Alternating Projections Methods for Discrete-time Stabilization of Quantum States

TL;DR

This paper introduces alternating projection methods for stabilizing quantum states, demonstrating their convergence properties and robustness, with applications to entanglement stabilization in quantum systems.

Contribution

It develops a novel framework for quantum state stabilization using alternating projections and analyzes their convergence and robustness, specifically applied to entangled states.

Findings

Sequences converge to the intersection of fixed point sets

The protocol is robust against randomization

Bounds on convergence speed are provided

Abstract

We study sequences (both cyclic and randomized) of idempotent completely-positive trace-preserving quantum maps, and show how they asymptotically converge to the intersection of their fixed point sets via alternating projection methods. We characterize the robustness features of the protocol against randomization and provide basic bounds on its convergence speed. The general results are then specialized to stabilizing en- tangled states in finite-dimensional multipartite quantum systems subject to a resource constraint, a problem of key interest for quantum information applications. We conclude by suggesting further developments, including techniques to enlarge the set of stabilizable states and ensure efficient, finite-time preparation.