Jointly constrained semidefinite bilinear programming with an application to Dobrushin curves

Huber, S; Koenig, R; Tomamichel, M

Jointly constrained semidefinite bilinear programming with an application to Dobrushin curves

Huber, S Koenig, R Tomamichel, M

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Publisher:: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2018, 66, (5), pp. 2934-2950
Issue Date:: 2018

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Field	Value	Language
dc.contributor.author	Huber, S
dc.contributor.author	Koenig, R
dc.contributor.author	Tomamichel, M https://orcid.org/0000-0001-5410-3329
dc.date.accessioned	2021-06-15T23:56:19Z
dc.date.available	2021-06-15T23:56:19Z
dc.date.issued	2018
dc.identifier.citation	IEEE Transactions on Information Theory, 2018, 66, (5), pp. 2934-2950
dc.identifier.issn	0018-9448
dc.identifier.issn	1557-9654
dc.identifier.uri	http://hdl.handle.net/10453/149543
dc.description.abstract	We propose a branch-and-bound algorithm for minimizing a bilinear functional of the form \[ f(X,Y) = \mathrm{tr}((X\otimes Y)Q)+\mathrm{tr}(AX)+\mathrm{tr}(BY) , \] of pairs of Hermitian matrices $(X,Y)$ restricted by joint semidefinite programming constraints. The functional is parametrized by self-adjoint matrices $Q$, $A$ and $B$. This problem generalizes that of a bilinear program, where $X$ and $Y$ belong to polyhedra. The algorithm converges to a global optimum and yields upper and lower bounds on its value in every step. Various problems in quantum information theory can be expressed in this form. As an example application, we compute Dobrushin curves of quantum channels, giving upper bounds on classical coding with energy constraints.
dc.language	English
dc.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
dc.relation	http://purl.org/au-research/grants/arc/DE160100821
dc.relation.ispartof	IEEE Transactions on Information Theory
dc.relation.isbasedon	10.1109/TIT.2019.2939474
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0801 Artificial Intelligence and Image Processing, 0906 Electrical and Electronic Engineering, 1005 Communications Technologies
dc.subject.classification	Networking & Telecommunications
dc.title	Jointly constrained semidefinite bilinear programming with an application to Dobrushin curves
dc.type	Journal Article
utslib.citation.volume	66
utslib.for	0801 Artificial Intelligence and Image Processing
utslib.for	0906 Electrical and Electronic Engineering
utslib.for	1005 Communications Technologies
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	closed_access	*
dc.date.updated	2021-06-15T23:56:17Z
pubs.issue	5
pubs.publication-status	Published
pubs.volume	66
utslib.citation.issue	5

Abstract:

We propose a branch-and-bound algorithm for minimizing a bilinear functional of the form \[ f(X,Y) = \mathrm{tr}((X\otimes Y)Q)+\mathrm{tr}(AX)+\mathrm{tr}(BY) , \] of pairs of Hermitian matrices $(X,Y)$ restricted by joint semidefinite programming constraints. The functional is parametrized by self-adjoint matrices $Q$, $A$ and $B$. This problem generalizes that of a bilinear program, where $X$ and $Y$ belong to polyhedra. The algorithm converges to a global optimum and yields upper and lower bounds on its value in every step. Various problems in quantum information theory can be expressed in this form. As an example application, we compute Dobrushin curves of quantum channels, giving upper bounds on classical coding with energy constraints.

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