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Simulation Codes for Certification of Genuine multipartite High-Dimensional Quantum Teleportation

Nengfei Gong

Published Mar 29, 2026• 1 citation
Publisher

Abstract

Written by Nengfei Gong This repository contains the simulation codes accompanying our research on certifying genuine multipartite high-dimensional quantum teleportation (HDQT). The codebase is divided into two main parts, implemented in Mathematica and MATLAB, respectively.This upload consists of 3 code files dedicated to the numerical analysis of genuine HDQT protocols: 1 Mathematica notebooks for calculating the optimal average teleportation fidelity over a given density of tripartite channel state. The methodology and theoretical framework implemented in these codes are derived from the seminal work presented in the following paper: "https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.22.054045". One can generalize corresponding codes for any d by following the similar rules. 2 MATLAB scripts/functions for computing the Genuine multipartite high-dimensional teleportation robustness (GHTR) of a given HDQT data and the Genuine multipartite high-dimensional entanglement robustness (GHER), which quantifies the channel entanglement. These codes are written in matlab and require CVX, QETLAB,and also the codes in "https://github.com/paulskrzypczyk/nonclassicalteleportation" (This seminal work has been a major inspiration for the construction of my codes)

DOI
10.5281/zenodo.19312120

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Written by Nengfei Gong This repository contains the simulation codes accompanying our research on certifying genuine multipartite high-dimensional quantum teleportation (HDQT). The codebase is divided into two main parts, implemented in Mathematica and MATLAB, respectively.This upload consists of 3 code files dedicated to the numerical analysis of genuine HDQT protocols: 1 Mathematica notebooks for calculating the optimal average teleportation fidelity over a given density of tripartite channel state. The methodology and theoretical framework implemented in these codes are derived from the seminal work presented in the following paper: "https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.22.054045". One can generalize corresponding codes for any d by following the similar rules. 2 MATLAB scripts/functions for computing the Genuine multipartite high-dimensional teleportation robustness (GHTR) of a given HDQT data and the Genuine multipartite high-dimensional entanglement robustness (GHER), which quantifies the channel entanglement. These codes are written in matlab and require CVX, QETLAB,and also the codes in "https://github.com/paulskrzypczyk/nonclassicalteleportation" (This seminal work has been a major inspiration for the construction of my codes)
Written by Nengfei Gong This repository contains the simulation codes accompanying our research on certifying genuine high-dimensional quantum teleportation (HDQT). The codebase is divided into two main parts, implemented in Mathematica and MATLAB, respectively.This upload consists of 7 code files dedicated to the numerical analysis of genuine HDQT protocols: 3 Mathematica notebooks for calculating the optimal average fidelity over a given density of channel state for high-dimensional quantum teleportation. The methodology and theoretical framework implemented in these codes are derived from the seminal work presented in the following paper: "https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.22.054045". One can generalize corresponding codes for any d by following the similar rules. 4 MATLAB scripts/functions for computing the Genuine High-dimensional teleportation robustness (GHTR) of a given HDQT data. These codes are written in matlab and require CVX, QETLAB,and also the codes in "https://github.com/paulskrzypczyk/nonclassicalteleportation" (This seminal work has been a major inspiration for the construction of my codes)
ℓ\ellℓ-Multiranks of Multipartite Quantum States via Tensor Flattening: A Mathematica Codebase
We present a Mathematica codebase for computing ℓ\ellℓ-multilinear ranks (ℓ\ellℓ-multiranks) of multiqudit quantum states using tensor-flattening techniques. By calculating the ranks of all bipartition-induced matricizations, the method provides an efficient criterion for detecting Genuine Multipartite Entangled (GME) states in systems with local dimension ddd. The code automatically generates all required tensor reshapes and outputs the full ℓ\ellℓ-multirank profile, offering a practical tool for characterizing entanglement in high-dimensional multiqudit systems.
Developing reliable methods for certifying the dimension of a given quantum system or process is essential to ensure the validity of claimed realization of high-dimensional (HD) quantum advantages. The existing criteria for certifying genuine HD quantum teleportation (HDQT) mainly focus on demonstrating the successful transmission of genuine HD quantum states. However, a complete certification of HDQT must also identify the entanglement dimension of resource, which is critical for verifying whether the transmission capacity and noise resilience meet the necessary thresholds. Here we propose two universal criteria (based on fidelity and robustness, respectively) for certifying genuine HDQT behaviors that can close this gap by fully identifying the dimension of the entanglement. Both criteria require only the input and output teleportation data and remain feasible under partial Bell-state measurements. Furthermore, the robustness-based criterion has stronger noise resistance and it requires no prior assumptions about local operations, making it robust even in black-box scenario. Our results establish a universal and reliable theoretical framework for validating the core quantum advantage in HDQT, pivotal for ensuring the reliable links in HD quantum networks.
Quantum secret-sharing is a fundamental technique in quantum communication and plays a crucial role in high-dimensional quantum secret transmission. This paper investigates the teleportation of arbitrary d-dimensional multipartite quantum secrets and proposes both deterministic and probabilistic teleportation protocols. The schemes employ generalized Bell-state measurements, generalized Pauli operators, and auxiliary particles to achieve efficient and secure quantum secret-sharing. The deterministic protocol employs maximally entangled channels to achieve perfect sharing with unit success probability. Moreover, the probabilistic protocol, assisted by auxiliary particles and generalized unitary operations, achieves perfect fidelity quantum secret sharing via non-maximally entangled channels. The protocols are further extended to arbitrary d-dimensional systems, and their robustness under several common quantum noise models is analyzed numerically. Compared with previous schemes, the proposed protocols support arbitrary multipartite entangled states, high-dimensional systems, non-maximally entangled channels, and noise analysis within a unified framework. These results enrich the theory of high-dimensional quantum communication and provide practical approaches for future quantum secret-sharing and secure quantum networks.
Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device independently. However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty in identifying optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this Letter, we explore a general and robust device-independent method that can be applied to various realistic multipartite quantum states in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly entangled Greenberger-Horne-Zeilinger states, showing that the method applies equally well to less standard states.
Recently Yeo and Chua [Phys. Rev. Lett. 96, 060502 (2006)] presented an explicit protocol for faithfully teleporting an arbitrary two-qubit state via a genuine four-qubit entanglement channel. Here we generalize completely their results to teleporting an arbitrary NNN-qubit state via genuine NNN-qubit entanglement channels. And we present the general form of the genuine multipartite entanglement channels, namely, the sufficient and necessary condition the genuine NNN-qubit entanglement channels must satisfy to teleport an arbitrary NNN-qubit state.