Entanglement distillation protocols and number theory

Journal Article · Thu Sep 15 04:00:00 EDT 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.72.032313· OSTI ID:20718499

Bombin, H; Martin-Delgado, M A ^[1]

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1. Departamento de Fisica Teorica I, Universidad Complutense, 28040 Madrid (Spain)

We show that the analysis of entanglement distillation protocols for qudits of arbitrary dimension D benefits from applying basic concepts from number theory, since the set Z{sub D}{sup n} associated with Bell diagonal states is a module rather than a vector space. We find that a partition of Z{sub D}{sup n} into divisor classes characterizes the invariant properties of mixed Bell diagonal states under local permutations. We construct a very general class of recursion protocols by means of unitary operations implementing these local permutations. We study these distillation protocols depending on whether we use twirling operations in the intermediate steps or not, and we study them both analytically and numerically with Monte Carlo methods. In the absence of twirling operations, we construct extensions of the quantum privacy algorithms valid for secure communications with qudits of any dimension D. When D is a prime number, we show that distillation protocols are optimal both qualitatively and quantitatively.

• OSTI ID: 20718499
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 72; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ALGORITHMS
DATA TRANSMISSION
MONTE CARLO METHOD
QUANTUM COMPUTERS
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
SECRECY PROTECTION
SPACE
VECTORS