Stability of encoded macroscopic quantum superpositions

TL;DR

This paper investigates the stability of GHZ-like quantum states with block-encoded structures, demonstrating that certain encodings, especially concatenated GHZ states, are significantly more resistant to decoherence, with implications for quantum technologies.

Contribution

The study introduces and analyzes block-encoded GHZ-like states, particularly concatenated GHZ states, showing their enhanced stability against noise compared to traditional GHZ states.

Findings

C-GHZ states exhibit increased robustness against decoherence.

Analytic and numerical methods confirm superior stability of C-GHZ states.

Bounds on entanglement and macroscopicity are established for these states.

Abstract

The multipartite Greenberger-Horne-Zeilinger (GHZ) state is a paradigmatic example of a highly entangled multipartite states with distinct quantum features. However, the GHZ state is very sensitive to generic decoherence processes, where its quantum features and in particular its entanglement diminish rapidly, thereby hindering possible practical applications e.g. in the context of quantum metrology. In this paper, we discuss GHZ-like quantum states with a block-local structure and show that they exhibit a drastically increased stability against noise for certain choices of block-encoding. We analyze in detail the decay of the interference terms, the entanglement in terms of distillable entanglement and Negativity as well as the notion of macroscopicity as measured by the so-called q-index, and provide general bounds on these quantities. We focus on an encoding where logical qubits are themselves encoded as GHZ states, which leads to so-called concatenated GHZ (C-GHZ) states. We compare the stability of C-GHZ states with other types of encodings, thereby showing the superior stability of the C-GHZ states. Analytic results are complemented by numerical studies, where tensor network techniques are used to investigate the quantum properties of multipartite entangled states under the influence of decoherence.