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Find link is a tool written by Edward Betts.Longer titles found: Subadditivity effect (view), Strong subadditivity of quantum entropy (view)
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Entanglement-assisted classical capacity
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demonstrates that this rate is optimal by making use of the strong subadditivity of quantum entropy. Classical capacity Quantum capacity Typical subspaceMeasure (mathematics) (5,449 words) [view diff] no match in snippet view article
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notionsBlancmange curve (3,185 words) [view diff] no match in snippet view article find links to article
In mathematics, the blancmange curve is a self-affine fractal curve constructible by midpoint subdivision. It is also known as the Takagi curve, afterUtility functions on indivisible goods (1,808 words) [view diff] exact match in snippet view article find links to article
is additive if and only if it is both submodular and supermodular. Subadditivity means that for every pair of disjoint sets A , B {\displaystyle A,B}RiskMetrics (1,552 words) [view diff] exact match in snippet view article find links to article
sizes in the portfolio. An important property of incremental risk is subadditivity. That is, the sum of the incremental risks of the positions in a portfolioEntropy (information theory) (9,711 words) [view diff] exact match in snippet view article
entropy was given by Aczél, Forte and Ng, via the following properties: Subadditivity: H ( X , Y ) ≤ H ( X ) + H ( Y ) {\displaystyle \mathrm {H} (X,Y)\leqUncertainty theory (Liu) (3,824 words) [view diff] exact match in snippet view article
mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms.[clarification needed] Mathematical measuresMatrix Chernoff bound (4,767 words) [view diff] exact match in snippet view article find links to article
{E} \mathbf {Y} )}.} This gives us the major result of the paper: the subadditivity of the log of the matrix generating function. Let X k {\displaystyleInfinite-dimensional Lebesgue measure (946 words) [view diff] exact match in snippet view article find links to article
{\displaystyle X} by null sets because by choosing a countable subcover, the σ-subadditivity of μ {\displaystyle \mu } implies that μ ( X ) = 0. {\displaystyle \muGraph entropy (914 words) [view diff] exact match in snippet view article find links to article
then H ( G 1 ) ≤ H ( G 2 ) {\displaystyle H(G_{1})\leq H(G_{2})} . Subadditivity. Given two graphs G 1 = ( V , E 1 ) {\displaystyle G_{1}=(V,E_{1})}Squashed entanglement (2,131 words) [view diff] exact match in snippet view article find links to article
S(A:B|\Lambda )\geq 0} . This inequality is often called the strong-subadditivity property of quantum entropy. Consider three random variables A , BNull set (1,730 words) [view diff] exact match in snippet view article find links to article
Any countable union of null sets is itself a null set (by countable subadditivity of μ {\displaystyle \mu } ). Any (measurable) subset of a null set isAbsolutely convex set (1,913 words) [view diff] exact match in snippet view article find links to article
{\displaystyle q:X\to \mathbb {R} } that satisfies the following conditions: Subadditivity/Triangle inequality: q ( x + y ) ≤ q ( x ) + q ( y ) {\displaystyleBorel–Cantelli lemma (1,815 words) [view diff] exact match in snippet view article find links to article
_{N\to \infty }\Pr \left(\bigcup _{n=N}^{\infty }E_{n}\right).} By subadditivity, Pr ( ⋃ n = N ∞ E n ) ≤ ∑ n = N ∞ Pr ( E n ) . {\displaystyle \Pr \left(\bigcupFrequency illusion (2,719 words) [view diff] exact match in snippet view article find links to article
2009). "On splitting and merging categories: A regression account of subadditivity". Memory & Cognition. 37 (4): 383–393. doi:10.3758/mc.37.4.383. ISSN 0090-502XSeminorm (6,139 words) [view diff] exact match in snippet view article find links to article
is called a seminorm if it satisfies the following two conditions: Subadditivity/Triangle inequality: p ( x + y ) ≤ p ( x ) + p ( y ) {\displaystyleSamir D. Mathur (514 words) [view diff] exact match in snippet view article find links to article
cannot restore unitarity. This result was obtained by applying Strong Subadditivity of Quantum Entropy to the evaporation of Hawking radiation. This ledAron Wall (460 words) [view diff] exact match in snippet view article find links to article
to quantum teleportation. Wall AC. Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy. Classical and QuantumContent (measure theory) (2,018 words) [view diff] exact match in snippet view article
{\mathcal {A}}\Rightarrow \mu (A\cup B)+\mu (A\cap B)=\mu (A)+\mu (B).} Subadditivity: A i ∈ A ( i = 1 , 2 , … , n ) ⇒ μ ( ⋃ i = 1 n A i ) ≤ ∑ i = 1 n μ (Rank (linear algebra) (4,390 words) [view diff] exact match in snippet view article
{rank} (BC)\leq \operatorname {rank} (B)+\operatorname {rank} (ABC).} Subadditivity: rank ( A + B ) ≤ rank ( A ) + rank ( B ) {\displaystyle \operatornameSigma-additive set function (1,622 words) [view diff] exact match in snippet view article find links to article
A)+2\mu (A\cap B).} However, the related properties of submodularity and subadditivity are not equivalent to each other. Note that modularity has a differentLawrence Ein (653 words) [view diff] exact match in snippet view article find links to article
Demailly, Jean-Pierre; Ein, Lawrence; Lazarsfeld, Robert (2000). "A subadditivity property of multiplier ideals". arXiv:math/0002035. with R. LazarsfeldNorm (mathematics) (5,671 words) [view diff] exact match in snippet view article
denotes the usual absolute value of a scalar s {\displaystyle s} : Subadditivity/Triangle inequality: p ( x + y ) ≤ p ( x ) + p ( y ) {\displaystyleMary Beth Ruskai (791 words) [view diff] exact match in snippet view article find links to article
to quantum mechanics. In 1972 she and Elliot Lieb proved the Strong Subadditivity of Quantum Entropy, which was described in 2005 as "the key result onCoherent risk measure (2,313 words) [view diff] exact match in snippet view article find links to article
H. (2019). "Bigger Is Not Always Safer: A Critical Analysis of the Subadditivity Assumption for Coherent Risk Measures". Risks. 7 (3): 91. doi:10.3390/risks7030091Holm–Bonferroni method (2,441 words) [view diff] exact match in snippet view article find links to article
{\frac {\alpha }{m_{0}}}\right\}\right)={\frac {\alpha }{m_{0}}}} . Subadditivity of the probability measure implies that Pr ( A ) ≤ ∑ i ∈ I 0 P ( { PMatthew Headrick (487 words) [view diff] exact match in snippet view article find links to article
Matthew; Takayanagi, Tadashi (2007). "Holographic proof of the strong subadditivity of entanglement entropy". Physical Review D. 76 (10): 106013. arXiv:0704Kolmogorov complexity (7,143 words) [view diff] exact match in snippet view article find links to article
writing out the string itself. Theorem. (extra information bounds, subadditivity) K ( x | y ) ≤ K ( x ) ≤ K ( x , y ) ≤ max ( K ( x | y ) + K ( y )Xiangyu Zhou (892 words) [view diff] exact match in snippet view article find links to article
S2CID 126209780. Guan, Qi'an; Zhou, Xiangyu (2020). "Restriction formula and subadditivity property related to multiplier ideal sheaves". Journal für die ReinePrice of anarchy in auctions (2,914 words) [view diff] exact match in snippet view article find links to article
Both of the above upper bounds on the PoA degrade gracefully when the subadditivity and no-overbidding assumptions are relaxed. E.g: if we assume that eachQuantum discord (2,370 words) [view diff] exact match in snippet view article find links to article
analogy to the Peres–Horodecki criterion and in relation to the strong subadditivity of the von Neumann entropy. Efforts have been made to extend the definitionGlossary of areas of mathematics (7,687 words) [view diff] exact match in snippet view article find links to article
mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Universal algebra a field studying theTrace inequality (4,515 words) [view diff] exact match in snippet view article find links to article
Ruskai, Mary Beth (2007). "Another short and elementary proof of strong subadditivity of quantum entropy". Reports on Mathematical Physics. 60 (1). ElsevierNetwork entropy (2,670 words) [view diff] exact match in snippet view article find links to article
not satisfy the property of sub-additivity (see Von Neumann entropy's subadditivity), expected to hold theoretically. A more grounded definition, satisfyingKuratowski closure axioms (3,764 words) [view diff] exact match in snippet view article find links to article
the equality in [K4] as an inclusion, giving the weaker axiom [K4''] (subadditivity): [K4''] It is subadditive: for all A , B ⊆ X {\displaystyle A,B\subseteqEntropy of network ensembles (1,971 words) [view diff] exact match in snippet view article find links to article
not satisfy the property of sub-additivity (see Von Neumann entropy's subadditivity), expected to hold theoretically. A more grounded definition, satisfyingList of women in mathematics (22,241 words) [view diff] exact match in snippet view article find links to article
mathematician, translator and biographer Mary Beth Ruskai (born 1944), proved subadditivity of quantum entropy, bounded the electrons in an atom, advocate for women