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TIPTOP SIGNED

Tensoring Positive Maps on Operator Structures

Total Cost €

0

EC-Contrib. €

0

Partnership

0

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Project "TIPTOP" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITE LYON 1 CLAUDE BERNARD 

Organization address
address: BOULEVARD DU 11 NOVEMBRE 1918 NUM43
city: VILLEURBANNE CEDEX
postcode: 69622
website: www.univ-Iyon1.fr

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Total cost 196˙707 €
 EC max contribution 196˙707 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2018
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2019
 Duration (year-month-day) from 2019-10-01   to  2021-09-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITE LYON 1 CLAUDE BERNARD FR (VILLEURBANNE CEDEX) coordinator 196˙707.00

Map

 Project objective

Many important problems in quantum information theory can be formulated in terms of how linear maps between matrix algebras behave under tensor powers. Examples include the distillation problem (fundamental for quantum communication), the problem of local entanglement annihilation (important for entanglement distribution in quantum networks), and the PPT squared conjecture important for (quantum key repeaters). Despite their importance for quantum communication, these problems are wide open, and no general theory is known for solving them. I realized that these problems can be formulated in the framework of abstract operator systems. Here, they correspond to characterizing which linear maps stay positive under tensor powers with respect to different operator system structures over the matrix algebras at the input and output. Completely positive maps and completely copositive maps (compositions of completely positive maps with a transposition) are always trivial examples, corresponding to known examples in quantum information theory. The question is, whether other examples exist. So far this type of problem has only been studied (indirectly) in the few special cases of operator systems over the matrix algebras corresponding to the above problems. There is a much richer theory of abstract operator systems (even over the matrix algebras) and different tensor products to combine them. In my project, I want to study such tensorization problems for other operator system structures over the matrix algebras and beyond. I want to understand how properties of these structures affect properties of linear maps under tensor powers, and find settings where only the trivial examples of completely positive and completely copositive maps stay positive under any tensor power. Finally, I aim to identify settings where tensorization problems become easier, and where I can construct examples of positive maps with properties we are currently lacking in quantum information theory.

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The information about "TIPTOP" are provided by the European Opendata Portal: CORDIS opendata.

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lastchecktime (2020-09-25 8:45:58) correctly updated