General Entanglement Breaking Channels

TL;DR

This work characterizes entanglement-breaking channels (EBT) as completely positive trace-preserving maps that render any entangled input separable, revealing their canonical Holevo form and equivalent rank-one Kraus representations. It establishes a spectrum of equivalent conditions via the Choi–Jamiolkowski isomorphism and analyzes the convex geometry of EBT maps, including the structure of extreme points and their relation to CQ/QC subclasses. While in qubits (d=2) extreme EBT maps align with extreme CQ maps, in higher dimensions there exist extreme EBT maps that are not CQ, with explicit constructions illustrating the richer extremal structure. The paper also develops representations of EBT channels in operator bases, linking the Holevo form to matrix decompositions and variance constraints, and discusses implications for channel capacity and entanglement preservation in quantum information processing.

Abstract

This paper studies the class of stochastic maps, or channels, whose action (when tensored with the identity) on an entangled state always yields a separable state. Such maps have a canonical form introduced by Holevo. Such maps are called entanglement breaking, and can always be written in a canonical form introduced by Holevo. Some special classes of these maps are considered and several equivalent characterizations given. Since the set of entanglement-breaking trace-preserving maps is convex, it can be described 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 > 2 the set of entanglement breaking maps has additional extreme points which are not extreme CQ maps.

Theorems & Definitions (8)

• Definition 1
• Theorem 2
• Theorem 3
• Theorem 4
• Theorem 5
• Theorem 6
• Lemma 7
• Lemma 8