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When Do Composed Maps Become Entanglement Breaking?

Christandl, Matthias ; Müller-Hermes, Alexander ; Wolf, Michael M.

Annales Henri Poincaré, 2019-07, Vol.20 (7), p.2295-2322 [Periódico revisado por pares]

Cham: Springer International Publishing

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Título:
When Do Composed Maps Become Entanglement Breaking?
Autor: Christandl, Matthias ; Müller-Hermes, Alexander ; Wolf, Michael M.
Assuntos: Breaking ; Classical and Quantum Gravitation ; Composition ; Depolarization ; Dynamical Systems and Ergodic Theory ; Elementary Particles ; Information theory ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Physics ; Physics and Astronomy ; Quantum entanglement ; Quantum Field Theory ; Quantum phenomena ; Quantum Physics ; Qubits (quantum computing) ; Relativity Theory ; Schmidt number ; Theoretical ; Upper bounds
É parte de: Annales Henri Poincaré, 2019-07, Vol.20 (7), p.2295-2322
Descrição: For many completely positive maps repeated compositions will eventually become entanglement breaking. To quantify this behaviour we develop a technique based on the Schmidt number: If a completely positive map breaks the entanglement with respect to any qubit ancilla, then applying it to part of a bipartite quantum state will result in a Schmidt number bounded away from the maximum possible value. Iterating this result puts a successively decreasing upper bound on the Schmidt number arising in this way from compositions of such a map. By applying this technique to completely positive maps in dimension three that are also completely copositive we prove the so-called PPT squared conjecture in this dimension. We then give more examples of completely positive maps where our technique can be applied, e.g. maps close to the completely depolarizing map, and maps of low rank. Finally, we study the PPT squared conjecture in more detail, establishing equivalent conjectures related to other parts of quantum information theory, and we prove the conjecture for Gaussian quantum channels.
Editor: Cham: Springer International Publishing
Idioma: Inglês

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When Do Composed Maps Become Entanglement Breaking?

Christandl, Matthias ; Müller-Hermes, Alexander ; Wolf, Michael M.

Cham: Springer International Publishing

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