Optimizing Quantum State Transformation Under Locality Constraint

TL;DR

This paper introduces a numerical framework for optimizing quantum state transformations under locality constraints, improving entanglement distillation for weakly entangled states using gradient-based optimization of local quantum channels.

Contribution

It presents a novel parametrization and optimization method for local quantum channels to enhance quantum state transformations under locality constraints.

Findings

Significantly improves entanglement distillation for weakly entangled states

Demonstrates effectiveness of gradient-based optimization on complex Stiefel manifold

Provides a versatile tool for quantum information processing tasks

Abstract

In this paper, we present a general numerical framework for both deterministic and probabilistic quantum state transformations, under locality constraints. For a given arbitrary bipartite initial state and a desired bipartite target state, we construct an optimized local quantum channel that transforms the initial state into the target state with high fidelity. To achieve this goal, local quantum channels are parametrized on a complex Stiefel manifold and optimized using gradient-based methods. We demonstrate that this approach significantly enhances entanglement distillation for weakly entangled states via two complementary strategies: optimized local state transformation and probabilistic local transformation. These results establish our method as a powerful and versatile tool for a broad class of quantum information processing tasks.