Practical scheme for efficient distillation of GHZ states

TL;DR

This paper presents a practical LOCC protocol for efficiently distilling high-fidelity GHZ states from noisy tripartite systems, using iterative non-linear transformations that converge subexponentially with simple operations.

Contribution

It introduces a novel iterative distillation scheme that corrects small errors in GHZ states with fewer resources and simpler operations than traditional methods.

Findings

Achieves subexponential convergence to pure GHZ states.

Employs simple unitary operations and measurements.

Demonstrates effectiveness through analytical and numerical results.

Abstract

We develop an efficient local operation and classical communication (LOCC) scheme for the distillation of Greenberger-Horne-Zeilinger (GHZ) states from tripartite systems subjected to both coherent and incoherent errors. The proposed method employs an iterative process that applies a postselection-based non-linear transformation to increase the entanglement of 3-qubit states. In contrast to traditional distillation protocols that require an exponential number of initial states as a resource, our method achieves subexponential convergence towards a pure GHZ state. The proposed scheme is practical in the sense that it employs a small set of relatively simple unitary operations and projective measurements in the computational basis. We systematically develop a double-iteration protocol by providing a mathematical framework for the transformation processes involved, emphasizing the role of unitary operations in correcting arbitrary small errors in the initial states. Through analytical derivations and numerical simulations, we demonstrate the protocol's ability to progressively eliminate noise and improve fidelity over subsequent iterations. Significantly, our protocol not only corrects for small arbitrary distortions in the GHZ states but also maintains operational simplicity, making it feasible for practical quantum computing applications.