Optimal Entanglement Transformations Among N-qubit W-Class States

TL;DR

This paper establishes conditions for optimal probabilistic transformations between N-qubit W-class states using LOCC, providing bounds, lower bounds, and insights into symmetric state transformations.

Contribution

It offers a necessary and sufficient condition for achieving the upper bound of transformation probability and analyzes the optimal procedures for symmetric W-class states.

Findings

Derived a condition for when the upper bound of transformation probability is attainable.

Provided lower bounds for transforming arbitrary W-class states.

Showed that optimal symmetric state transformations often require non-symmetric filters.

Abstract

We investigate the physically allowed probabilities for transforming one N-partite W-class state to another by means of local operations assisted with classical communication (LOCC). Recently, Kintas and Turgut have obtained an upper bound for the maximum probability of transforming two such states [arXiv:1003.2118v1]. Here, we provide a simple sufficient and necessary condition for when this upper bound can be satisfied and thus when optimality of state transformation can be achieved. Our discussion involves obtaining lower bounds for the transformation of arbitrary W-class states and showing precisely when this bound saturates the bound of [arXiv:1003.2118v1]. Finally, we consider the question of transforming symmetric W-class states and find that in general, the optimal one-shot procedure for converting two symmetric states requires a non-symmetric filter by all the parties.