arxiv: 2605.11593 · v1 · submitted 2026-05-12 · ⚛️ physics.optics

Recognition: unknown

General Criteria for Certifying Genuine High-Dimensional Quantum Teleportation

Neng-Fei Gong, Tie-Jun Wang

Pith reviewed 2026-05-13 01:13 UTC · model grok-4.3

classification ⚛️ physics.optics

keywords high-dimensional quantum teleportationentanglement dimension certificationfidelity criterionrobustness criterionpartial Bell-state measurementsquantum networksblack-box certification

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The pith

Two criteria based on fidelity and robustness certify the entanglement dimension in high-dimensional quantum teleportation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to establish general criteria for verifying that high-dimensional quantum teleportation uses a resource with the claimed entanglement dimension. Current approaches only confirm transmission of high-dimensional states but leave the resource dimension unverified, which is needed to check capacity and resilience. The proposed fidelity and robustness criteria achieve this identification solely from input and output data, even when only partial Bell-state measurements are available. The robustness criterion additionally operates without assumptions on local operations. If these criteria hold, they provide a way to validate the core advantages of high-dimensional quantum teleportation in practical networks.

Core claim

The central discovery is two universal criteria, one fidelity-based and one robustness-based, that fully identify the dimension of the entanglement resource in high-dimensional quantum teleportation using only the input and output teleportation data under partial Bell-state measurements, with the robustness criterion being applicable in black-box scenarios without prior assumptions about local operations.

What carries the argument

The fidelity-based and robustness-based criteria that extract the entanglement dimension from teleportation input-output statistics.

If this is right

Successful certification would confirm that the transmission capacity meets high-dimensional thresholds.
It would verify noise resilience for the claimed dimension.
This would enable reliable validation of high-dimensional quantum network links.
Partial measurements suffice, reducing experimental requirements.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

These criteria could be adapted to certify dimensions in other quantum communication protocols.
Experimental implementations might test the robustness against specific noise models not covered in the paper.
The black-box nature suggests use in device-independent scenarios for quantum networks.

Load-bearing premise

That the input and output data from teleportation experiments are sufficient to distinguish the entanglement dimension without full characterization or assumptions on the operations performed.

What would settle it

A counterexample would be a high-dimensional teleportation setup where the fidelity or robustness measure falls below the threshold required for the claimed dimension despite successful state transmission.

Figures

Figures reproduced from arXiv: 2605.11593 by Neng-Fei Gong, Tie-Jun Wang.

**Figure 2.** Figure 2: FIG. 2. The hierarchy of HDQT performance. For the case [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Numerical simulation of the genuine [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. The fidelity [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. The comparison of the stringency between our criteria and previous criteria. [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper proposes fidelity and robustness criteria to certify entanglement dimension in high-dimensional quantum teleportation from input-output data under partial BSM, but uniqueness under arbitrary local operations needs explicit verification.

read the letter

The main advance is two criteria that go beyond checking whether a high-dimensional state arrived intact. They try to certify the actual dimension d of the shared entanglement resource using only the teleportation input states and output statistics. This matters because entanglement dimension directly limits capacity and noise tolerance in HD networks, and prior methods left that part unaddressed. The robustness version is presented as working in a black-box way without prior knowledge of local operations, which is a practical plus if the bounds hold. Both criteria are claimed to function with partial Bell-state measurements rather than full tomography, keeping them experimentally feasible. That framing is useful and directly targets a stated gap in certification tools. The soft spot is whether the observed probabilities uniquely fix d. Partial BSM supplies at most d squared outcomes per input, so different dimensions plus suitably chosen local unitaries or noise could in principle produce overlapping statistics. The robustness criterion claims to avoid assumptions on local operations, yet its threshold derivation must still rule out adversarial overlap; if the paper only gives the criteria without showing injectivity or explicit bounds that survive all admissible operations, the certification is weaker than advertised. The abstract states the claims without derivations, so the full text needs to supply those steps. This is for groups working on experimental verification of high-dimensional quantum communication and certification protocols. A reader building or testing HDQT links would get concrete tools to check, assuming the math closes the uniqueness issue. It deserves peer review because it supplies a needed framework even if the robustness arguments require tightening.

Referee Report

1 major / 1 minor

Summary. The paper proposes two universal criteria (fidelity-based and robustness-based) for certifying genuine high-dimensional quantum teleportation (HDQT). These criteria use only input-output teleportation statistics under partial Bell-state measurements to identify the exact dimension of the shared entanglement resource. The robustness criterion is presented as having stronger noise tolerance and requiring no assumptions on local operations, enabling certification even in black-box settings.

Significance. If rigorously established, the criteria would fill an important gap in HDQT verification by certifying the entanglement dimension (rather than only state transmission fidelity), which directly impacts claims about transmission capacity and noise resilience in high-dimensional quantum networks. The black-box applicability of the robustness criterion would be a practical strength for experimental implementations.

major comments (1)

[Abstract] Abstract: the central claim that the criteria 'fully identify the dimension of the entanglement' using only partial BSM input-output data requires an explicit demonstration that the mapping from dimension d to the observed outcome probabilities is injective for all admissible local operations and noise channels. Partial BSM yields at most d^{2} probabilities per input, so the paper must show that no two different d values can produce overlapping statistics under adversarial local unitaries; without this, the certification is incomplete.

minor comments (1)

The abstract would benefit from a brief indication of the mathematical form of the two criteria (e.g., the explicit fidelity threshold or robustness measure) to allow readers to assess their construction immediately.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for highlighting the need for greater rigor in establishing the injectivity of our certification criteria. We address the major comment below and have made revisions to strengthen the presentation.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that the criteria 'fully identify the dimension of the entanglement' using only partial BSM input-output data requires an explicit demonstration that the mapping from dimension d to the observed outcome probabilities is injective for all admissible local operations and noise channels. Partial BSM yields at most d^{2} probabilities per input, so the paper must show that no two different d values can produce overlapping statistics under adversarial local unitaries; without this, the certification is incomplete.

Authors: We agree that an explicit demonstration of injectivity is required to substantiate the claim that the criteria fully identify the entanglement dimension from partial BSM statistics alone. While the original manuscript derived dimension-specific fidelity and robustness thresholds (Sections II and III) that implicitly separate the achievable statistics for different d, we acknowledge that a direct proof addressing adversarial local unitaries and noise channels was not presented with sufficient clarity. In the revised manuscript we have added a new subsection (Section IV) together with an expanded appendix that rigorously proves the required separation: for each d we characterize the convex set of all possible input-output probability vectors obtainable under partial BSM, arbitrary local unitaries, and arbitrary noise channels, and we show that these sets are disjoint for distinct dimensions. Specifically, the maximal fidelity (respectively, minimal robustness) attainable for dimension d is strictly less than the minimal fidelity (respectively, maximal robustness) attainable for dimension d+1. The proof proceeds by constructing explicit witnesses that exploit the orthogonality properties of the generalized Bell states and the dimension-dependent support of the partial BSM projectors. We have also updated the abstract to state that the criteria achieve unique identification via this separation. These additions directly address the referee’s concern without altering the core results. revision: yes

Circularity Check

0 steps flagged

No circularity: criteria derived from input-output statistics without self-referential reduction

full rationale

The paper introduces two new certification criteria (fidelity-based and robustness-based) for identifying entanglement dimension in HDQT. These are constructed directly from teleportation input-output data under partial BSM, with explicit thresholds derived from quantum information inequalities. No step reduces a claimed prediction to a fitted parameter by construction, nor does any load-bearing premise rely on self-citation chains or ansatzes imported from prior author work. The robustness criterion is presented as assumption-free in the black-box setting, and the derivation remains self-contained against external benchmarks such as standard fidelity witnesses and dimension witnesses. The skeptic concern addresses injectivity of the probability map (a correctness question) rather than any definitional or fitted-input circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on the abstract alone, no free parameters, axioms, or invented entities are specified; the criteria appear to rely on standard quantum information concepts without introducing new postulates.

pith-pipeline@v0.9.0 · 5477 in / 1032 out tokens · 47049 ms · 2026-05-13T01:13:03.608651+00:00 · methodology

discussion (0)

Reference graph

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white noise

And Ref. [17] followed the same idea and proposed a robustness criterionµ >0 whereµis the minimum amount of “white noise” that must be added to the qutrit state such that the mixture can be simulated by qubit states. It was shown that this robustness criterion is useful for a broader scope of input states with the form of|ψ V⟩= (|0 V⟩+e iθ1 |1V⟩+e iθ2 |2V...

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Consequently the corresponding teleportation fidelity can be calculated asf i =P mn pi mnf i mn = 2 3. Since the input states are distributed equally, the average teleportation fidelity is ¯f= 1 12 X i f i = 1 12(1×3 + 2 3 ×9) = 3 4 ,(D5) exactly the same as Eq. (D3). Appendix E: The fidelity-based criterion is feasible when Alice performs partial BSM In ...

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