scholarly journals Extremality of numerical radii of matrix commutators and Jordan products

2017 ◽  
Vol 533 ◽  
pp. 258-281
Author(s):  
Hwa-Long Gau ◽  
Kuo-Zhong Wang
Keyword(s):  
Jordan Products

scholarly journals Jordan products of quantum channels and their compatibility

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Mark Girard ◽  
Martin Plávala ◽  
Jamie Sikora
Keyword(s):  
Quantum State ◽  
Sufficient Conditions ◽  
The Other ◽  
Independent Interest ◽  
Quantum Channels ◽  
Semidefinite Programs ◽  
Jordan Product ◽  
Marginal Problem ◽  
Jordan Products ◽  
Product Of Matrices

AbstractGiven two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.

scholarly journals Minimal polynomials of additive commutators and Jordan products

1972 ◽  
Vol 22 (1) ◽  
pp. 12-33 ◽  
Author(s):  
Marvin Marcus ◽  
M.Shafqat Ali
Keyword(s):  
Minimal Polynomials ◽  
Jordan Products

scholarly journals On the eigenvalues of Jordan products

2003 ◽  
Vol 359 (1-3) ◽  
pp. 249-262 ◽  
Author(s):  
Enide Andrade Martins ◽  
Fernando C. Silva
Keyword(s):  
Jordan Products

scholarly journals On the invariant polynomials of Jordan products

2003 ◽  
Vol 360 ◽  
pp. 173-189 ◽  
Author(s):  
Enide Andrade Martins ◽  
Fernando C. Silva
Keyword(s):  
Invariant Polynomials ◽  
Jordan Products

scholarly journals Identities for Generalized Lie and Jordan Products on Totally Associative Triple Systems

2000 ◽  
Vol 231 (1) ◽  
pp. 387-405 ◽  
Author(s):  
Murray Bremner ◽  
Irvin Hentzel
Keyword(s):  
Triple Systems ◽  
Jordan Products

scholarly journals Derivation Requirements on Prime Near-Rings for Commutative Rings

2019 ◽  
Vol 20 (2) ◽  
pp. 139
Author(s):  
Dian Winda Setyawati ◽  
Mochammad Reza Habibi ◽  
Komar Baihaqi
Keyword(s):  
Commutative Rings ◽  
Previous Theorem ◽  
Jordan Product ◽  
Jordan Products

Near-ring is an extension of ring without having to fulfill a commutative of the addition operations and left distributive of the addition and multiplication operations It has been found that some theorems related to a prime near-rings are commutative rings involving the derivation of the Lie products and the derivation of the Jordan product. The contribution of this paper is developing the previous theorem by inserting derivations to the Lie products and the Jordan product. Keywords: Derivation, Prime Near-Ring, Lie Products and Jordan Products.

scholarly journals Maps preserving the fixed points of triple Jordan products of operators

2016 ◽  
Vol 27 (3) ◽  
pp. 850-854 ◽  
Author(s):  
Ali Taghavi ◽  
Roja Hosseinzadeh ◽  
Vahid Darvish
Keyword(s):  
Fixed Points ◽  
Jordan Products

scholarly journals Maps Preserving k-Jordan Products on Operator Algebras

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 814
Author(s):  
Xiaofei Qi ◽  
Miaomiao Wang
Keyword(s):  
Positive Integer ◽  
Operator Algebras ◽  
Jordan Product ◽  
Standard Operator ◽  
Standard Operator Algebras ◽  
Nonlinear Maps ◽  
Jordan Products ◽  
Additive Maps

For any positive integer k, the k-Jordan product of a , b in a ring R is defined by { a , b } k = { { a , b } k − 1 , b } 1 , where { a , b } 0 = a and { a , b } 1 = a b + b a . A map f on R is k-Jordan zero-product preserving if { f ( a ) , f ( b ) } k = 0 whenever { a , b } k = 0 for a , b ∈ R ; it is strong k-Jordan product preserving if { f ( a ) , f ( b ) } k = { a , b } k for all a , b ∈ R . In this paper, strong k-Jordan product preserving nonlinear maps on general rings and k-Jordan zero-product preserving additive maps on standard operator algebras are characterized, generalizing some known results.

scholarly journals Nonlinear maps preserving Jordan *-products

2014 ◽  
Vol 409 (1) ◽  
pp. 180-188 ◽  
Author(s):  
Liqing Dai ◽  
Fangyan Lu
Keyword(s):  
Nonlinear Maps ◽  
Jordan Products
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