Entanglement manipulation of multipartite pure states with finite rounds of classical communication

TL;DR

This paper explores the capabilities and limitations of finite-round classical communication in transforming multipartite pure quantum states, revealing new protocols, limitations, and effects such as locking and unlocking entanglement.

Contribution

It introduces explicit examples of state transformations requiring probabilistic steps, deterministic protocols within SLOCC classes, and analyzes multipartite effects like locking and unlocking of entanglement.

Findings

Explicit examples of probabilistic $LOCC_{ }$ transformations.

Identification of SLOCC classes with all-deterministic protocols.

Demonstration of transformations possible via separable operations but not $LOCC_{ }$.

Abstract

We studied pure state transformations using local operations assisted by finitely many rounds of classical communication ($LOCC_{\mathbb{N}}$) in C. Spee, J.I. de Vicente, D. Sauerwein, B. Kraus, arXiv:1606.04418 (2016). Here, we first of all present the details of some of the proofs and generalize the construction of examples of state transformations via $LOCC_{\mathbb{N}}$ which require a probabilistic step. However, we also present explicit examples of SLOCC classes where any separable transformation can be realized by a protocol in which each step is deterministic (all-det-$LOCC_{\mathbb{N}}$). Such transformations can be considered as natural generalizations of bipartite transformations. Furthermore, we provide examples of pure state transformations which are possible via separable transformations, but not via $LOCC_{\mathbb{N}}$. We also analyze an interesting genuinely multipartite effect which we call locking or unlocking the power of other parties. This means that one party can prevent or enable the implementation of LOCC transformations by other parties. Moreover, we investigate the maximally entangled set restricted to $LOCC_{\mathbb{N}}$ and show how easily computable bounds on some entanglement measures can be derived by restricting to $LOCC_{\mathbb{N}}$.