{123}} on H {\displaystyle {\mathcal {H}}} , we define a density matrix ρ 12 {\displaystyle
Strong subadditivity of quantum entropy
Strong_subadditivity_of_quantum_entropy
Probability density of electrons being somewhere
}(\mathbf {r} )\phi _{\nu }(\mathbf {r} )} where P is the density matrix. Electron densities are often rendered in terms of an isosurface (an isodensity
Electron_density
Background energy existing in space
nature of the particles (or fields) that generate vacuum energy, with a density such as that required by inflation theory, remains a mystery. Arthur C
Vacuum_energy
Time travel using quantum mechanics
proposal uses the following key equation to describe the fixed-point density matrix (ρCTC) for the CTC: ρ CTC = Tr A [ U ( ρ A ⊗ ρ CTC ) U † ] {\displaystyle
Quantum mechanics of time travel
Quantum_mechanics_of_time_travel
Algorithm in quantum information theory
probability distribution over pure states, and is represented by a density matrix of the general form ρ = ∑ i p i | ψ i ⟩ ⟨ ψ i | {\textstyle \rho =\sum
Algorithmic_cooling
Interpretation of quantum mechanics
of a "Bureau of Standards" measurement. That is, if one expresses a density matrix as a probability distribution over the outcomes of a SIC-POVM experiment
QBism
Computational quantum mechanical modelling method to investigate electronic structure
difficulties. There is no one-to-one correspondence between one-body density matrix n(r, r′) and the one-body potential V(r, r′). (All the eigenvalues of
Density_functional_theory
Information held in the state of a quantum system
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
Quantum_information
Computational physics simulation tool
optical equivalence theorem. This means that it is essentially the density matrix put into normal order. This makes it relatively easy to calculate compared
Husimi_Q_representation
Measure in quantum information theory
H_{AB}:=H_{A}\otimes H_{B}.} Let ρAB be a density matrix acting on states in HAB. The von Neumann entropy of a density matrix S(ρ), is the quantum mechanical analogy
Quantum_mutual_information
Integral equation in quantum simulations
"relevant" part of a quantum-mechanical system. It is formulated in the density matrix formalism and can be regarded as a generalization of the master equation
Nakajima–Zwanzig_equation
Phenomenon resulting from the superposition of two waves
information science Quantum computing Quantum chaos Decoherence EPR paradox Density matrix Scattering theory Quantum statistical mechanics Quantum machine learning
Wave_interference
Study of quantum systems changing with time
states. A more general description of a quantum system is the density matrix (or density operator), denoted ρ {\displaystyle \rho } , which can represent
Quantum_dynamics
Construct in quantum information theory
Entanglement witnesses can be linear or nonlinear functionals of the density matrix. If linear, then they can also be viewed as observables for which the
Entanglement_witness
Principle in theoretical physics
function, they re-emit new photons in a thermal mixed state described by a density matrix. This would mean that quantum mechanics would have to be modified because
Holographic_principle
Ensemble of states at a constant temperature
represented by a density matrix, denoted by ρ ^ {\displaystyle {\hat {\rho }}} . In basis-free notation, the canonical ensemble is the density matrix[citation
Canonical_ensemble
Scientific law regarding conservation of a physical property
current density. In fact as in the former scalar case, also in the vector case A(y) usually corresponding to the Jacobian of a current density matrix J(y):
Conservation_law
Method in computational chemistry
Cμi for the μ'th basis function in the i'th molecular orbital, the density matrix terms are: D μ ν = 2 ∑ i C μ i C ν i ∗ {\displaystyle \mathbf {D_{\mu
Mulliken_population_analysis
Thought experiment in theoretical quantum physics
expresses this as follows: "There is a paradox only if we suppose that a density matrix (i.e. a probability distribution) is something 'physically real' and
Wigner's_friend
Principle of quantum mechanics
information science Quantum computing Quantum chaos Decoherence EPR paradox Density matrix Scattering theory Quantum statistical mechanics Quantum machine learning
Quantum_superposition
bipartite quantum system. If ϱ A , B {\displaystyle \varrho _{A,B}} is the density matrix of a system ( A , B ) {\displaystyle (A,B)} composed of two subsystems
Squashed_entanglement
Matrix in which most of the elements are zero
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict
Sparse_matrix
Measure of covariance of components of a random vector
covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the
Covariance_matrix
Generalized measurement in quantum mechanics
{\displaystyle i_{0}} . When the state being measured is described by a density matrix ρ A {\displaystyle \rho _{A}} , the corresponding post-measurement state
POVM
Concept in statistics mathematics
(or smoothing) d×d matrix which is symmetric and positive definite; K is the kernel function which is a symmetric multivariate density; K H ( x ) = | H
Multivariate kernel density estimation
Multivariate_kernel_density_estimation
Measure of connection disorder in a network
constructed from a density matrix ρ {\displaystyle \rho } : historically, the first proposed candidate for such a density matrix has been an expression
Network_entropy
Force resulting from the quantisation of a field
allows the energy density in very small regions of space to be negative relative to the ordinary vacuum energy, and the energy densities cannot be arbitrarily
Casimir_effect
Principle in quantum information science
}A_{n})})} where ρ A 1 A k {\displaystyle \rho _{A_{1}A_{k}}} is the density matrix of the substate consisting of qubits A 1 {\displaystyle A_{1}} and A
Monogamy_of_entanglement
Concept in quantum electronics
model (density matrix) which can behave differently depending on the set of initial parameters (coupling strength between the X and multi-X, density of states
Multiple_exciton_generation
Effect of an electron's interaction with the electromagnetic field
will use the density matrix formalism, and the optical Bloch equations for this. The main idea here is that the non-diagonal density matrix elements can
Electric_dipole_transition
In mathematics, a linear operator acting on inner product space
quantum mechanics), such operators represent quantum states, via the density matrix formalism. Take the inner product ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot
Positive_operator
Quantum mechanics principle
|y\rangle {\Big )}} is necessarily antisymmetric. To prove it, consider the matrix element ⟨ ψ | ( ( | x ⟩ + | y ⟩ ) ⊗ ( | x ⟩ + | y ⟩ ) ) . {\displaystyle
Pauli_exclusion_principle
Topics referred to by the same term
system on a block device, as in the Unix File System Superblock, in the density matrix renormalization group numerical technique Superblock algorithm, in the
Superblock
Description of continuous random distribution
In probability theory, a probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function
Probability_density_function
Approximating method in quantum mechanics
an upper bound to the ground state energy. The Hartree–Fock method, density matrix renormalization group, and Ritz method apply the variational method
Variational method (quantum mechanics)
Variational_method_(quantum_mechanics)
Relativistic wave equation in quantum mechanics
after he did not manage to use it to establish the equivalence between matrix mechanics and wave mechanics, like he could for the Schrödinger equation
Klein–Gordon_equation
State invariant involving qubits
{M}}^{2})}}} in which ρ M {\displaystyle \rho _{\mathcal {M}}} is the reduced density matrix (or its continuous-variable analogue) across the bipartition M {\displaystyle
Concurrence (quantum computing)
Concurrence_(quantum_computing)
High-temperature expansion in statistical mechanics
distribution that can be formulated using, e.g., a wavefunction, a density matrix, or a phase-space distribution. Conceptually, there is always, at least
Cluster_expansion
DENSITY MATRIX
DENSITY MATRIX
Girl/Female
Muslim
Identity
Girl/Female
Indian
Another Name of Happness
Girl/Female
Indian, Punjabi, Sikh
Deity
Girl/Female
Hindu, Indian
People who Give
Boy/Male
Muslim
Identity
Biblical
a bush; enmity
Girl/Female
Indian
Surname or Lastname
English (Somerset)
English (Somerset) : apparently a habitational name from an unidentified place. It is probably a variant of Denslow or possibly Denley, neither of which are of identified origin.
Boy/Male
Arabic, Gujarati, Hindu, Indian, Kannada, Muslim
Identity
Boy/Male
Indian
Royal Boy
Girl/Female
British, English, Greek, Jamaican
Deity
Boy/Male
Bengali, Christian, Gujarati, Hindu, Indian, Kannada, Malayalam, Punjabi, Sanskrit, Sikh, Tamil
Deity
Girl/Female
Biblical
A bush, enmity.
Girl/Female
Biblical
A bush, enmity.
Biblical
a bush; enmity
Girl/Female
Indian
Identity
Girl/Female
Arabic
Entity; Strong Existence
Girl/Female
Tamil
Deity
Girl/Female
American, Australian
God is My Judge
Girl/Female
Indian
Deity
DENSITY MATRIX
DENSITY MATRIX
Female
Hebrew
(ש××›Ö´×™× ×”) Variant spelling of Hebrew Shekinah, SHECHINA means "God" or "God's holy spirit."
Girl/Female
Indian, Sikh
Wish
Girl/Female
Hindu, Indian, Kannada
Rained; Pure
Boy/Male
British, Chinese, Christian, Danish, English, German, Swedish
From the Valley; Man from the Lowlands
Girl/Female
Gujarati, Hindu, Indian, Kannada, Telugu
An Arrow; Dart
Girl/Female
Australian, French, Latin
Laurel
Female
Scandinavian
Scandinavian form of Old Norse Ingigerðr, INGEGERD means "Ing's enclosure."
Boy/Male
Biblical
Hoarse, dry, hot.
Girl/Female
Afghan, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
A Song; Melody
Boy/Male
Latin
Conqueror.
DENSITY MATRIX
DENSITY MATRIX
DENSITY MATRIX
DENSITY MATRIX
DENSITY MATRIX
n.
The quality or state of being porous; -- opposed to density.
n.
Poverty; indigence.
n.
Grossness; coarseness; thickness; density.
n.
The condition of being the same with something described or asserted, or of possessing a character claimed; as, to establish the identity of stolen goods.
n.
The ratio of mass, or quantity of matter, to bulk or volume, esp. as compared with the mass and volume of a portion of some substance used as a standard.
n.
The quality of being dense; density.
n.
A degree of firmness, density, or spissitude.
n.
The quality or state of being tenuous; thinness, applied to a broad substance; slenderness, applied to anything that is long; as, the tenuity of a leaf; the tenuity of a hair.
n.
Enmity.
n.
Rarily; rareness; thinness, as of a fluid; as, the tenuity of the air; the tenuity of the blood.
n.
The quality of being dense, close, or thick; compactness; -- opposed to rarity.
n.
The quality or state of being venous.
a.
Having equal density, as different regions of a medium; passing through points at which the density is equal; as, an isopycnic line or surface.
n.
The collection of attributes which make up the nature of a god; divinity; godhead; as, the deity of the Supreme Being is seen in his works.
n.
Thickness; density; compactness.
n.
A condition in which the circulation is retarded, and the entire mass of blood is less oxygenated than it normally is.
n.
Depth of shade.
n.
The quality or state of being tense, or strained to stiffness; tension; tenseness.
pl.
of Identity
n.
Refinement; delicacy.