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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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Cebyšev’s type inequalities for positive linear maps of selfadjoint operators in Hilbert spaces [PDF]
Mathematica Moravica, 2017 Some inequalities for positive linear maps of continuous synchronous (asynchronous) functions of selfadjoint linear operators in Hilbert spaces, under suitable assumptions for the involved operators, are given.
Sever Silvestru Dragomir
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Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps [PDF]
Quantum, 2021 Although quantum channels underlie the dynamics of quantum states, maps which are not physical channels — that is, not completely positive — can often be encountered in settings such as entanglement detection, non-Markovian quantum dynamics, or error ...
Bartosz Regula, Ryuji Takagi, Mile Gu
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Physical Implementability of Linear Maps and Its Application in Error Mitigation [PDF]
Quantum, 2021 Completely positive and trace-preserving maps characterize physically implementable quantum operations. On the other hand, general linear maps, such as positive but not completely positive maps, which can not be physically implemented, are fundamental ...
Jiaqing Jiang, Kun Wang, Xin Wang
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Diagonal unitary and orthogonal symmetries in quantum theory [PDF]
Quantum, 2021 We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions.
Satvik Singh, Ion Nechita
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Exponential Inequalities for Positive Linear Mappings [PDF]
Journal of Function Spaces, 2018 In this article, we present exponential-type inequalities for positive linear mappings and Hilbert space operators, by means of convexity and the Mond-Pečarić method. The obtained results refine and generalize some known results. As an application, we present extensions for operator-like geometric and harmonic means inequalities.
Mohammad Sababheh +2 more
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Improvements of operator reverse AM-GM inequality involving positive linear maps
Journal of Inequalities and Applications, 2020 In this paper, we shall present some reverse arithmetic-geometric mean operator inequalities for unital positive linear maps. These inequalities improve some corresponding results due to Xue (J. Inequal. Appl. 2017:283, 2017).
Shazia Karim +2 more
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Pure Maps between Euclidean Jordan Algebras [PDF]
Electronic Proceedings in Theoretical Computer Science, 2019 We propose a definition of purity for positive linear maps between Euclidean Jordan Algebras (EJA) that generalizes the notion of purity for quantum systems.
Abraham Westerbaan +2 more
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Positive linear maps and spreads of normal matrices
, 2022 We obtain some inequalities involving positive linear maps on matrix algebra.
Sharma, Rajesh, Pal, Manish
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Quantum Programs as Kleisli Maps [PDF]
Electronic Proceedings in Theoretical Computer Science, 2017 Furber and Jacobs have shown in their study of quantum computation that the category of commutative C*-algebras and PU-maps (positive linear maps which preserve the unit) is isomorphic to the Kleisli category of a comonad on the category of commutative C*
Abraham Westerbaan
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