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searching for Positive operator 67 found (86 total)

Local hidden-variable theory (1,179 words) [view diff] exact match in snippet view article find links to article

Hidden-variable models have been constructed for Werner states even if positive operator-valued measurements (POVM) are allowed, not only von Neumann measurements

Naimark's dilation theorem (1,489 words) [view diff] exact match in snippet view article find links to article

theory, Naimark's dilation theorem is a result that characterizes positive operator valued measures. It can be viewed as a consequence of Stinespring's

Hyponormal operator (238 words) [view diff] exact match in snippet view article find links to article

) p − ( T T ∗ ) p {\displaystyle (T^{*}T)^{p}-(TT^{*})^{p}} is a positive operator.) If p = 1 {\displaystyle p=1} , then T is called a hyponormal operator

Effect algebra (2,132 words) [view diff] exact match in snippet view article find links to article

are used to express concepts in quantum theory, the definition of a positive operator-valued measure may be cast in terms of effect algebra morphisms as

Hegerfeldt's theorem (522 words) [view diff] no match in snippet view article find links to article

it is possible to construct localization observables in terms of positive-operator valued measures that are compatible with the restrictions imposed

Krein–Rutman theorem (381 words) [view diff] exact match in snippet view article find links to article

such that T ( u ) = r ( T ) u {\displaystyle T(u)=r(T)u} . If the positive operator T {\displaystyle T} is assumed to be ideal irreducible, namely, there

SIC-POVM (3,617 words) [view diff] exact match in snippet view article find links to article

quantum information theory, symmetric, informationally complete, positive operator-valued measures (SIC-POVMs) are a particular type of generalized measurement

Square root of a matrix (4,651 words) [view diff] exact match in snippet view article find links to article

operator U and positive operator P such that A = U P ; {\displaystyle A=UP;} this is the polar decomposition of A. The positive operator P is the unique

Quantum Markov chain (201 words) [view diff] exact match in snippet view article find links to article

density matrix, and the projection operators are to be replaced by positive operator valued measures. More precisely, a quantum Markov chain is a pair

Quantum Bayesianism (8,310 words) [view diff] exact match in snippet view article find links to article

any single measurement that is a minimal, informationally complete positive operator-valued measure (POVM), this is especially clear: A quantum state is

Born rule (2,256 words) [view diff] no match in snippet view article find links to article

applications, this treatment of the Born rule is generalized using positive-operator-valued measures (POVM). A POVM is a measure whose values are positive

Classical capacity (4,635 words) [view diff] exact match in snippet view article find links to article

things from quantum mechanics. First, a quantum state is a unit trace, positive operator known as a density operator. Usually, we denote it by ρ {\displaystyle

Commutator subspace (1,881 words) [view diff] exact match in snippet view article find links to article

between a positive operator and its diagonalisation is a sum of commutators. That is, A − diag(μ(A)) belongs to Com(J) for every positive operator A in J

Complementarity (physics) (3,047 words) [view diff] no match in snippet view article

complementarity has also been applied to quantum measurements described by positive-operator-valued measures (POVMs). While the concept of complementarity can

Howard Brandt (419 words) [view diff] exact match in snippet view article find links to article

4,553,068), and co-inventor of a quantum key receiver based on a positive operator valued measure (US Patent 5,999,285). His broad research interests

Canonical quantization (4,736 words) [view diff] exact match in snippet view article find links to article

of the operators is governed by the Hamiltonian, which must be a positive operator. A state | 0 ⟩ {\displaystyle |0\rangle } annihilated by the Hamiltonian

Kaplansky density theorem (524 words) [view diff] exact match in snippet view article find links to article

approximations with respect to the strong operator topology. 1) If h is a positive operator in (A−)1, then h is in the strong-operator closure of the set of self-adjoint

Dixmier trace (644 words) [view diff] exact match in snippet view article find links to article

1/3, ... has Dixmier trace equal to 1. If the eigenvalues μi of the positive operator T have the property that ζ T ( s ) = Tr ⁡ ( T s ) = ∑ μ i s {\displaystyle

Mathematical formulation of quantum mechanics (8,107 words) [view diff] exact match in snippet view article find links to article

(PVM) described in the measurement postulate(s) can be generalized to positive operator-valued measures (POVM), which is the most general kind of measurement

Complexification (Lie group) (7,216 words) [view diff] exact match in snippet view article

an invertible operator g lies in GC if the unitary operator u and positive operator p in its polar decomposition g = u ⋅ p both lie in GC. Thus u lies

Quantum mechanics (12,153 words) [view diff] exact match in snippet view article find links to article

specify the state of a subsystem of a larger system, analogously, positive operator-valued measures (POVMs) describe the effect on a subsystem of a measurement

Antieigenvalue theory (197 words) [view diff] exact match in snippet view article find links to article

turning angles. Gustafson, Karl (1968), "The angle of an operator and positive operator products", Bulletin of the American Mathematical Society, 74 (3):

Quantum information (4,547 words) [view diff] case mismatch in snippet view article find links to article

Einstein's thought experiments Interpretations of quantum mechanics Positive Operator Valued Measure (POVM) Quantum clock Quantum entanglement Quantum foundations

Indian Institute of Science Education and Research, Thiruvananthapuram (1,429 words) [view diff] case mismatch in snippet view article find links to article

chemistry Physical chemistry Theoretical chemistry School of Mathematics Positive Operator Theory Partial differential equation Stochastic process Numerical

Unbounded operator (4,635 words) [view diff] exact match in snippet view article find links to article

T on a Hilbert space H is called bounded from below if T + a is a positive operator for some real number a. That is, ⟨Tx|x⟩ ≥ −a ||x||2 for all x in the

Equiangular lines (1,209 words) [view diff] no match in snippet view article find links to article

J.; Grassl, M. (2010-04-01). "Symmetric informationally complete positive-operator-valued measures: A new computer study". Journal of Mathematical Physics

Quantum instrument (1,041 words) [view diff] exact match in snippet view article find links to article

i } {\displaystyle \{{\mathcal {E}}_{i}\}} immediately induces a positive operator-valued measurement (POVM): M i := ∑ a K a ( i ) † K a ( i ) {\displaystyle

Sigma-additive set function (1,650 words) [view diff] exact match in snippet view article find links to article

Banach algebra. Another example, also from quantum mechanics, is the positive operator-valued measure. Additive map – Z-module homomorphism Hahn–Kolmogorov

Ornstein–Uhlenbeck operator (947 words) [view diff] exact match in snippet view article find links to article

scalar functions to produce scalar functions. Note that A = −Δ is a positive operator, whereas Δ is a dissipative operator. Using spectral theory, one can

Quantum finite automaton (3,639 words) [view diff] exact match in snippet view article find links to article

Precise measurements are also not possible, and one instead uses positive operator-valued measures to describe the measurement process. Finally, each

Nuclear operator (4,791 words) [view diff] exact match in snippet view article find links to article

of R and it is defined as follows: Since R is a continuous compact positive operator, there exists a (possibly finite) sequence λ 1 > λ 2 > ⋯ {\displaystyle

Two-state vector formalism (1,394 words) [view diff] exact match in snippet view article find links to article

measurement Delayed choice experiment Wheeler–Feynman absorber theory Positive operator valued measure Schottky, Walter (1921). "Das Kausalproblem der Quantentheorie

Prime number (14,179 words) [view diff] no match in snippet view article find links to article

as mutually unbiased bases and symmetric informationally complete positive-operator-valued measures. The evolutionary strategy used by cicadas of the

Gelfand–Naimark–Segal construction (2,463 words) [view diff] exact match in snippet view article find links to article

g(x^{*}x)=\langle \pi (x)\xi ,\pi (x)T_{g}\,\xi \rangle } for some positive operator T g {\displaystyle T_{g}} in π ( A ) ′ {\displaystyle \pi (A)'} with

Quantum Theory: Concepts and Methods (1,771 words) [view diff] exact match in snippet view article find links to article

ISSN 1572-9516. S2CID 119382552. Brandt, Howard E. (May 1999). "Positive operator valued measure in quantum information processing". American Journal

Calkin correspondence (753 words) [view diff] exact match in snippet view article find links to article

operators and positive sequences, hence the map μ: J+ → j+ from a positive operator to its singular values implements the Calkin correspondence. Another

Gleason's theorem (4,107 words) [view diff] no match in snippet view article find links to article

analogous result for a more general class of measurements, known as positive-operator-valued measures (POVMs). The set of all POVMs includes the set of

Quantum Markov semigroup (1,633 words) [view diff] exact match in snippet view article find links to article

cone of positive elements in A {\displaystyle {\mathcal {A}}} , a positive operator T : A → A {\displaystyle T:{\mathcal {A}}\rightarrow {\mathcal {A}}}

Central carrier (957 words) [view diff] exact match in snippet view article find links to article

⇒ ETF has polar decomposition UH for some partial isometry U and positive operator H in M. ⇒ Ran(U) = Ran(ETF) ⊂ Ran(E). Also, Ker(U) = Ran(H)⊥ = Ran(ETF)⊥

Singular trace (3,733 words) [view diff] exact match in snippet view article find links to article

sequence space j such that for every positive operator A belonging to J. Here μ: J+ → j+ is the map from a positive operator to its singular values. A singular

Von Neumann entropy (5,061 words) [view diff] exact match in snippet view article find links to article

distribution. A quantum measurement can be specified mathematically as a positive operator valued measure, or POVM. In the simplest case, a system with a finite-dimensional

Hilbert space (17,469 words) [view diff] exact match in snippet view article find links to article

other parts of a system in a manner that is described instead by a positive operator valued measure. Thus the structure both of the states and observables

Uncertainty principle (19,263 words) [view diff] exact match in snippet view article find links to article

challenge for quantum theories; some progress has been made using positive operator-valued measure concepts. In 1945, Leonid Mandelstam and Igor Tamm

Subnormal operator (1,513 words) [view diff] exact match in snippet view article find links to article

if in its polar decomposition A = UP, the partial isometry U and positive operator P commute. Given a quasinormal A, the idea is to construct dilations

Entanglement witness (932 words) [view diff] exact match in snippet view article find links to article

{\displaystyle H_{A}\otimes H_{B}} . A mixed state ρ is then a trace-class positive operator on the state space which has trace 1. We can view the family of states

Measurement in quantum mechanics (8,320 words) [view diff] no match in snippet view article find links to article

operator. In functional analysis and quantum measurement theory, a positive-operator-valued measure (POVM) is a measure whose values are positive semi-definite

Generalizations of Pauli matrices (2,766 words) [view diff] exact match in snippet view article find links to article

further. Appleby, D. M. (May 2005). "Symmetric informationally complete–positive operator valued measures and the extended Clifford group". Journal of Mathematical

Contraction (operator theory) (2,901 words) [view diff] exact match in snippet view article

the closure of the ranges Ran(DT) and Ran(DT*) respectively. The positive operator DT induces an inner product on H {\displaystyle {\mathcal {H}}} .

Extensions of symmetric operators (3,248 words) [view diff] exact match in snippet view article find links to article

replaced by self-adjointness for positive operators. Theorem—A symmetric positive operator A {\displaystyle A} is self-adjoint if and only if its Cayley transform

Entanglement distillation (6,316 words) [view diff] no match in snippet view article find links to article

state of spin up and spin down. This treatment corresponds to a POVM (positive-operator-valued measurement). To obtain a perfectly entangled state of two

Andrew M. Gleason (5,389 words) [view diff] exact match in snippet view article find links to article

the lattice of projections of a Hilbert space can be defined by a positive operator with unit trace. Though Richard Kadison proved this was false for

James P. Gordon (1,938 words) [view diff] no match in snippet view article find links to article

that work was an early version of what is currently referred to as positive-operator valued measure (POVM) in the context of quantum measurement theory

Choi–Jamiołkowski isomorphism (3,205 words) [view diff] case mismatch in snippet view article find links to article

qubit ancilla measurement. By combining this scheme with the POVM (Positive Operator-Valued Measure) scheme on site D, the gates V U {\displaystyle VU}

Reproducing kernel Hilbert space (6,323 words) [view diff] exact match in snippet view article find links to article

{\displaystyle T_{K}} is a compact, continuous, self-adjoint, and positive operator. The spectral theorem for self-adjoint operators implies that there

Boiling water reactor safety systems (8,158 words) [view diff] exact match in snippet view article find links to article

when no voids exist, water is cold, and water is dense) without positive operator confirmation that such decreases in period are their intention. Prior

Fidelity of quantum states (4,020 words) [view diff] exact match in snippet view article find links to article

U} . Let { E k } k {\displaystyle \{E_{k}\}_{k}} be an arbitrary positive operator-valued measure (POVM); that is, a set of positive semidefinite operators

Compartmental models (epidemiology) (17,824 words) [view diff] exact match in snippet view article

described by a matrix. So, the next step is to construct a linear positive operator that provides the next generation of infected people when applied

Generalized probabilistic theory (1,850 words) [view diff] case mismatch in snippet view article find links to article

matrices, i.e. by the density matrices. Measurements are identified with Positive Operator valued Measures (POVMs), and the physical operations are completely

Jordan operator algebra (2,686 words) [view diff] exact match in snippet view article find links to article

JBW algebra that are faithful, i.e. do not vanish on any non-zero positive operator. The theory can be deduced from the original theory for von Neumann

Karl Edwin Gustafson (908 words) [view diff] exact match in snippet view article find links to article

April 27, 2022. Gustafson, Karl (1968). "The angle of an operator and positive operator products". Bulletin of the American Mathematical Society. 74 (3):

Quantum t-design (2,477 words) [view diff] exact match in snippet view article find links to article

complex projective t-designs, are symmetric informationally complete positive operator-valued measures (POVMs), which are complex projective 2-design. Since

Quantum cloning (3,063 words) [view diff] exact match in snippet view article find links to article

combination of quantum teleportation and quantum cloning. This process uses positive operator-valued measurements, maximally entangled states, and quantum teleportation

Grunsky matrix (6,334 words) [view diff] exact match in snippet view article find links to article

{\displaystyle (Au,u)=(Tu,Tu)=\|Tu\|^{2}\geq 0,} so that A is a positive operator. By the spectral theorem for compact self-adjoint operators, there

Invariant convex cone (3,569 words) [view diff] exact match in snippet view article find links to article

skew-adjoint operator T with respect to this inner product with –T2 a positive operator. An orthonormal basis can be chosen so that T has 2 × 2 skew-symmetric

Coherent states in mathematical physics (5,762 words) [view diff] exact match in snippet view article find links to article

(x))\left|\psi \right\rangle } , T {\displaystyle T} is a bounded, positive operator with bounded inverse and d μ {\displaystyle d\mu } is a quasi-invariant

Neumann–Poincaré operator (11,017 words) [view diff] exact match in snippet view article find links to article

\displaystyle {(Au,u)=(Tu,Tu)=\|Tu\|^{2}\geq 0,}} so that A is a positive operator. By the spectral theorem for compact self-adjoint operators, there

Incompatibility of quantum measurements (3,103 words) [view diff] exact match in snippet view article find links to article

M_{2}:{\mathcal {A}}_{2}\to {\mathcal {B}}(\mathbb {H} )} be two positive operator-valued measures (POVMs), where ( X 1 , A 1 ) , ( X 2 , A 2 ) {\displaystyle