Results 51 to 60 of about 1,504,261 (185)
Some inequalities for positive linear maps
Linear Algebra and its Applications, 2012 Let \(M_{n}( \mathbb{C} )\) be the algebra of all \(n\times n\) complex matrices and let \(\phi :M_{n}( \mathbb{C} )\rightarrow M_{n}( \mathbb{C} )\) be a positive unital map. The authors prove that if \(A\in M_{n}( \mathbb{C} )\), then \[ \phi (A^{\ast }A)-\phi (A)^{\ast }\phi (A)\leq \inf_{z\in \mathbb{C} }\left\| A-z\right\|.
Bhatia, Rajendra, Sharma, Rajesh
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Extreme positive linear maps onC *-algebras
Mathematische Zeitschrift, 1988 Let A be a unital \(C^ *\)-algebra and let B be a von Neumann algebra. Let S(A,B) be the convex set of unital positive linear maps between A and B. We prove that the extreme points of S(A,B) are exactly the unital algebra homomorphisms if and only if A is abelian and, either B is abelian or dim A\(
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Distinguishing between statistical and systematic errors in quantum process tomography
New Journal of Physics, 2019 It is generally assumed that every process in quantum physics can be described mathematically by a completely positive map. However, experimentally reconstructed processes are not necessarily completely positive due to statistical or systematic errors ...
Sabine Wölk +3 more
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Entanglement witnesses arising from Choi type positive linear maps
, 2012 We construct optimal PPTES witnesses to detect $3\otimes 3$ PPT entangled edge states of type $(6,8)$ constructed recently \cite{kye_osaka}. To do this, we consider positive linear maps which are variants of the Choi type map involving complex numbers ...
Augusiak R +9 more
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Randomized Benchmarking beyond Groups
PRX Quantum, 2022 Randomized benchmarking (RB) is the gold standard for experimentally evaluating the quality of quantum operations. The current framework for RB is centered on groups and their representations but this can be problematic.
Jianxin Chen, Dawei Ding, Cupjin Huang
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New tools for investigating positive maps in matrix algebras
, 2012 We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as reduction map ...
Bhatia +29 more
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On positive linear maps preserving invertibility
Journal of Functional Analysis, 1984 A positive linear map \(\Phi\) between two \(C^*\)-algebras is a Jordan homomorphism if \(\Phi\) preserves invertibility and the range of \(\Phi\) is a \(C^*\)-algebra. A counterexample is given for the case that the range of \(\Phi\) is not assumed to be a \(C^*\)-algebra; this answers a question raised by \textit{B. Russo} [Proc. Am. Math. Soc.
Choi, M-D. +4 more
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Artifact-Free Image Style Transfer by Using Feature Map Clamping
IEEE Access, 2020 Style transfer is an application that applies colors and patterns of a style image to a content image. In the previous style transfer method, a decoder was trained by using only positive valued feature maps from the last rectified linear unit (ReLU ...
Hyeonjin Lee, Hyun-Chul Choi
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Remarks on an operator Wielandt inequality
, 2015 Let $A$ be a positive operator on a Hilbert space $\mathcal{H}$ with $00.$$ We consider several upper bounds for $\frac{1}{2}|\Gamma+\Gamma^{*}|$.
Zhang, Pingping
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Positive linear maps on operator algebras [PDF]
Communications in Mathematical Physics, 1976 Given a family of completely positive maps, indexed by a group, from aC*-algebra into itself, we are concerned with its dilation to a group of *-automorphisms on a larger algebra. A Schwarz-type inequality forn-positive *-linear mappings from an involutive algebra into the bounded linear operators on a hilbert space is obtained. Strongly continuous one-
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