Composition of PPT maps
| Autor: | Vern I. Paulsen, Nicholas A. Manor, Matthew Kennedy |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Nuclear and High Energy Physics
Trace (linear algebra) FOS: Physical sciences General Physics and Astronomy Quantum entanglement 01 natural sciences Theoretical Computer Science Combinatorics Set (abstract data type) 0103 physical sciences FOS: Mathematics 0101 mathematics Operator Algebras (math.OA) Mathematical Physics Mathematics Conjecture 010102 general mathematics Mathematics - Operator Algebras Zero (complex analysis) Statistical and Nonlinear Physics Mathematical Physics (math-ph) Composition (combinatorics) Functional Analysis (math.FA) Mathematics - Functional Analysis Computational Theory and Mathematics Iterated function Graph (abstract data type) 010307 mathematical physics |
| Zdroj: | Quantum Information and Computation. 18:472-480 |
| ISSN: | 1533-7146 |
| Popis: | M. Christandl conjectured that the composition of any trace preserving PPT map with itself is entanglement breaking. We prove that Christandl's conjecture holds asymptotically by showing that the distance between the iterates of any unital or trace preserving PPT map and the set of entanglement breaking maps tends to zero. Finally, for every graph we define a one-parameter family of maps on matrices and determine the least value of the parameter such that the map is variously, positive, completely positive, PPT and entanglement breaking in terms of properties of the graph. Our estimates are sharp enough to conclude that Christandl's conjecture holds for these families. Comment: 10 pages |
| Databáze: | OpenAIRE |
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