Remote state preparation of single-partite high-dimensional states in complex Hilbert spaces

TL;DR

This paper presents practical schemes for remotely preparing high-dimensional quantum states in complex Hilbert spaces, utilizing minimal resources and adaptable to current technology, with potential applications in quantum information processing.

Contribution

It introduces new methods for remote state preparation of high-dimensional states using orthogonal measurements and entangled resources, adaptable to various state dimensions and entanglement types.

Findings

Exact preparation of four- and eight-level states demonstrated

Schemes work with both maximally and non-maximally entangled states

Encoding in spatial modes avoids collection operations

Abstract

High-dimensional quantum systems offer a new playground for quantum information applications due to their remarkable advantages such as higher capacity and noise resistance. We propose potentially practical schemes for remotely preparing four- and eight-level equatorial states in complex Hilbert spaces exactly by identifying a set of orthogonal measurement bases. In these minimal-resource-consuming schemes, both pre-shared maximally and non-maximally entangled states are taken into account. The three-, five-, six-, and seven-level equatorial states in complex Hilbert spaces can also be obtained by adjusting the parameters of the desired states. The evaluations indicate that our high-dimensional RSP schemes might be possible with current technology. The collection operations, necessary for our high-dimensional RSP schemes via partially entangled channels, can be avoided by encoding the computational basis in the spatial modes of single-photon systems.