The operational advantages provided by non-classical teleportation

Patryk Lipka-Bartosik; Paul Skrzypczyk

REVIEW 1 major objections 4 minor 1 cited by

The operational advantages provided by non-classical teleportation

T0 review · 1 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that a single quantity, the robustness of teleportation, exactly measures the maximum advantage a quantum teleportation scheme offers over classical schemes in two operational tasks: teleporting quantum correlations and…

desk verdict Solid core, shaky completeness appendix: the operational identities for robustness of teleportation are worth a referee's time, but the complete-monotones proof has a real quantifier gap and the free-set definition needs clarifying. read the letter →

arxiv 1908.05107 v2 pith:NMHMPVTV submitted 2019-08-14 quant-ph

Patryk Lipka-Bartosik , Paul Skrzypczyk This is my paper · ORCID

classification quant-ph

keywords robustnessofteleportationquantumcorrelationssubchanneldiscriminationmemoryentanglementresourcetheorysemidefiniteprogramming

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper aims to give operational meaning to the previously formal observation that every entangled state yields non-classical teleportation. It shows that the robustness of teleportation, T(Λ), exactly equals the maximum advantage a quantum teleportation instrument offers over every classical instrument in two tasks: teleporting quantum correlations and discriminating quantum subchannels with side information. In both tasks the advantage ratio equals 1+T(Λ). Because T(Λ)>0 whenever the shared state is entangled and a Bell measurement is used, every entangled state, including bound-entangled states that fail the standard average-fidelity test, outperforms all separable states in both tasks. The paper also shows that the average fidelity of teleportation is a special case of the first task, which explains why that benchmark cannot see the usefulness of bound entanglement.

What carries the argument

The central object is the robustness of teleportation T(Λ), the minimal weight of noise that must be mixed into the teleportation data so that it becomes reproducible by a classical teleportation instrument built from a separable shared state or a separable measurement. The argument is carried by the Choi–Jamiołkowski representation of the teleportation instrument: in this representation the free instruments are exactly the separable operators satisfying a no-signaling sum condition, which turns the definition of T(Λ) into a semidefinite program. Its dual solution provides entanglement witnesses, and these witnesses are used to build the games that saturate the 1+T(Λ) bound in both tasks. The same representation shows that the scores of the two games are complete monotones for the classical and quantum simulation orders.

What would settle it

An explicit teleportation instrument Λ with computed robustness T(Λ) for which any game of teleporting quantum correlations has ratio q(G,Λ)/q_c(G) strictly greater than 1+T(Λ), or any subchannel-discrimination instance with p_succ/p_c_succ strictly greater than 1+T(Λ), would refute the central claim.

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Extended reading notes

Core claim

The central claim is an exact identity in two parts. For any teleportation instrument Λ, the optimal advantage in a game of teleporting quantum correlations over the best classical instrument is max_G q(G,Λ)/q_c(G) = 1+T(Λ); likewise, the optimal advantage in subchannel discrimination with side information over all classical strategies is max_E p_succ(E,A)/p_c_succ(E) = 1+T(Λ). The proof constructs, from the primal and dual solutions of the semidefinite program defining T(Λ), explicit games that saturate the bound, and shows that no game can exceed it. A direct corollary is that every entangled state, when used with a Bell measurement, is a strictly better teleportation resource and a strictly better quantum memory than any separable state; in particular, bound-entangled states are useful in both tasks even though they do not beat the classical threshold for average teleportation fidelity.

Load-bearing premise

The derivation relies on identifying the free teleportation instruments with those whose Choi operators are separable and satisfy the no-signaling sum condition; if a different free set were intended, the claimed advantages would need to be recomputed, and the characterization is proved in detail only for separable shared states, with the separable-measurement case sketched as essentially the same.

Editorial extensions

If this is right

Every entangled state, including bound-entangled states, becomes a strictly better resource than all separable states for teleporting quantum correlations, not just for teleporting unknown quantum states.
Every entangled state can serve as a useful quantum memory in subchannel discrimination, and optimizing the measurement as well yields the maximal advantage 1+R_E(ρ) over all classical strategies.
The average fidelity of teleportation is reinterpreted as the score of a particular game with classically correlated inputs, clarifying why it is an incomplete benchmark for entanglement usefulness.
The two task scores form complete sets of monotones: Λ can quantum-simulate Λ' if and only if q(G,Λ) ≥ q(G,Λ') for all games, and can classically simulate Λ' if and only if p_succ(E,Λ) ≥ p_succ(E,Λ') for all instruments E.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Since T(Λ) can be estimated from tomographically complete teleportation data, the equality suggests a direct experimental prediction: the same number that quantifies non-classicality of the data should also appear as the measured advantage in either game, without additional fitting parameters.
The dual witnesses that certify T(Λ) can be read as explicit optimal strategies for the correlation-teleportation game, which may guide the design of protocols that actually achieve the predicted advantage.
The same robustness-and-discrimination pattern likely extends to other resource theories whose free operations satisfy a no-signaling structure, making 'maximal advantage = 1 + robustness' a candidate general principle.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague,

Here is my take on Lipka-Bartosik & Skrzypczyk, arXiv:1908.05107. The paper has a solid core and one shaky appendix. The core—the two operational identities showing that the robustness of teleportation equals the maximal advantage in teleporting quantum correlations and in subchannel discrimination with side information—is a genuine contribution. The SDP duality proofs in Appendices D and E look careful and correct, and the reduction of ordinary average fidelity to a special correlation game is a neat conceptual step. The consequence that every entangled state is useful in two concrete tasks, including as a quantum memory for subchannel discrimination, is substantial and answers an open question from the authors' earlier work.

The central measure T(Λ) is imported from their own published paper, but that is not circular: they use the published definition and prove new equalities around it. Self-citation here is not a weakness.

Now the soft spots. Appendix F, which claims complete sets of monotones for the two simulation orders, has a genuine quantifier error. Equation (F5) does not follow from (F4): the max over the simulating instrument is inside, so you cannot fix a unitary correction and treat the resulting Δa as a single operator. The same issue appears in the p_succ argument around (F11). As written, the contradiction proof does not go through. This does not affect the main identities (13) and (17), but it does invalidate the advertised completeness claims (20) and (21). The authors may be able to repair this with a standard separation argument, but as it stands the appendix is not correct.

The second issue is less fatal but needs addressing. The main text defines the free set F through separable shared states, while Appendix B.b and the subchannel-discrimination task use "separable state or separable measurement." The converse direction of the key characterization (B21) is only demonstrated via a purification of the reduced state, which gives a separable measurement, not a separable state. If the intended free set is the union, the construction may be sufficient, but the text should say so explicitly and verify the POVM conditions. If F is really only separable states, then the SDP in (B22) is not justified. This is a clarity gap, not necessarily a fatal one, but a referee should not let it pass.

Overall: useful paper, honestly argued in the main line, with one genuinely flawed appendix and one definitional inconsistency. The central operational result deserves engagement. I would send it to peer review with instructions to fix or soften Appendix F and to clarify the free set. If those are addressed, the paper is publishable.

Recommendation: serious referee, conditional accept.

Referee Report

1 major / 4 minor

Summary. The paper develops a resource-theoretic treatment of quantum teleportation in which a teleportation instrument Λ is free (classical) if it can be realized by a separable shared state or a separable measurement. The central quantity is the robustness of teleportation T(Λ), defined via a convex optimization. The main results are: (i) for every entangled state, a Bell measurement yields T(Λ)>0, and T(Λ) exactly equals the maximal advantage, over all classical instruments, in a game of teleporting quantum correlations (Eq. 13); (ii) T(Λ) exactly equals the maximal advantage in subchannel discrimination with side information (Eq. 17), giving operational meaning to the robustness of entanglement via Eq. (19); and (iii) the two task scores provide complete sets of monotones for quantum and classical simulation orders (Eqs. (20) and (21)). These are supported by SDP-based proofs in Appendices B–E and a simulation-completeness proof in Appendix F.

Significance. If the results are correct, they would resolve an open question from [21] by showing that every entangled state is useful for a suitably generalized teleportation task, and they would place the robustness of teleportation in the same family as robustness measures for entanglement, steering, and measurement incompatibility by giving it a clean operational interpretation in a discrimination task. The paper also makes a strong structural claim by showing that the two game scores are complete monotones for natural partial orders on teleportation instruments. The SDP duality arguments for Eqs. (13) and (17) are detailed and, conditional on the free-set characterization, appear sound. However, two load-bearing proof gaps, in the free-set characterization (Appendix B.b) and in the completeness-of-monotones proof (Appendix F), currently prevent the stated claims from being fully established.

major comments (1)

[Section III.B.3 and Appendix F (both claims)] The two completeness claims in Eqs. (20) and (21) are presented as equivalent characterizations of the simulation orders. Because the proof of the converse direction in Appendix F fails for the reason described above, the 'only if' direction of these equivalences is not established. The forward direction (simulation implies ordering of scores) is a simple subset argument and is fine, but the reverse direction requires a genuinely different argument, likely using convex separation or the SDP dual, rather than the pointwise contradiction attempted here. This is not a minor presentational issue; it is an essential part of the resource-theoretic contribution.

minor comments (4)

[Appendix C.b, Eq. (C1)] The proof of convexity of T(Λ) is incorrect as written: it claims T(Λ') ≤ tr Σ_a Λ'_a[ω_x]' and equates this trace with p T(Λ1) + (1−p) T(Λ2), but the objective value in the defining optimization (6) is the scalar r, not a trace of the noise instrument. The convexity property is standard and can be proven from the SDP formulation, but the displayed argument should be corrected.
[Main text, Eq. (4) and Appendix B.b] The definition of the free set F in the main text only mentions separable shared states, while Appendix B.b considers a free set generated by either a separable shared state or a separable measurement. This discrepancy should be resolved explicitly; the choice of free set changes the benchmarks q_c and p_c_succ and hence the numerical values of the advantages in Eqs. (13) and (17).
[Appendix B, Eqs. (B18)–(B20)] The system labels in the construction are inconsistent: the operators Y_a are initially defined on V B, but in Eq. (B18) they are written as Y^{V A}_a and multiplied by operators acting on a purification system A. This makes it difficult to verify the claimed identities and POVM conditions, and contributed to the gap noted in the second major comment.
[Throughout] There are several typographical errors, including 'classicaly' in Appendix F, 'Prcoessing' in reference [19], and 'Journa' in reference [50]. These do not affect the technical content but should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the operational advantages are proven by SDP duality from an independently defined robustness measure, not built into the definitions.

full rationale

The derivation of the two main equalities, Eqs. (13) and (17), is not circular. T(Λ) is imported from prior work [21] as a pre-existing robustness measure defined by the convex decomposition in Eq. (6) relative to the free set F of classical teleportation instruments and the set R of arbitrary instruments. The game scores q(G,Λ) and p_succ(E,A) are defined independently in Eqs. (12) and (15), and the classical benchmarks q_c(G) and p_c_succ(E) are natural operational benchmarks, not restatements of T. The proofs in Appendices D and E establish 1+T(Λ) by first proving an upper bound via the primal inequality Ja ≤ (1+T(Λ))Fa of Eq. (B27) and then constructing saturating games from the dual SDP (B26). The equalities are therefore genuine theorems obtained by convex duality rather than identities inserted by definition. The use of Eq. (18) from [22] to obtain Eq. (19) is a self-citation (Skrzypczyk is a co-author), but that result is published, peer-reviewed, and used as an external input; the central claims (13) and (17) do not depend on it, so the self-citation is not load-bearing. The flagged weakness in the converse direction of the free-set characterization (B21), where the separable-measurement case is only asserted to be 'essentially the same' as the separable-state case, is a proof gap or correctness risk rather than a circularity: the paper does not assume the conclusion it is proving. No fitted parameters are renamed as predictions, and no known empirical result is merely relabelled under new coordinates.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters are fitted; all quantitative statements are derived from SDP duality. The inputs are standard quantum information formalism, the definition of the free set F, and the definitions of the two simulation preorders. These are stated assumptions, not introduced ad hoc to force the target results.

assumptions (4)

standard math Finite-dimensional Hilbert spaces; all states, channels, and measurements are represented by CPTP maps, POVMs, and density operators.
Used throughout; stated in Appendix A.
domain assumption The teleportation instrument is defined by Eq. (2) and satisfies the no-signaling condition (3); full information is obtained by probing with a tomographically complete set of input states (complete teleportation experiment).
This assumption makes RoT independent of the input set, as proven in Appendix B. Experiments with finite sets only approximate this.
domain assumption Classical teleportation instruments are exactly those arising from a separable shared state or a separable measurement, with Choi operators characterized by (B21).
This defines the free set F that benchmarks the advantages. The proof of (B21) for the separable measurement case is only sketched.
domain assumption The two simulation preorders, quantum (10) and classical (11), are defined with arbitrary pre- and post-processing channels and classical post-processing.
These are the free operations of the resource theory; the completeness of monotones is defined relative to them.

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Pith. "Pith review of The operational advantages provided by non-classical teleportation." pith.science (2026). https://pith.science/paper/NMHMPVTV

@misc{pith2026190805107,
  author       = {Pith},
  title        = {Pith review of: The operational advantages provided by non-classical teleportation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NMHMPVTV}},
  note         = {Machine review of arXiv:1908.05107}
}

read the original abstract

The standard benchmark for teleportation is the average fidelity of teleportation and according to this benchmark not all states are useful for teleportation. It was recently shown however that all entangled states lead to non-classical teleportation, with there being no classical scheme able to reproduce the states teleported to Bob. Here we study the operational significance of this result. On the one hand we demonstrate that every entangled state is useful for teleportation if a generalization of the average fidelity of teleportation is considered which concerns teleporting quantum correlations. On the other hand, we show the strength of a particular entangled state and entangled measurement for teleportation -- as quantified by the robustness of teleportation -- precisely characterizes their ability to offer an advantage in the task of subchannel discrimination with side information. This connection allows us to prove that every entangled state outperforms all separable states when acting as a quantum memory in this discrimination task. Finally, within the context of a resource theory of teleportation, we show that the two operational tasks considered provide complete sets of monotones for two partial orders based upon the notion of teleportation simulation, one classical, and one quantum.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Weight of informativeness, state exclusion games and excludible information
quant-ph 2019-08 accept novelty 6.0 of 10

The weight of informativeness of a measurement exactly quantifies the optimal advantage in quantum state exclusion games and equals the single-shot excludible information of the associated quantum-to-classical channel.

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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Hasegawa, R

Y . Hasegawa, R. Ikuta, N. Matsuda, K. Tamaki, H.-K. Lo, T. Ya- mamoto, K. Azuma, and N. Imoto, Nat. Commun. 10, 378 (2019)

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More explicitly, we consider the following scenario:

Teleportation of quantum correlations Consider a game played between a Veriﬁer and Bob who tries to convince the Veriﬁer about his ability to transfer corre- lations between two spatially separated labs. More explicitly, we consider the following scenario:

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The Veriﬁer prepares an arbitrary bipartite state σV’V and shares one part of this state with Bob

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Bob inputs the state he received into a teleportation in- strument Λ′ = {Λ′ b V→B}b which he can locally sim- ulate using Λ, obtaining measurement outcome b and stateσV′B b = (IV′ ⊗ Λ′ b V→B)[σV′V]

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Conditioned on the value ofb Bob applies locally a uni- tary correctionU B b to his share of the state and returns the output state and outcome of the measurement to the Veriﬁer

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If the teleported state is the same as the target state, then Bob receives a scoref(b)≥ 0

The Veriﬁer assesses the quality of the teleportation in- strument by checking the overlap between the joint state after correction (IV′ ⊗U B b )[σV′B b ] and a pre-deﬁned set of target states{ξV′B b }. If the teleported state is the same as the target state, then Bob receives a scoref(b)≥ 0. The game is fully speciﬁed by a tupleG ={σ, ξb,f (b)}. The aver...

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The task is speciﬁed by a collection of subchannels, E ={Ex}, which form an instrument

Subchannel discrimination with quantum side information and ﬁxed measurement Let us now consider the task of subchannel discrimination, where the player is allowed to use a quantum memory to as- sist them, and only has the ability to perform a ﬁxed entan- gled measurement. The task is speciﬁed by a collection of subchannels, E ={Ex}, which form an instrum...

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Alice sends one half of the state ρV Ato the Veriﬁer

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