Entanglement Breaking Channels

Abstract

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.

Operator-sum representation for bosonic Gaussian channels

“…It is also known that every entanglement breaking channel has a description in terms of rank one Kraus operators [35]. We demonstrate these aspects using our Kraus operators {T ℓ (κ)}.…”

“…And a theorem of Choi [30] gives a necessary and sufficient test for extremality of a channel in terms of Kraus operators. It is known that a channel is entanglement breaking if and only if it can be described in terms of a set of rank one Kraus operators [35][36][37]. Further, the work of [38] and [39,40] relate error correctability to the structure of the Kraus operators of a channel.…”

Generalized state spaces and nonlocality in fault-tolerant quantum-computing schemes

“…While Lemma 5 establishes a difference between cubeseparable operations and entangling operations, operations that create Bell diagonal states are entanglement breaking (they break entanglement between the two-qubits and the rest of the universe [26]) and so they cannot be used to generate multiparty entanglement by themselves (and indeed they can be classically efficiently simulated [11]). In Lemma 8 we will present examples of quantum operations that are cube separable despite being capable of generating some form of multiparticle entanglement.…”

Мультипликативность $p$-норм вполне положительных отображений и проблема аддитивности в квантовой теории информации

“…Каналы, удовлетворяющие условию (i), были введены в работе [26], а сфор-мулированная выше характеризация получена в [33]. Следуя [33], мы будем называть такие отображения разрушающими сцепленность (р.с.).…”

“…Следуя [33], мы будем называть такие отображения разрушающими сцепленность (р.с.). Отображе-ние (56) является каналом тогда и только тогда, когда выполняется соотноше-ние полноты…”