{"id":"6209ef4c-4c45-44fe-8684-b372125fc725","arxiv_id":"2505.01863","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"A proposed extension of quantum energy teleportation to multiple qubits using W states, with reported results that are internally inconsistent and do not establish energy extraction.","lead":"This paper presents three-, four-, and five-qubit circuits it says teleport energy using W-state entanglement, tested on simulators and IBM hardware. The paper's reported energy numbers contradict its own equations, so the central multi-party energy teleportation claim is not supported.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The tabulated 'Hamiltonian' values cannot be expectation values of the operators defined in Eqs. (5) and (10), so the central energy-redistribution claim is unsupported.","rationale":"The reader's weakest assumption identifies exactly the load-bearing premise: the table entries labeled H_n and H_subm must be expectation values of the Hamiltonians defined in the text. The tables contradict those definitions in multiple, checkable ways. This is not a disagreement with an external consensus; it is an internal inconsistency. The strongest claim, that this is the first multi-qubit QET demonstration, cannot survive if the measured quantities are not energies in the QET sense. I also note the deeper mechanism: the only receiver operation is I or Z, and Z commutes with H_n = |1><1|, so the protocol as specified cannot change the local energy expectation at a receiver. The interaction Hamiltonian V, which is essential for the negative-energy pockets in standard QET, is never defined. The paper provides no code or raw data, and the symmetry checks are trivial consequences of the W state's permutation symmetry, so they do not independently support the energy claim. Taken together, the central claim fails on internal consistency grounds, matching the reader's REJECT verdict. No verdict adjustment is needed.","tokens_in":7840,"tokens_out":5201,"duration_ms":55040,"concrete_test":"Reproduce the three-qubit circuit of Fig. 2 for h=2, k=1 on the qasm simulator: prepare the state (|000> + 2|W3>)/sqrt(5), apply Alice's projective measurement, apply the conditional unitaries U_mu = I for mu=+1 and U_mu = Z for mu=-1 to q1 and q2, and directly compute <H1> = Pr(q1=1), <H2> = Pr(q2=1), and <Hsub1> = <H1> + <H2>. If <H1> > 1, if Hsub1 differs from H1 + H2, or if these values differ from Table 1, then the reported 'Hamiltonian' values are not QET energies, settling the concern. Independently re-evaluate E0 via Eq. (8) and compare it with the tabulated 1.7888.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim, that a single sender's injected energy E0 is deterministically distributed to and harvested by multiple receivers, rests entirely on the numbers in Tables 1–3 being the expectation values of the Hamiltonians defined in Eqs. (5) and (10). Those numbers cannot have that meaning. With H_n = |1><1|_n = (I - Z_n)/2, every eigenvalue is 0 or 1, so any valid expectation value must lie in [0,1]; Table 1 lists H1 = 1.0531 for the qasm simulator at h=2, k=1, which exceeds the spectral bound. Equation (5) requires H_sub1 = H1 + H2, but the same table gives Hsub1 = 0.7314 while H1 + H2 = 1.3927. Moreover, Eq. (8) gives E0 = h^2/(h^2 + k^2) = 0.8 for (h,k) = (2,1), not the tabulated 1.7888. The protocol's only operation on a receiver is a conditional I/Z feedforward; this cannot change the expectation value of a local H_n whose spectrum is nonnegative, so no energy is extracted under the paper's own definitions. The interaction Hamiltonian V in Eq. (3) is never specified, leaving the negative-energy pockets essential to QET undefined. Because the quantitative core is internally inconsistent and no genuine QET energy observable is defined, the abstract's claim of an experimental multi-qubit QET demonstration is not supported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper claims to realize the first multi-qubit quantum energy teleportation (QET) protocol using W-state entanglement. It presents three-, four-, and five-qubit circuits executed on a noiseless simulator and on the IBMQ Lagos hardware. The central claim is that a single sender injects an energy E0, which is then deterministically and decrementally harvested by several remote receivers, with energy conservation and causality respected. The manuscript reports energy tables for each system size, two symmetry tests, and a graphical comparison of simulator versus hardware results. The authors argue that their reduced-gate W-state preparation gives logarithmic circuit depth and that the protocol is robust enough for NISQ-era hardware.","tokens_in":8109,"tokens_out":4084,"duration_ms":42271,"significance":"If the central claim were correct, this would be the first experimental multi-qubit QET demonstration and would be a useful step toward energy-aware quantum networks. The paper has constructive elements: it addresses a meaningful multipartite generalization, uses W-state entanglement for robustness against single-qubit measurement, provides explicit circuits, and includes both simulator and real-hardware runs. However, the quantitative core of the paper is internally inconsistent: the tabulated energy values do not follow from the operators and formulas defined in the text, the stated injected energy E0 disagrees with Eq. (8), the subsystem Hamiltonians violate Eq. (5), and no extractable-work observable or interaction Hamiltonian V is defined. Because the central energy-distribution claim rests entirely on these numbers, the result is not supported by the manuscript as written. The significance of the paper is therefore contingent on a major revision that supplies a consistent energy accounting and a genuine QET observable.","major_comments":[{"comment":"The entries labelled H_n are not expectation values of the operator defined in Eq. (10). That operator, H_n = |1><1|_n = (I-Z_n)/2, has spectrum {0,1}, so any valid expectation value must lie in [0,1]. For the qasm simulator with (h,k)=(2,1), Table 1 reports H1 = 1.0531, which exceeds the maximum eigenvalue of the operator. The same table gives H2 = 0.3396 for the same settings, which is not inconsistent by itself, but the H1 value cannot be an expectation value of the defined Hamiltonian. This invalidates the identification of the tabulated numbers with the energies of the protocol.","section":"§5, Table 1; §3.2, Eq. (10)"},{"comment":"The reported injected energy E0 does not follow from the stated formula. Equation (8) gives E0 = h^2/(h^2+k^2), which for (h,k)=(2,1) equals 0.8, whereas Table 1 reports E0 = 1.7888. For (h,k)=(1,1), Eq. (8) gives 0.5, while the table reports 0.7071. The discrepancy is systematic and large, so the claim that E0 is the injected energy and that the harvested energies conserve energy against E0 cannot be checked from the equations given.","section":"§3.2, Eq. (8); §5, Table 1"},{"comment":"The subsystem Hamiltonians violate their defining relation. Equation (5) defines H_subm = sum_{i=m}^{N-1} H_i, so for three qubits H_sub1 = H1 + H2. For the qasm simulator with (h,k)=(2,1), Table 1 gives H_sub1 = 0.7314 while H1 + H2 = 1.0531 + 0.3396 = 1.3927. The (h,k)=(1,1) row gives H_sub1 = 0.1809 versus H1 + H2 = 0.5255 + 0.1702 = 0.6957. Thus the decremental pattern in the tables is not the sum of the individual qubit energies, contradicting the manuscript's own definition.","section":"§3.1, Eq. (5); §5, Table 1"},{"comment":"No genuine QET energy-extraction mechanism is defined. The only receiver operation is the conditional feed-forward U_mu = I or Z on each receiver qubit. Since Z commutes with the local Hamiltonian H_n = |1><1|_n and the spectrum of H_n is nonnegative, applying this unitary cannot change the expectation value of H_n in the post-measurement state. The protocol also never specifies the interaction Hamiltonian V appearing in Eq. (3), which is the term responsible for negative-energy pockets in standard QET. Consequently, the paper provides no calculation showing that energy can be extracted from the receivers under the stated operators.","section":"§3.3 and §3.4"},{"comment":"The symmetry tests are built into the construction and do not provide independent support for the QET claim. The W state is permutation-symmetric by construction, so exchange symmetry under swapping receiver order is guaranteed for any symmetric observable and does not test the protocol. Similarly, H_subm is defined as a sum of identical local projectors over the remaining qubits, so measuring this sum from different nodes trivially gives the same value. Passing these checks therefore says nothing about whether energy was teleported.","section":"§4, Symmetry Test"}],"minor_comments":[{"comment":"The state in Eq. (7) is written with h and k as real nonnegative parameters, but the text does not state their normalization convention beyond the denominator sqrt(h^2+k^2); please clarify whether the parameters are meant to be directly comparable to the experimental amplitudes or are simply circuit angles.","section":"§3.2, Eq. (7)"},{"comment":"The tables use inconsistent notation: the total Hamiltonian is called Htot in Tables 1–3 but H_total in Eq. (3); the injected energy is E0 in Eq. (8) and Eo in the tables. Please unify the notation.","section":"§5, Table headings"},{"comment":"The device name is written both as 'IBMQ Lagos' and 'ibm lagos'; please use a single consistent name. The error map in Figure 9 is not clearly connected to the measured energy deviations, and its role in the analysis should be stated.","section":"§6 and Figure 9"},{"comment":"The conclusion repeats the claim of 'first experimental realisation' and 'energy conservation' without referring to the specific equations that would back these statements; please cite the relevant calculations or data tables explicitly.","section":"§7"}],"recommendation":"reject","confidential_remarks":"The manuscript's quantitative claims are contradicted by its own definitions in multiple independent places, so the rejection is based on technical grounds rather than novelty. I do not see evidence of deliberate misrepresentation, but the reported tables and formulas should be independently audited before any resubmission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nI read the Khan et al. manuscript on multi-qubit QET with W states. The idea is a natural extension of the two-qubit QET experiments: use the W state's robustness to single-qubit measurement so that several receivers can harvest energy after one sender's measurement. That framing is sensible, and the authors did run real circuits on IBM Lagos for 3, 4, and 5 qubits. Credit where due: the circuits are drawn clearly, the hardware runs are there, and the prose explaining LOCC and the speed-of-light limit is fine.\n\nBut the quantitative core does not hold up. The tabulated values in Tables 1–3 cannot be expectation values of the Hamiltonians defined in Eqs. (5) and (10). With H_n = |1><1|_n, every eigenvalue is 0 or 1, yet Table 1 lists H1 = 1.0531 on the simulator. Equation (5) requires H_sub1 = H1 + H2, but the table gives Hsub1 = 0.7314 while H1 + H2 = 1.3927. And Eq. (8) gives E0 = 0.8 for (h,k)=(2,1), not the tabulated 1.7888. These are not minor typos; they break the central claim that a single injected energy is deterministically and decrementally harvested. The protocol's only receiver operation is a conditional I/Z feedforward, which cannot lower the expectation value of a nonnegative operator like |1><1|, so no energy is extracted under the paper's own definitions. The interaction Hamiltonian V in Eq. (3) is never specified, which is the piece that creates the negative-energy pockets essential to QET.\n\nThe symmetry tests are also empty: the W state is permutation-symmetric by construction, so exchange and 'translational' symmetry pass automatically, regardless of any QET protocol. The complexity reduction is attributed to Ref. [14], so the genuinely new component is the circuit extension to 3–5 qubits, which is small.\n\nI see no path to salvage the current claims without a complete redefinition of the measured observables and a new derivation of the extraction mechanism. The paper is not ready for peer review; it should be returned to the authors. A serious referee would spend the whole report listing the same contradictions.\n\nRecommendation: desk reject, but with a detailed note telling the authors to fix the definitions and recompute if they want to resubmit.","headline":"The paper's quantitative core is internally inconsistent — the tabulated values cannot be expectation values of the defined Hamiltonians — so the claimed multi-qubit QET demonstration is unsupported.","tokens_in":8665,"tokens_out":1824,"would_cite":false,"duration_ms":16545,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.67.-a","03.67.Hk","03.65.Ud"],"model":"deepseek-v4-flash","headline":"The paper claims that a W-state circuit enables the first multi-qubit quantum energy teleportation, with one sender's injected energy harvested in decreasing shares by several receivers.","keywords":["quantum energy teleportation","W state","multiqubit entanglement","energy transfer","LOCC","projective measurement","superconducting hardware","quantum networks"],"falsifier":"The decisive calculation is to take the prepared W-state circuit with the stated h,k, run Alice's X measurement and each receiver's conditional unitary, then evaluate Tr(rho_i |1><1|_i) on each receiver's reduced state; the paper's Eq. (5) identity H_sub1 = H_1 + H_2 can then be checked against Tables 1-3 in one pass, and the tables already contain all quantities needed to see whether the numbers are consistent with the operators they are named after.","tokens_in":7543,"feed_emoji":"⚡","tokens_out":9109,"duration_ms":85326,"temperature":0.7,"pith_summary":"This paper sets out to establish that quantum energy teleportation, previously demonstrated only on two qubits, can be extended to three, four, and five qubits using W-state entanglement. Its central assertion is that a single sender who injects energy E0 by measurement can, through one classical bit, enable several distant receivers to harvest that energy in deterministic, decreasing shares. If true, this would make QET a realistic mechanism for energy distribution in multi-node quantum networks rather than a two-party curiosity. The paper also claims that the harvest pattern is invariant under changing which receiver goes first and under exchanging receivers, and that the total harvested energy never exceeds the injected amount.","feed_headline":"First multi-qubit energy teleportation claimed via W states","feed_subtitle":"Three-, four-, and five-qubit circuits show a sender's injected energy shared out in decreasing amounts.","key_machinery":"The engine of the protocol is the n-qubit W state, |W_n> = (|100...0> + |010...0> + ... + |00...01>)/$\\sqrt$(n), which keeps all qubits entangled in a single-excitation superposition and, unlike the GHZ state, retains entanglement of the unmeasured parties after one qubit is measured. The energy bookkeeping runs on the single-qubit projectors H_i = |1><1|_i and their partial sums H_subm, with the total Hamiltonian H_total = sum H_i + V and E0 = $h^{2}$/($h^{2}$+$k^{2}$) determined by the weights of the vacuum and W components of the initial state. The circuit preparation uses an efficient W-state construction whose gate count scales logarithmically in the number of qubits.","core_discovery":"On the paper's own terms, the discovery is that a W-state multipartite entangled channel supports a multi-receiver QET protocol: after preparing a W state with tunable weight of the single-excitation term, Alice performs a projective measurement with outcome mu = +/-1, sends that bit over a classical channel, and each receiver applies a conditional unitary (identity for mu = +1, Z for mu = -1) before measuring the local energy. The measured subsystem Hamiltonians H_subm decrease monotonically with m, so the injected energy E0 appears to be distributed decrementally across the network. The paper reports this pattern both in noiseless simulation and on a real superconducting device, and says the protocol passes translational-symmetry and exchange-symmetry checks, confirming that the decrement is intrinsic to the W-state resource rather than an artifact of a particular ordering.","pith_inferences":["A test the paper does not run is to reconstruct the post-feed-forward density matrix of each receiver and compute Tr(rho_i |1><1|_i) directly from the circuit; matching the tabulated decrement would confirm the numbers are expectation values of the stated operators.","Sweeping the h,k parameters beyond the two values used here would probe whether the decrement scales linearly with E0 as the paper's formula implies; a nonlinear scaling would point to the tables' numbers being operator-independent artifacts.","If the identification of H_n with |1><1|_n is maintained, the protocol is actually teleporting an excitation of the computational basis, and the connection to thermodynamic energy would require adding a genuine interaction term V rather than setting it to zero after measurement.","The same W-state architecture could be used for multi-receiver entanglement-assisted communication tasks beyond energy, such as broadcast remote state preparation, since only one classical bit and the same conditional unitaries are involved."],"forward_implications":["If the claim holds, QET moves from a two-party effect to a network effect: energy injected at one node can be split among any number of entangled receivers.","The protocol conserves energy: the sum of all harvested subsystem energies stays below E0, and causality is preserved because each receiver needs the classical bit before acting.","Because the W state survives single-qubit measurement, the remaining receivers can still harvest after one measurement, which the paper argues is impossible with GHZ-type states.","The measured translational and exchange symmetry of the harvest pattern means the decremental distribution is a property of the W-state protocol, not of a specific measurement order.","The reduced-gate W-state preparation gives a practical logarithmic circuit depth, so the scheme is not limited to three qubits and extends to larger registers."],"supporting_citations":[{"why":"Supplies the QET protocol's theoretical basis that local operations and classical communication can extract energy from entangled ground states.","marker":"[1]"},{"why":"The prior two-qubit hardware demonstration that this paper extends to multiple receivers.","marker":"[4]"},{"why":"The first realization of QET on quantum hardware, used as the baseline for claiming multi-qubit novelty.","marker":"[5]"},{"why":"The W-state preparation scheme used to entangle sender and receivers.","marker":"[7]"},{"why":"Establishes W and GHZ as inequivalent entangled states, motivating the choice of W for post-measurement robustness.","marker":"[12]"},{"why":"Supports the claim that W states remain entangled under single-particle measurement or loss.","marker":"[13]"},{"why":"Provides the efficient W-state circuit whose gate count the paper reduces to logarithmic depth.","marker":"[14]"},{"why":"Grounds the zero-point-energy picture: ground-state entanglement is what makes QET possible.","marker":"[17]"},{"why":"Relates injected energy to the entanglement structure, underpinning the E0 formula.","marker":"[20]"}],"fun_headline_variants":["Multi-qubit energy teleportation via W states demonstrated","Energy teleportation scaled to multiple qubits with W states","W-state network shares quantum energy across many qubits","Multi-receiver energy teleportation real with W-state entanglement","W-state entanglement teleports energy to many receivers"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the values reported as H_n and H_subm in Tables 1-3 are energies in the QET sense, i.e., expectation values of H_n=|1><1|_n and the subsystem sums defined in Eq. (5); the paper's own numbers (e.g., H_1=1.0531 in Table 1, which exceeds the maximum eigenvalue of |1><1|) show this identification cannot be taken for granted, so if it fails the central claim collapses.","fun_headline_variants_meta":{"raw":{"variants":["Multi-qubit energy teleportation via W states demonstrated","Energy teleportation scaled to multiple qubits with W states","W-state network shares quantum energy across many qubits","Multi-receiver energy teleportation real with W-state entanglement","W-state entanglement teleports energy to many receivers"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00073,"raw_usage":{"total_tokens":3211,"prompt_tokens":833,"completion_tokens":2378,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":449,"completion_tokens_details":{"reasoning_tokens":2298}},"tokens_in":449,"tokens_out":2378,"duration_ms":17085,"temperature":1.0,"reasoning_tokens":2298,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:08:33.887074+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"The decisive calculation is to take the prepared W-state circuit with the stated h,k, run Alice's X measurement and each receiver's conditional unitary, then evaluate Tr(rho_i |1><1|_i) on each receiver's reduced state; the paper's Eq. (5) identity H_sub1 = H_1 + H_2 can then be checked against Tables 1-3 in one pass, and the tables already contain all quantities needed to see whether the numbers are consistent with the operators they are named after.","supporting_citations":[{"cited_title":"Quantum energy tele- portation without a limit of distance","cited_arxiv_id":null,"evidence_quote":"Supplies the QET protocol's theoretical basis that local operations and classical communication can extract energy from entangled ground states."},{"cited_title":"Demonstration of quantum energy teleporta- tion on superconducting quantum hardware","cited_arxiv_id":null,"evidence_quote":"The prior two-qubit hardware demonstration that this paper extends to multiple receivers."},{"cited_title":"Preparation of partially entangled W state and deterministic multi-controlled teleportation","cited_arxiv_id":null,"evidence_quote":"The W-state preparation scheme used to entangle sender and receivers."},{"cited_title":"Ignacio Cirac","cited_arxiv_id":null,"evidence_quote":"Establishes W and GHZ as inequivalent entangled states, motivating the choice of W for post-measurement robustness."},{"cited_title":"Generating multi-atom entangled W states via light-matter inter- face based fusion mechanism","cited_arxiv_id":null,"evidence_quote":"Supports the claim that W states remain entangled under single-particle measurement or loss."},{"cited_title":"Efficient quantum algo- rithms for GHZ and W states, and implementation on the IBM quantum computer","cited_arxiv_id":null,"evidence_quote":"Provides the efficient W-state circuit whose gate count the paper reduces to logarithmic depth."},{"cited_title":"Ground-state entanglement gives birth to quantum energy teleportation","cited_arxiv_id":null,"evidence_quote":"Grounds the zero-point-energy picture: ground-state entanglement is what makes QET possible."},{"cited_title":"Energy entanglement relation for quantum energy tele- portation","cited_arxiv_id":null,"evidence_quote":"Relates injected energy to the entanglement structure, underpinning the E0 formula."}],"review_version":1}