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.
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 teleportation, a cornerstone of quantum information science, allows for the transfer of an unknown quantum state from a sender (Alice) to a receiver (Bob) using a shared entangled resource and classical communication. A fundamental challenge arises when the state to be teleported is unclonable, as dictated by the no-cloning theorem, precluding direct comparison between the initial and teleported states for certification. This paper proposes a robust Bell-certification scheme for validating the successful teleportation of such unclonable quantum states. We move beyond conventional fidelity benchmarks, which prove insufficient for unknown states, by focusing on the integrity of the Bell state entanglement and the correctness of the Bell measurement performed by Alice. Our methodology leverages the inherent properties of maximally entangled Bell states as the resource, combined with a verifiable Bell measurement analysis and a rigorous assessment of the classical communication channel. We detail how the quality of the shared entangled pair, potentially characterized by entanglement witnesses or purity measures, directly contributes to the certification of the teleportation process. Furthermore, we analyze the scheme's resilience to common noise models, such as depolarizing channels affecting the resource state, demonstrating how fluctuations in resource entanglement propagate to the certification confidence. The proposed Bell-certification provides a crucial framework for ensuring the reliability of quantum teleportation protocols in practical applications where direct state verification is impossible or impractical, paving the way for more secure and verifiable quantum communication and computation architectures.
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)
Certifying quantum behavior from classically accessible data is essential for secure communication and scalable quantum technologies. While powerful certification methods such as Bell nonlocality and quantum steering exist, their implementation typically requires entanglement or additional assumptions, and experimental demonstrations mainly focus on low-dimensional systems. In minimal prepare-and-measure scenarios, where a sender encodes information into quantum states and a receiver performs a single measurement, robust certification becomes particularly challenging, especially in the presence of noise and in higher-dimensional Hilbert spaces. Here, we propose, design, and experimentally implement a protocol that certifies quantumness between two distant parties without the need for preshared resources or measurement incompatibility. The experiments are carried out using the orbital angular momentum degrees of freedom of single photons, chosen for providing increased dimensionality that is scalable. We demonstrate the robustness of the protocol through rank-stability analysis of the observed correlations, which enables the certification of non-classicality even in the presence of noise. Our results provide a practical route to validate high-dimensional quantum communication systems and open new possibilities for secure and dimension-efficient quantum information processing.
Genuine high-dimensional (HD) quantum steering was recently proposed for certifying HD entanglement in the one-sided device-independent setting, as quantified by the Schmidt number [ Phys. Rev. Lett. 126 , 200404 ( 2021 ) PRLTAO 0031-9007 10.1103/PhysRevLett.126.200404 ]. As one of the central challenges in the steering test is the tolerated noise threshold, here we develop a more robust method for certifying genuine HD steering in noisy environments. We derive genuine HD steering criteria using multiple mutually unbiased bases, surpassing the previous restriction of only two measurement settings. Although the present multisetting criteria are not tight, we theoretically show that they are more robust to noise than the tight two-setting criteria. To test the practicality of our method under realistic conditions, we report an experimental demonstration using photonic orbital angular momentum entangled states in dimensions d = 3 , 4 , 5 . Our work offers a more robust way to witness the entanglement dimension in practical one-sided device-independent quantum information processing.
High-dimensional entanglement offers significant advantages over its low-dimensional counterpart in various information-processing tasks. However, to harness these advantages, it is crucial that the quantum channels used to store or transmit the subsystems of an entangled system not only preserve entanglement but also maintain its dimensionality above a certain threshold. The maximum entanglement dimension that a channel can preserve is referred to as its effective dimensionality, since the channel cannot be used to transmit information of dimension greater than that in a single use. In this work, we present a method to certify whether a quantum channel can preserve entanglement dimension above a given threshold. Unlike existing approaches, our method is faithful, i.e., it can be applied to any channel, and avoids common assumptions such as preparation of entangled states, auxiliary side channels, or perfect measurement devices. Moreover, the method can be extended to faithfully certify other classes of non-resource-breaking channels, such as non-nonpositive-partial-transpose-breaking channels (non-NPT-breaking channels). Finally, we discuss possible experimental realizations of our certification scheme through explicit examples.