Bipartite Entanglement in Continuous-Variable Cluster States

TL;DR

This paper investigates the entanglement characteristics of Gaussian continuous-variable cluster states, comparing idealized and practical states, and examines how loss impacts their suitability for quantum computing.

Contribution

It provides an analytic comparison of bipartite entanglement in ideal and Gaussian cluster states, including effects of photonic loss, for continuous-variable quantum computing.

Findings

Idealized states exhibit higher entanglement than Gaussian approximations.

Photonic loss significantly reduces entanglement in practical states.

Gaussian cluster states' entanglement limits their use in quantum computation.

Abstract

We present a study of the entanglement properties of Gaussian cluster states, proposed as a universal resource for continuous-variable quantum computing. A central aim is to compare mathematically-idealized cluster states defined using quadrature eigenstates, which have infinite squeezing and cannot exist in nature, with Gaussian approximations which are experimentally accessible. Adopting widely-used definitions, we first review the key concepts, by analysing a process of teleportation along a continuous-variable quantum wire in the language of matrix product states. Next we consider the bipartite entanglement properties of the wire, providing analytic results. We proceed to grid cluster states, which are universal for the qubit case. To extend our analysis of the bipartite entanglement, we adopt the entropic-entanglement width, a specialized entanglement measure introduced recently by Van den Nest M et al., Phys. Rev. Lett. 97 150504 (2006), adapting their definition to the continuous-variable context. Finally we add the effects of photonic loss, extending our arguments to mixed states. Cumulatively our results point to key differences in the properties of idealized and Gaussian cluster states. Even modest loss rates are found to strongly limit the amount of entanglement. We discuss the implications for the potential of continuous-variable analogues of measurement-based quantum computation.