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REVIEW 3 major objections 4 minor 23 references

Does Entanglement Correlation in Ground State Guarantee Quantum Energy Teleportation?

T0 review · 3 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read The paper claims that entanglement in a toric-code ground state does not guarantee quantum energy teleportation under a parity-measurement protocol.

desk verdict A new but overclaimed no-go result: the parity-measurement calculation on the toric code is likely correct, yet the written proof does not cover general LOCC and contains a flawed lemma. read the letter →

arxiv 2502.07097 v1 pith:NJUO4ZXV submitted 2025-02-10 quant-ph cond-mat.other

Taisanul Haque This is my paper · ORCID
classification quant-phcond-mat.other PACS 03.67.-a03.65.Ud
keywords quantumenergyteleportationtoriccodeentanglementtopologicalorderprojectivemeasurementLOCCextraction
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

Quantum energy teleportation (QET) is a two-step protocol meant to extract energy from a ground state: measure one subsystem, then use the measurement result to choose a local operation on a distant subsystem. The paper tests whether entanglement in the ground state is enough to make this work, using the toric code, a topological spin model whose ground state has long-range entanglement. Alice measures all but one spin with a parity projective measurement, and Bob applies a local rotation to the remaining spin. The computed energy change is $E_B - E_A = 4\sin^2\theta(n_y^2+n_z^2) \ge 0$, so Bob can never lower the energy. The paper concludes that entanglement correlation alone does not guarantee QET, at least for this measurement scheme.

What carries the argument

The engine of the argument is the stabilizer structure of the toric code, with Hamiltonian $H = -\sum_v A_v - \sum_p B_p$ on an $L\times L$ torus, whose ground state $|\xi\rangle$ obeys $A_v|\xi\rangle = B_p|\xi\rangle = |\xi\rangle$ for all vertices $v$ and plaquettes $p$. Alice's measurement is the projector $M_A(k)=\frac{1}{2}(I+k\,\sigma^x_{\pi(2)}\cdots\sigma^x_{\pi(n)})$ for $k=\pm1$, and Bob's operation is restricted to $U_B(k)=\cos\theta + i k\sin\theta\,\hat{n}\cdot\vec{\sigma}_B$. The calculation uses commutators $[H,\hat{n}\cdot\vec{\sigma}_B]$ and stabilizer identities to collapse the energy difference to the final nonnegative expression $4\sin^2\theta(n_y^2+n_z^2)$.

What would settle it

Compute the energy difference for the same toric-code measurement but with Bob allowed to choose independent unitaries for $k=+1$ and $k=-1$, or a non-unitary local operation; finding any choice with $E_B-E_A<0$ would falsify the blanket no-go. A smaller check is to evaluate $\langle \xi|M_A(k)\sigma^l_{r_1} A M_A(k)|\xi\rangle$ directly on a small torus and verify whether it vanishes without relying on the sign step in Lemma V.3.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central discovery is a no-go result: in the toric-code ground state, a parity projective measurement on all but one spin breaks the correlation between the bipartition, and yet no local unitary of the form used by Bob can extract energy. The energy difference evaluates to $E_B - E_A = 4\sin^2\theta(n_y^2+n_z^2) \ge 0$, so Bob's operation can only leave the energy unchanged or increase it. Because the toric-code ground state is entangled, the example is presented as evidence that the general belief — entanglement correlation between two sites guarantees successful QET — is not true in this topological model. The paper states the conclusion plainly: "Therefore it suggests, no energy teleportation!"

Load-bearing premise

The no-go result assumes Bob's local operation must be the same-axis, same-angle rotation $U_B(k)=\cos\theta + i k\sin\theta\, \hat{n}\cdot\vec{\sigma}_B$ for both measurement outcomes, and it relies on the vanishing of a stabilizer expectation value that a direct check of Lemma V.3 would need to confirm.

Editorial extensions

If this is right

  • In the protocol studied, Bob's best allowed rotation gives $E_B - E_A = 0$; no rotation makes the energy negative.
  • The long-range entanglement of the toric-code ground state is not sufficient for QET under this parity-measurement scheme, contradicting the belief stated in the introduction.
  • The measurement creates exactly two magnetic anyons next to Bob's spin, and within the allowed unitary family these excitations provide no energy extraction.
  • If the calculation is correct, QET feasibility has to be assessed protocol by protocol; ground-state entanglement alone is not a sufficient criterion.

Reading between the lines

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

  • General LOCC lets Bob choose different unitaries for the two outcomes, while the paper forces one axis and angle for both; allowing $U_B(+1)\neq U_B(-1)$ could reopen the possibility of $E_B-E_A<0$ in the same setup.
  • The result points to a distinction between total entanglement and usable correlation: a single spin in the toric code is maximally entangled with the rest, yet the parity measurement may destroy the alignment that a QET operation needs.
  • The same calculation could be run in other topologically ordered models, such as Levin-Wen string-net or X-cube stabilizer states; a similar nonnegative energy difference there would show the obstruction is topological, not specific to the toric code.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper studies quantum energy teleportation (QET) in the toric code. Alice performs a projective measurement on all but one spin, and Bob subsequently applies a local unitary conditioned on the measurement outcome. The author derives the energy difference EB - EA = 4 sin^2(theta)(n_y^2 + n_z^2) >= 0 for Bob's unitaries of the form U_B(k) = cos(theta) + i k sin(theta) n·sigma, and concludes that no LOCC can achieve QET, so ground-state entanglement does not guarantee energy teleportation. The calculation is analytic and self-contained, but it applies only to a restricted family of Bob's unitaries, and the proof of a key lemma contains a sign error.

Significance. If established for general LOCC, this would be a noteworthy counterexample to the common belief that entanglement in the ground state suffices for QET, and it would connect QET with topological order. The paper is commendably direct: it uses no fitting or numerical extrapolation, and it gives a concrete formula for a specific measurement-and-feedback protocol in an exactly solvable model. However, the actual result is much narrower than the stated conclusion. The no-go claim covers only inverse-related rotations with a single axis and angle, not general outcome-dependent LOCC, and the proof has a gap in Lemma V.3. As it stands, the contribution is a partial calculation rather than a demonstration that entanglement does not guarantee QET.

major comments (3)
  1. [Section V.B, Eq. (6)] The no-go conclusion is not supported because Bob's local unitary is restricted to the family U_B(k) = cos(theta) + i k sin(theta) n·sigma with the same axis n and the same angle theta for both measurement outcomes. General QET LOCC allows an independent unitary U_B(k) for each outcome k, and more generally any CPTP map on Bob's spin. The derivation of Eqs. (10)-(11) relies on the specific k-dependence of this family: the first sum in Eq. (10) contains the factor i k and does not obviously vanish when U_+ and U_- are independent, and the second sum does not factor in the same way. Since no argument is given for general U_B(k), the paper proves at most a no-go for this one-parameter family, not the statement in the abstract and conclusion that 'there is no LOCC for successful QET.'
  2. [Section V.B, Lemma V.3] The proof of Lemma V.3 contains a sign error. From [A, M_A(k)] = 0 and {sigma^l_{r1}, A} = 0, one obtains A M_A(k) sigma^l_{r1} = - M_A(k) sigma^l_{r1} A. Therefore the displayed equality -<xi|A^dagger M_A(k) sigma^l_{r1}|xi> = -<xi|M_A(k) sigma^l_{r1} A|xi> is wrong; the right-hand side should be +<xi|M_A(k) sigma^l_{r1} A|xi>. Consequently the chain shows only that the quantity equals itself and does not prove that it vanishes. Since Lemma V.3 is used to drop the (z,x) and (x,y) terms in the reduction to Eq. (11), the derivation of the final inequality is incomplete.
  3. [Section V.B, Eq. (10)] The claim that the first term in Eq. (10) vanishes is asserted rather than demonstrated. This term is sum_k i k sin(2theta)/2 <xi|M_A(k)[H, n·sigma]M_A(k)|xi>, and after substituting Eq. (9) it involves expectations of products such as M_A(k) B sigma^x_{r1} M_A(k) and M_A(k) A sigma^y_{r1} M_A(k). Lemma V.1 concerns M_A(k) B M_A(k) and does not directly control these expressions with an additional Pauli operator, while Lemma V.2 concerns single-Pauli expectation values in the ground state, not the post-measurement states appearing here. Without an explicit proof, the reduction from Eq. (10) to Eq. (11) is a gap; if the first term were nonzero, it could make EB - EA negative and energy teleportation possible even within the restricted family.
minor comments (4)
  1. [Abstract and Section I] There are several typos and stylistic issues, e.g., 'an unique' in the abstract, 'Moeover' in the introduction, and 'a measurements' in Section II.A; these should be corrected.
  2. [Section V.A] The discussion after the definition of M_A(k) is confusing: the sentence 'If we choose a permutation pi such that there are m < n numbers of identity maps in M_A(k)' needs clarification, since 'identity maps' presumably refers to fixed points of the permutation, and the counting of measured spins is not clearly explained.
  3. [Figure 4 and surrounding text] The notation r1, d1, u2, l1, B1, B2 is used in the proof but the red dots in Figure 4 are not labeled in the text, making it hard to follow which spins are involved in the commutator calculation.
  4. [Section V.B, Eq. (10)] The switch between 'theta' and the symbol 'theta' in the surrounding text is inconsistent; the same symbol should be used throughout.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the toric-code energy-difference calculation is a self-contained analytic derivation from the stated Hamiltonian and measurement protocol.

full rationale

The paper's central claim is that for the toric-code ground state with Alice's parity measurement, Bob's restricted local unitary U_B(k)=cos(theta)+i k sin(theta) n·sigma gives EB-EA >= 0, so QET does not occur for that protocol. The derivation is a direct algebraic evaluation: equations (5)-(11) expand the measurement-averaged energy difference using the stabilizer identities Av|xi>=|xi>, Bp|xi>=|xi>, the PVM structure of MA(k), and the Pauli anticommutation relations used in Lemmas V.1-V.3. No parameter is fitted to data, no quantity is defined in terms of the target conclusion, and no external or prior result is invoked to force the result. The only self-citation, [12], supports a background remark that entanglement is not a necessary QET resource; it is not used in the toric-code calculation and therefore is not load-bearing. The no-go conclusion is broader than what the restricted unitary family proves (general LOCC with outcome-dependent unitaries is not analyzed), but that is a completeness/correctness concern, not a circularity: the calculation's assumptions are stated, and the energy difference is obtained from those assumptions rather than assumed. Accordingly, no circular step is identified.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard stabilizer properties of the toric code and the QET energy-balance criterion. No free parameters are fitted. The main additional assumptions are the restricted form of Bob's unitary and the interpretation of the energy extraction condition; neither is supported by external evidence beyond the paper's own definitions.

assumptions (5)
  • domain assumption The toric code ground state |xi> satisfies A_v|xi> = |xi> and B_p|xi> = |xi> for all v and p, and is one of the four degenerate ground states on a torus.
    Used in Eq. (4) and throughout Section V to evaluate expectation values of stabilizer operators.
  • domain assumption The energy extraction condition for QET is E_B - E_A < 0, where E_A and E_B are global energy expectations after Alice's measurement and after Bob's operation.
    Defined in Eqs. (1) and (2); this is the standard QET criterion.
  • ad hoc to paper Bob's local unitary is of the restricted form U_B(k) = cos(theta) + i k sin(theta) n dot sigma with the same theta and n for both outcomes.
    Section V.B states this as a 'general local unitary', but it is a restricted family; independent unitaries per outcome are not treated.
  • standard math Lemma V.2: the expectation value of any single Pauli operator in the ground state is zero.
    Proved in Lemma V.2 using stabilizer anti-commutation; used in the simplification of the second term.
  • standard math Lemma V.1: M_A(k) B M_A(k) is either zero or M_A(k) B for plaquette operators.
    Proved in Lemma V.1 using the commutation of the PVM with the plaquette operators.

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Cite this review

Pith. "Pith review of Does Entanglement Correlation in Ground State Guarantee Quantum Energy Teleportation?." pith.science (2026). https://pith.science/paper/NJUO4ZXV

@misc{pith2026250207097,
  author       = {Pith},
  title        = {Pith review of: Does Entanglement Correlation in Ground State Guarantee Quantum Energy Teleportation?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NJUO4ZXV}},
  note         = {Machine review of arXiv:2502.07097}
}
read the original abstract

Although extraction of energy from the ground state is forbidden, one can utilize Quantum Energy Teleportation (QET) protocol for energy extraction -- a two-step protocol involving quantum measurements followed by LOCC. This is an unique method to ``extract energy from ground states'' of quantum systems. QET requires some correlation in the ground state, and entanglement correlation plays a crucial roles as a resource. The general belief is that if the ground state is quantum-correlated via entanglement for two different sites in a quantum system, and if we perform measurements on one of the sites, we can find an LOCC for the other site to successfully accomplish QET. In this paper, we show that this belief may not be true in the case of the Toric Code. We demonstrate this by performing a PVM measurements on spins in the Toric Code. Based on the measurement outcomes, we found that there is no LOCC for successful QET.

Figures

Figures reproduced from arXiv: 2502.07097 by the authors.

Figure 1
Figure 1. FIG. 1. The [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Two different kind of Wilson loops are illustrated. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. A bipartite system with 2 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The red dots are the potential spins in our measure [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Works this paper leans on

23 extracted references · 15 canonical work pages

  1. [1]

    Therefore it suggests, no energy teleportation! 6 VI. CONCLUSION In this paper we demonstrated that even if a quan- tum system has entangled ground state, QET may not be feasible i.e., for a given measurements scheme, which breakdowns all the quantum correlation including entan- glement between bipartite system, there may not exist any LOCC, which lowers ...

    work page

  2. [2]

    Hotta, A protocol for quantum energy distribution, Physics Letters A 372, 5671–5676 (2008)

    M. Hotta, A protocol for quantum energy distribution, Physics Letters A 372, 5671–5676 (2008)

    work page 2008

  3. [3]

    Hotta, Quantum energy teleportation in spin chain systems, Journal of the Physical Society of Japan 78, 034001 (2009)

    M. Hotta, Quantum energy teleportation in spin chain systems, Journal of the Physical Society of Japan 78, 034001 (2009)

    work page 2009

  4. [4]

    Hotta, Energy entanglement relation for quantum energy teleportation, Physics Letters A 374, 3416–3421 (2010)

    M. Hotta, Energy entanglement relation for quantum energy teleportation, Physics Letters A 374, 3416–3421 (2010)

    work page 2010

  5. [5]

    Hotta, Quantum energy teleportation: An introduc- tory review (2011), arXiv:1101.3954 [quant-ph]

    M. Hotta, Quantum energy teleportation: An introduc- tory review (2011), arXiv:1101.3954 [quant-ph]

    arXiv 2011

  6. [6]

    Nambu and M

    Y. Nambu and M. Hotta, Quantum energy teleportation with a linear harmonic chain, Phys. Rev. A 82, 042329 (2010)

    work page 2010

  7. [7]

    Hotta, Quantum energy teleportation with trapped ions, Phys

    M. Hotta, Quantum energy teleportation with trapped ions, Phys. Rev. A 80, 042323 (2009)

    work page 2009

  8. [8]

    G. Yusa, W. Izumida, and M. Hotta, Quantum energy teleportation in a quantum hall system, Phys. Rev. A 84, 032336 (2011)

    work page 2011

Show all 23 references
  1. [9]

    Hotta, Controlled hawking process by quantum en- ergy teleportation, Phys

    M. Hotta, Controlled hawking process by quantum en- ergy teleportation, Phys. Rev. D 81, 044025 (2010)

    2010

  2. [10]

    N. A. Rodr ´ ıguez-Briones, H. Katiyar, E. Mart ´ ın- Mart ´ ınez, and R. Laflamme, Experimental Activation of Strong Local Passive States with Quantum Information, Phys. Rev. Lett. 130, 110801 (2023), arXiv:2203.16269 [quant-ph]

    2023 arXiv

  3. [11]

    Ikeda, Demonstration of quantum energy teleporta- tion on superconducting quantum hardware, Phys

    K. Ikeda, Demonstration of quantum energy teleporta- tion on superconducting quantum hardware, Phys. Rev. Appl. 20, 024051 (2023)

    2023

  4. [12]

    M. R. Frey, K. Gerlach, and M. Hotta, Quantum en- ergy teleportation between spin particles in a gibbs state, Journal of Physics A: Mathematical and Theoretical 46, 455304 (2013)

    2013

  5. [13]

    Haque, Aspects of quantum energy teleportation (2024), arXiv:2411.08927 [quant-ph]

    T. Haque, Aspects of quantum energy teleportation (2024), arXiv:2411.08927 [quant-ph]

    2024 arXiv

  6. [14]

    Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303, 2–30 (2003)

    A. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303, 2–30 (2003)

    2003

  7. [15]

    Kitaev, Anyons in an exactly solved model and be- yond, Annals of Physics 321, 2–111 (2006)

    A. Kitaev, Anyons in an exactly solved model and be- yond, Annals of Physics 321, 2–111 (2006)

    2006

  8. [16]

    Kitaev and J

    A. Kitaev and J. Preskill, Topological entanglement entropy, Physical Review Letters 96, 10.1103/phys- revlett.96.110404 (2006)

    2006 doi

  9. [17]

    X. G. Wen, Topological Order in Rigid States, Int. J. Mod. Phys. B 4, 239 (1990)

    1990

  10. [18]

    Levin and X.-G

    M. Levin and X.-G. Wen, Detecting topological order in a ground state wave function, Phys. Rev. Lett. 96, 110405 (2006)

    2006

  11. [19]

    Nayak, S

    C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-abelian anyons and topological quan- tum computation, Rev. Mod. Phys. 80, 1083 (2008)

    2008

  12. [20]

    Dennis, A

    E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topological quantum memory, Journal of Mathematical Physics 43, 4452–4505 (2002)

    2002

  13. [21]

    B. M. Terhal, Quantum error correction for quantum memories, Reviews of Modern Physics 87, 307–346 (2015)

    2015

  14. [22]

    Wilczek, Magnetic flux, angular momentum, and statistics, Phys

    F. Wilczek, Magnetic flux, angular momentum, and statistics, Phys. Rev. Lett. 48, 1144 (1982)

    1982

  15. [23]

    Hamma, R

    A. Hamma, R. Ionicioiu, and P. Zanardi, Bipartite entan- glement and entropic boundary law in lattice spin sys- tems, Phys. Rev. A 71, 022315 (2005)

    2005

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