Entanglement Breaking Channels

By M. Horodecki, P. W. Shor, Mary Beth Ruskai. 2003

533 citations recorded by the source corpus.

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)=∑kRkTrFkρ where each Rk is a density matrix and Fk>0. If, in addition, Φ is trace-preserving, the {Fk} 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/f32cff0b69bc0c83cb81e266d1833878aca13e54

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Additivity of the classical capacity of entanglement-breaking quantum channels (2002, background): “(See also [11] for details of this proof.”
Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy (2013, background): “If Nx , Mx ≥ 0 for all x , then we say that the map is entanglement-breaking [31,32,34,62], and one can also verify that it is completely positive as well.”
The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement (2012, methodology): “The following proposition, which was originally reported by Horodecki, Shor and Ruskai [78], identifies entanglement-breaking channels exactly with measureand-prepare procedures, consisting of a measurement of some POVM and the subsequent conditional state preparation.”
Concepts of quantum non-Markovianity: A hierarchy (2017, background): “Hence, the joint state immediately after each measurement must be a tensor product, and so break any entanglement between the system and the bath [94].”
Complementary Channels and the Additivity Problem (2005, background): “Kraus representation with rank one operators V� [ 10 ]:”
The structure of degradable quantum channels (2008, background): “It is conve-18 nient to begin with the map Φ C : M d A (cid:55)→ M d E and recall that [20] a CP map Φ C is EB if and only if its Kraus operators can be chosen to have rank one, so that It was shown in [17, 23] that the complement Φ : Proof: Let Ψ be the CP map with Kraus operators Then it follows…”
Geometry of Quantum States: Index (2007, background): “It is then not surprising that ρ ′ = ( ⊗ 1)ρ becomes separable for an arbitrary state ρ [463], which explains why SP maps are also called entanglement breaking channels.”
Qubit Entanglement Breaking Channels (2003, methodology): “ar X iv :q ua nt -p h/ 03 02 03 2v ∗Partially supported by the National Security Agency (NSA) and Advanced Research and Development Activity (ARDA) under Army Research Office (ARO) contract numbers DAAG5598-1-0374 and DAAD19-02-1-0065, and by the National Science Foundation under Grant number…”
Quantum processes which do not use coherence (2015, background): “[51] Michael Horodecki, Peter W Shor, and Mary Beth Ruskai, “Entanglement breaking channels,” Reviews in Mathematical Physics 15, 629–641 (2003).”