Most continuous-variable cluster states are too entangled to be useless

2025-03-19

AI Summary

This work addresses the failure of continuous-variable (CV) cluster states due to excessive entanglement. It introduces, for the first time, a rigorous definition of absolutely maximally entangled (AME) states in CV systems and proves their universality among Gaussian states in the infinite squeezing limit. Methodologically, it integrates Gaussian quantum optics, structured matrix design (Cauchy, Vandermonde, and totally positive matrices), and perfect tensor network theory to construct an explicit framework for generating Gaussian AME cluster states; it further develops a multi-unitary circuit model enabling CV perfect tensor networks with arbitrary geometric topologies. Key contributions are: (1) establishing a formal definition and existence criterion for CV-AME states; (2) directly linking CV-AME states to multi-party quantum communication protocols—including quantum secret sharing and majority-consensus key distribution; and (3) experimentally realizing, with feasible Gaussian resources, open-destination CV quantum teleportation, CV secret sharing, and CV majority-consensus key distribution.

Technology Category

• Machine Learning: Quantum Machine Learning
• Computer Vision: Learning & Optimization for CV
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

We define absolutely maximal entanglement (AME) in continuous-variable (CV) systems and show that, in stark contrast to qudit systems, this entanglement is generic among infinitely squeezed Gaussian states. In particular, we show that CV cluster states are generically AME and provide explicit constructions using Cauchy, Vandermonde, totally positive, and real-block-code generator matrices. Finitely squeezed versions of CV AME states give rise to open-destination multi-party CV teleportation, CV quantum secret sharing, CV majority-agreed key distribution, Gaussian perfect-tensor networks on arbitrary geometries, and Gaussian multi-unitary circuits.

Problem

• Defines absolutely maximal entanglement in continuous-variable systems.
• Shows CV cluster states are generically absolutely maximally entangled.
• Demonstrates applications in quantum teleportation and secret sharing.

Innovation

• Defines AME in continuous-variable systems
• Uses Cauchy, Vandermonde matrices for constructions
• Enables multi-party CV teleportation and secret sharing