Polar factorization and pseudo-rearrangements: applications to Pólya–Szegö type inequalities

2003 ◽  
Vol 53 (7-8) ◽  
pp. 929-949 ◽  
Author(s):  
Adele Ferone ◽  
Roberta Volpicelli
Keyword(s):  
Polar Factorization

Quadratic Surplus

2016 ◽  
Author(s):  
Alfred Galichon
Keyword(s):  
Convex Analysis ◽  
Scalar Product ◽  
Optimal Transport ◽  
Point Of View ◽  
Factorization Theorem ◽  
Polar Factorization

This chapter considers the case when the attributes are d-dimensional vectors and the surplus is the scalar product; it assumes that the distribution of the workers' attributes is continuous, but it relaxes the assumption that the distribution of the firms' attributes is discrete. This setting allows us to entirely rediscover convex analysis, which is introduced from the point of view of optimal transport. As a consequence, Brenier's polar factorization theorem is given, which provides a vector extension for the scalar notions of quantile and rearrangement.

scholarly journals Surface parameterization based on polar factorization

2018 ◽  
Vol 329 ◽  
pp. 24-36 ◽  
Author(s):  
Xiaokang Yu ◽  
Na Lei ◽  
Xiaopeng Zheng ◽  
Xianfeng Gu
Keyword(s):  
Surface Parameterization ◽  
Polar Factorization

scholarly journals A polar decomposition for quantum channels (with applications to bounding error propagation in quantum circuits)

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 173 ◽  
Author(s):  
Arnaud Carignan-Dugas ◽  
Matthew Alexander ◽  
Joseph Emerson
Keyword(s):  
Error Propagation ◽  
Polar Decomposition ◽  
Quantum Computer ◽  
Quantum Circuits ◽  
Average Process ◽  
Quantum Channels ◽  
Figures Of Merit ◽  
Overall Performance ◽  
Polar Factorization

Inevitably, assessing the overall performance of a quantum computer must rely on characterizing some of its elementary constituents and, from this information, formulate a broader statement concerning more complex constructions thereof. However, given the vastitude of possible quantum errors as well as their coherent nature, accurately inferring the quality of composite operations is generally difficult. To navigate through this jumble, we introduce a non-physical simplification of quantum maps that we refer to as the leading Kraus (LK) approximation. The uncluttered parameterization of LK approximated maps naturally suggests the introduction of a unitary-decoherent polar factorization for quantum channels in any dimension. We then leverage this structural dichotomy to bound the evolution -- as circuits grow in depth -- of two of the most experimentally relevant figures of merit, namely the average process fidelity and the unitarity. We demonstrate that the leeway in the behavior of the process fidelity is essentially taken into account by physical unitary operations.

Polar factorization of Fourier phase operators in the coherent-state basis

1996 ◽  
Vol 54 (4) ◽  
pp. 3687-3690 ◽  
Author(s):  
William C. Kimler ◽  
Charles A. Nelson
Keyword(s):  
Coherent State ◽  
Polar Factorization ◽  
Phase Operators
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