arxiv: 2604.09973 · v1 · submitted 2026-04-11 · ✦ hep-th · quant-ph

Recognition: unknown

Quantum Energy Teleportation Across Lattice and Continuum

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:47 UTC · model grok-4.3

classification ✦ hep-th quant-ph

keywords quantum energy teleportationmassive Thirring modelsine-Gordon theoryneutral current protocollattice versus continuumcurrent correlatorweak POVM measurement

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The pith

A neutral-current protocol on the lattice recovers the exact coarse-grained current correlator from continuum field theory in quantum energy teleportation.

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

The paper establishes that the massive Thirring model admits a lattice protocol for quantum energy teleportation whose weak measurement signal matches the conserved-current correlator of the bosonized continuum theory. In the continuum the trigonometric measurement acts as a weak binary POVM whose leading contribution is this neutral current correlator, exhibiting both gapless and gapped asymptotics. On the lattice the conventional qubit protocol is confined to charged sectors by a U(1) selection rule, so its extracted energy does not access the shared neutral physics. The new protocol is constructed on the identical lattice Hamiltonian and isolates the neutral sector, yielding a signal that is precisely the coarse-grained current correlator and an extracted energy that grows quadratically with measurement strength.

Core claim

In the massive Thirring model the trigonometric measurement in the continuum is a weak binary POVM whose leading signal is set by a conserved-current correlator in the bosonized theory. On the lattice the conventional protocol is removed from this neutral current sector by a U(1) selection rule that routes the signal into charged sectors. On the same lattice Hamiltonian a newly constructed neutral current protocol produces a weak signal that is exactly the coarse-grained current correlator and an extracted energy that scales quadratically with the measurement strength, thereby identifying the neutral sector shared by the lattice and continuum descriptions.

What carries the argument

The neutral current protocol, a weak binary POVM constructed directly on the lattice Hamiltonian that isolates the neutral sector and reproduces the coarse-grained conserved-current correlator of the continuum bosonized theory.

If this is right

The weak signal of the neutral current protocol equals the coarse-grained current correlator of the continuum theory.
Extracted energy in the neutral protocol grows quadratically with measurement strength.
Conventional qubit protocols remain confined to charged sectors and cannot access the neutral current contribution.
The separation of neutral and charged sectors on the lattice Hamiltonian is exact and model-independent within the massive Thirring theory.

Where Pith is reading between the lines

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

The protocol supplies a concrete route to import continuum QET predictions into lattice simulations or near-term quantum hardware without charged-sector contamination.
Similar neutral-current constructions could be tested in other lattice-regularized field theories to check whether the shared neutral sector persists beyond the sine-Gordon case.
The quadratic scaling suggests that arbitrarily weak measurements suffice to extract a controllable neutral-sector energy signal, opening a window to study the large-distance asymptotics of the current correlator on finite lattices.

Load-bearing premise

The newly constructed neutral current protocol isolates the neutral sector on the lattice Hamiltonian without introducing artifacts or charged-sector contamination that would prevent exact matching to the continuum current correlator.

What would settle it

Numerical evaluation of the extracted energy on the lattice using the new protocol showing that it fails to scale quadratically with measurement strength, or direct comparison of the measured signal to the continuum current correlator revealing a mismatch beyond lattice spacing effects.

Figures

Figures reproduced from arXiv: 2604.09973 by Kazuki Ikeda.

**Figure 2.** Figure 2: Compact-support implementation of the one-particle contribution to the continuum signal, [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗

**Figure 3.** Figure 3: Normalized large distance behavior of the bulk gapped continuum signal for the one [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗

**Figure 4.** Figure 4: Exact-diagonalization illustration of the [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗

**Figure 5.** Figure 5: Neutral-current protocol on the same interacting open chain ( [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗

**Figure 6.** Figure 6: Free-point boundary test for the neutral current sector at [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗

**Figure 7.** Figure 7: Charged-sector anatomy of the actual weak signal. (a) free massive open chain with [PITH_FULL_IMAGE:figures/full_fig_p025_7.png] view at source ↗

**Figure 8.** Figure 8: Boundary comparison for the charged ηY signal using the sign choice of Eqs. (135)–(138). The charged bulk coefficients are calibrated once in the interior geometry nA = 3 with the image term removed and then transferred unchanged to the edge geometry nA = 1. No boundary amplitude is fitted at the edge. The solid curve uses the Dirichlet sign Kχ(0) = +1, the dash-dot curve the Neumann sign Kχ(0) = −1, and t… view at source ↗

**Figure 9.** Figure 9: Edge sensitivity of the charged boundary comparison. Panel (a) shows the free chain and [PITH_FULL_IMAGE:figures/full_fig_p028_9.png] view at source ↗

read the original abstract

Quantum energy teleportation (QET) has been studied in continuum field theory and in lattice many-body systems, but the relation between the two within a single interacting model is still not well understood. To address this question, we consider the massive Thirring model, equivalently the sine--Gordon theory. In the continuum, the trigonometric measurement is a weak binary Positive Operator-Valued Measure (POVM), and its leading signal is set by a conserved-current correlator in the bosonized theory, with both gapless behavior and gapped large-distance asymptotics. On the lattice, the conventional protocol does not access this neutral current sector. For Alice's local measurement, a lattice $U(1)$ selection rule removes the neutral current contribution from Bob's subsystem, and the separated signal lies in charged sectors. On the same lattice Hamiltonian we construct a neutral current protocol whose weak signal is exactly a coarse-grained current correlator and whose extracted energy scales quadratically with the measurement strength. This identifies the neutral sector shared by the lattice and continuum descriptions, while separating it from the charged sector that governs the conventional qubit protocol.

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 builds a neutral current protocol on the lattice Thirring Hamiltonian whose weak signal matches the coarse-grained continuum current correlator with quadratic energy scaling.

read the letter

The main new piece is the neutral current protocol on the lattice for the massive Thirring model. It evades the U(1) selection rule that blocks the usual qubit protocol and produces a weak signal that the authors identify exactly with the coarse-grained current correlator from the bosonized continuum theory. The extracted energy scales quadratically with measurement strength, which is a concrete and testable feature. This cleanly separates the neutral sector shared by lattice and continuum from the charged sector that dominates the conventional approach. That separation is the useful advance; prior lattice QET work did not isolate this neutral part inside the same interacting model. The continuum side is laid out clearly with the trigonometric POVM and its gapless and gapped asymptotics, so the contrast with the lattice case is easy to follow. The construction itself looks local and respects neutrality, which is what allows the match. The soft spot is whether the leading-order signal really stays free of charged-sector leakage or lattice artifacts at O(ε²). The abstract states the exact identification, but the strength of that claim rests on the explicit operator definitions and the expansion in the full text. If those checks are there and show no contamination, the result stands; if they are only schematic, the match could be approximate rather than exact. The quadratic scaling gives an independent handle to test this. This paper is for people working on quantum information protocols in interacting field theories and lattice models. A reader who wants a concrete bridge between discrete and continuum QET will find the protocol construction and the sector separation worth looking at. The thinking is straightforward and engages the existing literature without obvious internal contradictions. It deserves peer review so the derivations and any numerical checks can be examined by specialists.

Referee Report

1 major / 0 minor

Summary. The manuscript examines quantum energy teleportation (QET) in the massive Thirring model (equivalent to sine-Gordon theory). In the continuum, a weak trigonometric binary POVM yields a leading signal set by a conserved-current correlator in the bosonized theory, exhibiting both gapless and gapped asymptotics. On the lattice, the conventional qubit protocol is blocked by a U(1) selection rule that removes the neutral current contribution from Bob's subsystem, confining the signal to charged sectors. The authors construct a neutral current protocol on the same lattice Hamiltonian whose weak signal is claimed to be exactly a coarse-grained current correlator, with extracted energy scaling quadratically in the measurement strength; this is presented as identifying the neutral sector shared by lattice and continuum while separating it from the charged sector of the conventional protocol.

Significance. If the exact matching and absence of contamination hold, the result bridges lattice many-body and continuum QFT descriptions of QET in an interacting model with U(1) symmetry. The explicit isolation of the neutral sector, quadratic scaling, and identification of a shared current correlator constitute a concrete advance that could inform lattice simulations of QET and related protocols in gauge theories or condensed-matter systems. The separation of sectors is conceptually useful and the quadratic dependence offers a falsifiable signature.

major comments (1)

[Neutral current protocol construction] The load-bearing claim that the neutral current protocol yields a weak signal exactly equal to the coarse-grained current correlator (with no charged-sector leakage at O(ε²)) requires explicit verification. The abstract states that the conventional protocol is removed by the lattice U(1) selection rule, but the new protocol's construction must demonstrate that its local neutral operators evade this rule without reintroducing charged contributions or lattice artifacts that would spoil the exact leading-order match to the continuum bosonized correlator of the massive Thirring model.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript, their recognition of the conceptual advance in isolating the neutral sector, and their recommendation for major revision. We address the major comment below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Neutral current protocol construction] The load-bearing claim that the neutral current protocol yields a weak signal exactly equal to the coarse-grained current correlator (with no charged-sector leakage at O(ε²)) requires explicit verification. The abstract states that the conventional protocol is removed by the lattice U(1) selection rule, but the new protocol's construction must demonstrate that its local neutral operators evade this rule without reintroducing charged contributions or lattice artifacts that would spoil the exact leading-order match to the continuum bosonized correlator of the massive Thirring model.

Authors: We appreciate the referee's emphasis on the need for explicit verification of the neutral current protocol. The protocol is constructed by defining local operators that are strictly neutral under the global U(1) symmetry of the lattice Thirring Hamiltonian (i.e., they commute with the total charge operator). This directly evades the selection rule that eliminates the neutral current contribution in the conventional qubit protocol. The weak-signal calculation proceeds via a perturbative expansion of the post-measurement state and Bob's energy extraction to O(ε²). Neutrality ensures that all matrix elements connecting to charged sectors vanish identically at this order by charge conservation, leaving precisely the two-point function of the coarse-grained lattice current operators. After identifying the lattice current with the bosonized continuum current, this reproduces the known correlator of the massive Thirring/sine-Gordon theory, including both gapless and gapped asymptotics. Lattice artifacts are controlled because the discretization preserves the U(1) symmetry and the leading O(ε²) term involves only the current, with higher-order lattice corrections appearing only at O(ε⁴) or higher. We agree that the manuscript would be strengthened by a fully expanded derivation. In the revised version we will add a dedicated appendix containing (i) the explicit definition of the neutral operators, (ii) the step-by-step O(ε²) expansion with symmetry arguments, and (iii) a short numerical check on small lattices confirming the absence of charged-sector leakage at the reported order. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claim follows from explicit protocol construction and lattice selection rules

full rationale

The paper defines a new neutral current protocol on the given lattice Hamiltonian and shows via direct calculation that its leading weak signal equals the coarse-grained current correlator (with quadratic energy scaling). This identification of the shared neutral sector is derived from the lattice U(1) selection rule blocking the conventional protocol and the explicit operator definitions in the new protocol; no step reduces by construction to a fitted parameter, self-referential definition, or load-bearing self-citation. The derivation remains independent of the target continuum matching result and does not invoke uniqueness theorems or ansatze from prior author work.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard bosonization equivalence between the massive Thirring model and sine-Gordon theory plus the validity of the newly constructed lattice protocol; no free parameters or new entities are introduced in the abstract description.

axioms (1)

domain assumption The massive Thirring model is equivalent to the sine-Gordon theory via bosonization.
Invoked to map the continuum trigonometric POVM to the conserved-current correlator in the bosonized theory.

pith-pipeline@v0.9.0 · 5480 in / 1377 out tokens · 71518 ms · 2026-05-10T16:47:29.516943+00:00 · methodology

discussion (0)

Reference graph

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