Teleportation criteria identify entanglement dimension in quantum networks

Neng-Fei Gong and Tie-Jun Wang, both of Beijing University of Posts and Telecommunications, have proposed two new criteria, based on fidelity and robustness, for verifying genuine high-dimensional quantum teleportation (HDQT). Their work goes beyond simply demonstrating successful transmission by identifying the dimension of the entanglement used in the process, a critical step for building reliable quantum networks.

The researchers detail that a complete certification of HDQT must verify whether the transmission capacity and noise resilience meet necessary thresholds. These criteria require only input and output teleportation data and function even with partial Bell-state measurements, establishing a framework for validating core quantum advantages in HDQT.

Fidelity Criterion Certifies Minimum HD Quantum Teleportation Dimension

These criteria allow for verification of genuine high-dimensional quantum teleportation (HDQT) by pinpointing the dimension of the entanglement itself, a critical step in assessing the capacity and resilience of quantum communication links. The work details a fidelity-based criterion and a robustness criterion. Previously, researchers demonstrated HDQT using a fidelity value greater than 2/3 and a robustness criterion defined by a minimum amount of “white noise” added to the qutrit state that could still be simulated by qubit states.

The current research expands this by proposing universal criteria applicable to teleporting d-dimensional states, offering a more comprehensive assessment of entanglement dimension. This advancement is particularly important as quantum networks grow in complexity, demanding rigorous methods for validating the resources used for communication. While fidelity remains a common metric in quantum information processing, its limitations in verification prompted the development of a robustness-based criterion.

This alternative approach introduces the concept of generalized genuine d’-dimensional quantum teleportation robustness (GHTR(d’)), defined as the minimum amount of generalized noise needed to make the teleportation data simulable with a channel state possessing only (d’-1)-dimensional entanglement. A positive value for GHTR(d’) definitively certifies genuine d’-dimensional quantum teleportation, offering a more resilient and versatile method for verification. This is especially valuable in scenarios where the internal workings of the teleportation setup are unknown, as the robustness criterion requires no prior assumptions about local operations.

The practicality of these criteria is further enhanced by their compatibility with partial Bell-state measurements (BSM). The new fidelity-based criterion remains feasible even when Alice performs only partial BSM, significantly reducing the experimental overhead. The results establish a universal and reliable theoretical framework for validating the core quantum advantage in HDQT, ensuring reliable links in HD quantum networks.

Robustness Criterion Identifies Entanglement Dimension in HD Quantum Teleportation

The newly proposed robustness-based criterion offers a distinct advantage over fidelity-based approaches by exhibiting stronger resistance to noise and operating without prior assumptions about local operations performed on the quantum system. This “black-box” functionality means the criteria can validate teleportation quality even without detailed knowledge of the experimental setup, a significant benefit for practical implementation. The authors note that previous methods could only confirm the transmission of a genuine high-dimensional state, but not the dimension of the entanglement powering that transmission, leaving a critical gap in verification.

Closing this gap ensures that the full capacity and noise resilience of the teleportation channel are met, essential requirements for dependable communication. The team’s approach formalizes the assessment of genuine d’-dimensional QT behavior by defining a set of teleportation data as exhibiting this behavior only if it cannot be simulated using a channel state with entanglement dimension at most d’-1.

This definition allows for a rigorous test of whether a given teleportation process truly relies on high-dimensional entanglement, rather than merely mimicking it with lower-dimensional resources. The criteria are designed to be executed solely on analyzing input-output state pairs, streamlining the certification process and making it more accessible for wider adoption.

Genuine HDQT Requires Verifying Entanglement, Not Just State Transfer

This distinction is critical for verifying whether the capacity and noise resilience of a teleportation channel meet necessary performance thresholds, ensuring reliable quantum communication. Researchers have now proposed two universal criteria, based on fidelity and robustness, to fully characterize the entanglement dimension driving HDQT processes. These new criteria move beyond simply confirming that teleportation occurs to determining how it happens, specifically whether the entanglement genuinely spans the higher dimensions necessary for the claimed quantum advantage.

The development of these criteria addresses a fundamental gap in existing certification protocols, which previously could not definitively prove the use of high-dimensional entanglement. The researchers detail that a universal certification should rely solely on analyzing input-output state pairs from the teleportation data, streamlining the verification process and reducing the technical demands on experimental setups.

This is achieved through a formalized definition of genuine d’-dimensional quantum teleportation behavior, establishing a clear benchmark for assessing the underlying quantum resources. Numerical simulations further demonstrate the equivalence between the robustness-based criterion (GHTR_(d^′)) and the generalized high-dimensional entanglement robustness (GHER_(d^′)), reinforcing the validity of the proposed approach. The team’s work highlights a subtle but important distinction between HDQT fidelity and genuine HD entanglement, noting that high fidelity does not automatically guarantee the use of high-dimensional resources.

Teleportation Protocol for Certifying d-Dimensional Quantum States

Such criteria are useful for experimenters to verify that the setup is capable of teleporting genuine HD quantum states. Unlike fidelity, which can be sensitive to optimal local operations, the robustness criterion functions effectively even without prior knowledge of the experimental setup, a “black-box scenario”.

The objective of the convex program associated with this criterion is to minimize the total amount of noise needed to render the teleportation data simulable with lower-dimensional entanglement, providing a direct measure of its robustness. The work establishes a universal and reliable theoretical framework for validating the core quantum advantage in HDQT, ensuring reliable links in HD quantum networks.

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