The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Entanglement Breaking Channels
Open accessAbstract
This paper studies the class of stochastic maps, or channels, for which (I⊗Φ)(Γ) is always separable (even for entangled Γ). Such maps are called entanglement breaking, and can always be written in the form Φ(ρ)=∑k R k Tr F k ρ where each R k is a density matrix and F k>0. If, in addition, Φ is trace-preserving, the {F k} must form a positive operator valued measure (POVM). Some special classes of these maps are considered and other characterizations given. Since the set of entanglement-breaking trace-preserving maps is convex, it can be characterized by its extreme points. The only extreme points of the set of completely positive trace preserving maps which are also entanglement breaking are those known as classical-quantum or CQ. However, for d≥3, the set of entanglement breaking maps has additional extreme points which are not extreme CQ maps.
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Citations
Cites
Completely positive linear maps on complex matrices
Choi, M.-D. (1975) · Linear Algebra and its Applications · doi:10.1016/0024-3795(75)90075-0 · Cited by 2,659 · cited 4×
“E) Υ ◦ Φ is completely positive for all positivity preserving maps Υ.”
BackgroundInfluentialLinear transformations which preserve trace and positive semidefiniteness of operators
Jamiołkowski, A. (1972) · Reports on Mathematical Physics · doi:10.1016/0034-4877(72)90011-0 · Cited by 1,512
An analysis of completely-positive trace-preserving maps on M2
Beth Ruskai, M., Szarek, S., & Werner, E. (2002) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(01)00547-x · Cited by 366
Cited by
Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.865 · Cited by 10,118
Self-citationWilde, M. M. (2013) · doi:10.1017/cbo9781139525343 · Cited by 1,138
Wilde, M. M., Winter, A., & Yang, D. (2014) · Communications in Mathematical Physics · doi:10.1007/s00220-014-2122-x · Cited by 516
Concepts of quantum non-Markovianity: A hierarchy
Li, L., Hall, M. J. W., & Wiseman, H. M. (2018) · Physics Reports · doi:10.1016/j.physrep.2018.07.001 · Cited by 353
Quantum channels and memory effects
Caruso, F., Giovannetti, V., Lupo, C., & Mancini, S. (2012) · arXiv · doi:10.48550/arxiv.1207.5435 · Cited by 331
Metadata
- Authors
- Horodecki, M., Shor, P. W., & Ruskai, M. B.
- Venue
- Reviews in Mathematical Physics
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 2003-08
- Volume
- 15
- Issue
- 06
- Pages
- 629-641
- ISSN
- 0129-055X (ISSN-L)
- 1793-6659
- OpenAlex
- W2123829027
- Cited by
- 604
- References
- 3
- FWCI
- 14.84
- Type
- journal article
- Language
- en
- Open access
- green
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