# Deterministic transformations of three-qubit entangled pure states

## TL;DR

This paper characterizes deterministic local transformations of three-qubit pure states within GHZ and W entanglement classes, revealing conditions under which such transformations are possible with unit probability.

## Contribution

It provides the most general two-outcome measurement operations for deterministic transformations within the same entanglement class of three-qubit states.

## Key findings

- Standard GHZ state cannot be deterministically transformed into a GHZ-type state with all nonzero bipartite entanglements.
- Transformations are possible with certainty when the target state has at least one zero bipartite concurrence.
- The study explores transformations under local measurements by one or multiple parties.

## Abstract

The states of three-qubit systems split into two inequivalent types of genuine tripartite entanglement, namely the Greenberger-Horne-Zeilinger (GHZ) type and the $W$ type. A state belonging to one of these classes can be stochastically transformed only into a state within the same class by local operations and classical communications. We provide local quantum operations, consisting of the most general two-outcome measurement operators, for the deterministic transformations of three-qubit pure states in which the initial and the target states are in the same class. We explore these transformations, originally having standard GHZ and standard $W$ states, under the local measurement operations carried out by a single party and $p$ ($p=2,3$) parties (successively). We find a notable result that the standard GHZ state cannot be deterministically transformed to a GHZ-type state in which all its bipartite entanglements are nonzero, i.e., a transformation can be achieved with unit probability when the target state has at least one vanishing bipartite concurrence.