Entropy geometry of a two-level open quantum system predicts a specific ratio between cubic and quintic nonlinear coefficients in the Markovian limit. Two candidate values currently have theoretical support: α/β=6 ("Route B") and α/β=5/3 ("Route A," currently the better-supported of the two). We propose a circuit QED experiment using a superconducting transmon qubit under continuous measurement to test this prediction directly. Phase evolution data are fit to αL−βL² with α and β as independent free parameters; their ratio is the experimental output, discriminating between Route A, Route B, and neither. The experiment is feasible with existing hardware at 3σ significance with 10⁴ experimental runs. v2 correction (Aug 2026): the original Falsification Condition treated α/β=6 as the framework's default/expected prediction. This is corrected throughout: five separate attempted derivations of α/β=6 find no independent theoretical support, while a genuine variational derivation gives α/β=5/3, confirmed four separate times. This strengthens rather than weakens the experimental design — the three-hypothesis structure (H1: α/β=6; H2: α/β=5/3; H3: neither) is exactly the right experiment, now presented evenhandedly. All three figures have been regenerated to show both hypotheses with equal visual weight (the original figures visually singled out α/β=6 as "the prediction"). No change to the experimental protocol, run-count requirements, or feasibility analysis.
Entropy geometry of a two-level open quantum system predicts a specific ratio between cubic and quintic nonlinear coefficients in the Markovian limit. Two candidate values currently have theoretical support: α/β=6 ("Route B") and α/β=5/3 ("Route A," currently the better-supported of the two). We propose a circuit QED experiment using a superconducting transmon qubit under continuous measurement to test this prediction directly. Phase evolution data are fit to αL−βL² with α and β as independent free parameters; their ratio is the experimental output, discriminating between Route A, Route B, and neither. The experiment is feasible with existing hardware at 3σ significance with 10⁴ experimental runs. v2 correction (Aug 2026): the original Falsification Condition treated α/β=6 as the framework's default/expected prediction. This is corrected throughout: five separate attempted derivations of α/β=6 find no independent theoretical support, while a genuine variational derivation gives α/β=5/3, confirmed four separate times. This strengthens rather than weakens the experimental design — the three-hypothesis structure (H1: α/β=6; H2: α/β=5/3; H3: neither) is exactly the right experiment, now presented evenhandedly. All three figures have been regenerated to show both hypotheses with equal visual weight (the original figures visually singled out α/β=6 as "the prediction"). No change to the experimental protocol, run-count requirements, or feasibility analysis.
The quantum–classical boundary is one of the deepest unsolved problems in physics. The Information Bottleneck Theorem of the Order Parameter Spacetime Theory provides a precise criterion: when the total information dissipation coefficient Υ=0, the system resides in the quantum sector (unitary evolution, entanglement conservation); when Υ>0, irreversible classicality emerges. How can this binary criterion be tested experimentally? This paper reveals that the binary nature of the Information Bottleneck Theorem—the transition of entanglement from "strict conservation" to "onset of decay"—does not manifest as a discontinuous jump of entanglement, but rather as a nonlinear signature in the decoherence rate. This nonlinearity originates from complex metric back-reaction: information dissipation alters the spacetime geometry, and the geometry in turn modifies the dissipation rate, forming an information–geometry closed loop. Specifically, for a two-qubit entangled state evolving under a pure dephasing channel, the standard Lindblad theory predicts that log C(t) is a straight line; the complex metric back-reaction predicts that log C(t) bends upward—the decay rate slows down as entanglement decreases, i.e., entanglement is protected. At the critical coupling α=1/r₀², the theory predicts exact protection of entanglement (C(t)=constant); in the strong-coupling regime α>1/r₀², the theory predicts that in the initial stage entanglement exceeds its maximum value (C>1). This paper provides a complete theoretical prediction and data analysis scheme to test these predictions using existing experimental data. The decision logic is binary: either log C(t) is a straight line (α=0, complex metric back-reaction falsified), or it is not (α>0, information–geometry closed loop verified).
H. Billah and M.M.H. Sarker contributed equally to this work. Interpreting a fixed quantum circuit's output as evidence of a hardware effect requires ruling out two things usually conflated with it: finite-sample fluctuation, and structure already present in the circuit's own noiseless output. Less commonly checked is a third: whether the reference circuit compared against is the one actually executed, once compiler-level qubit routing is accounted for. We execute a fixed 35-qubit, 243-gate diagnostic circuit on IBM Heron-family hardware (three runs, two backends) and show this third check is essential: the routed circuit submitted to hardware has different noiseless predictions than the logical circuit intended, for several qubits. Against the correct, routed-circuit reference, the aggregate deviation is significant in two of three runs, and four registers (0, 9, 14, 27) show a significant output-probability deviation in every run — though we distinguish a high-confidence subset, {0, 9, 27}, with tightly time-matched calibration, from qubit 14, included only on an exploratory basis given its calibration was retrieved roughly two weeks post-execution. Same-backend replicates correlate more strongly by the Pearson measure, though a rank-based (Spearman) test shows this gap does not survive at the level of register ordering, indicating substantial leverage from a small number of registers rather than a broadly robust pattern; these three executions also share a byte-identical payload and are not independent replications in the strictest sense. The mechanism is only partially resolved: independent single-qubit readout error and raw gate count are ruled out as complete explanations for most of these registers, but the simplest version of the leading hypothesis for the single most-affected register does not reproduce the observed cross-backend pattern even with live, backend-specific timing data. A second, structurally different circuit validated only in simulation calibrates the statistical procedure's behavior under one synthetic noise model; it does not itself establish generality to real hardware, and the specific register set found here should not be expected to generalize beyond this study. Note on scope: this is a methodology and case-study contribution centered on executed-circuit references for fixed-circuit diagnostics, not a characterization of IBM Heron hardware in general or a randomized-benchmarking experiment in the formal sense. Supporting data, the routed OpenQASM circuits, raw measurement counts, and analysis code for this study are available on request from the corresponding author. Affiliation: Sonicium Quantum Lab Ltd., Dhaka, Bangladesh.
Consolidated edition. This version merges the three previous papers of the programme into a single document, reordered by logical dependency rather than chronology so that the surviving core is separable from the speculation built on it. 63 pages, 26 sections in 7 parts, 8 appendices. Eloy René Becerra Daly What is established, in decreasing order of confidence [EXACT] Identities. The Λ-hierarchy reduces to τ = ℏ/E and ℓ = the reduced Compton wavelength. The accessible information satisfies IQ = (γ/τ)β exactly. A distinguished point at D/L = 1/2 carries four coincident properties — exactly one bit, the entanglement sudden-death point for C0 = 1, the maximum of D·C̄ at L²/4, and a Bures arc of π/3 — all invariant in β, τ and L. [OBS] Verification. D + C = 1 holds to machine precision across 650 circuits on two IBM backends and ~5.5×106 shots. [THM] Limits. A no-go theorem shows the temporal exponent of dephasing is independent of the pulse-sequence filter, which removes the derivation previously claimed for Axiom 3 and relabels it as an empirical postulate. [THM] The transferable result. Pollard's criterion used as a licence condition: β ≤ 1 certifies that the curve admits a positive rate density, β > 1 proves that none exists. In reliability engineering an infant-mortality exponent licenses reading the batch as heterogeneous, while a wear-out exponent forbids it under any partition. Six transfers are registered, each with the observation that would retire it. The inference this work does not license A fitted β < 1 is not evidence of quantum behaviour. The theorem establishes representability of the curve, not identification of the mechanism — the map from mechanism to curve is many-to-one — so what follows is weaker and sufficient: the data cannot be adduced as evidence of coherence, because a classical account of them exists. The decisive test, which is not performed here On a single sample, the anomalous-diffusion exponent and the stretched-relaxation exponent must satisfy β = (1 + αdiff)/2, with β ≥ 1/2 as a corollary. Both quantities are already tabulated in the NMR relaxometry and diffusion-imaging literature for overlapping sample sets. No new experiment is required to attempt this refutation. Errata to previous versions The critical qubit number is n* = 1.848, not 2.6. The LIGO ringdown significance, with the internal error scaled by √(χ²/ν) = 1.669 as the catalogue's own goodness of fit requires, is 12.5σ; we record that our first correction of it, 20.9σ, was itself wrong for neglecting that scaling, and that the originally published 13.8σ was closer to the defensible value than our correction. A reported 18 kHz emergence mode lies below the Rayleigh limit of its own data. The published comoving density of remnants corresponds to Ω = 0.063, not the 0.12 it is stated to reproduce. Endpoint, labelled CONJ throughout The programme closes with a dark-matter candidate: Planck-scale black-hole remnants at Mmin = mP/(2√π) = 6.140 µg, an exact identity rather than the approximation 0.28 mP under which it was published. Evaluating it shows the usual dismissal to be right for the wrong reason: the remnant carries 148.6 J at galactic velocity and one transit is expected per 0.86 km²·yr, so rarity is not the obstacle; but the mean free path in rock is 1023 light years and the probability of one interaction while crossing the Earth is 10-32. The candidate is cross-section-limited, not exposure-limited, and the two demand opposite experiments. Four falsifiers are given, two requiring no new instrument. Reproducibility Every numerical claim is recomputed from the equations by a dependency-free implementation: 354 regression tests and 37 published-number checks, over a registry of 138 equations each carrying source, evidence level and declared domain. Where a published number could not be reproduced it is recorded as an erratum rather than adjusted; where a correction of ours proved wrong it is recorded as such. The register documents 27 inconsistencies, of which 11 remain open, each with the observation that would close it.
In quantum information processing, it is important to witness the entropy of the message in the device-independent way which was proposed recently [R. Chaves, J. B. Brask, and N. Brunner, Phys. Rev. Lett. 115, 110501 (2015)]. In this paper, we theoretically obtain the minimal quantum entropy for three widely used linear dimension witnesses, which is considered ``a difficult question.'' Then we experimentally test the classical and quantum entropy in a device-independent manner. The experimental results agree well with the theoretical analysis, demonstrating that entropy is needed in quantum systems that is lower than the entropy needed in classical systems with the given value of the dimension witness.
The paper is an elaborate comparative assessment of the most relevant entropy-based quantities to be applied in quantifying quantum entanglement in pure, mixed, bipartite, and multipartite quantum systems. The study fills the existing gap in the literature in which most of the previous literature examines individual measures, but a lot of knowledge is lacking on what these measures are regarding their strengths, weaknesses, and the operational usefulness against each other. The study can prove the behaviour of each measure under noise, decoherence, dimensional scaling, and variation of state-type by analysing von Neumann entropy, the Tsallis entropy, entropy of entanglement of formation, concurrence and logarithmic negativity. Numerical studies with pure two-qubit states, Werner states, GHZ states, W states and mixed random states demonstrate specific sensitivity properties and computational limitations which ensure that no single measure can be a universal quantifier. The paper goes on to say that entropy-only measures do not work in mixed regimes because of a dominance in classical correlations. The results have several important implications to quantum communication, quantum simulation, and quantum computing in the NISQ-era, where the choice of measurement has a direct impact on benchmarking, error-correction scheme, and protocol performance based on entanglement. The paper ends with a recommendation of contextual, purpose-based scheme of selecting entanglement measures and suggests a further study on scalable benchmarking, hybrid quantifiers, and operational performance-based entanglement measurements. These observations reinforce the theoretical premise of entanglement studies and enable the advancement of more effective quantum technologies in the field of practice.
CORRECTION NOTICE (v5, 2026-09-06). The central result of v1-v4 is WITHDRAWN. This record has not been peer reviewed. Issued 2026-09-06 by the author (v5 of this record). This notice was added to the archived record; the manuscript itself is unaltered. This record has not been peer reviewed. What is wrong The force exponent reported here as alpha = 3.92 +/- 0.16 is an artifact of the fitting procedure, not a property of the data. The fit was unweighted least squares in linear space applied to a steeply falling profile, which places 95.8 percent of its objective on the single point at the shortest retained separation. Re-fitting the same data with nothing discarded, changing only the error model, gives 2.82 (relative-error weighting) or 2.89 (log-space regression). Across fifteen combinations of standard estimator and fit window the exponent spans 2.53 to 3.92, and the value published here is the largest of them. What the data show instead, and how firmly The retraction is certain. The replacement is not. On the open 24-site chain the same data give alpha = 2.6 +/- 0.2, where the interval is the spread of a plateau in the local logarithmic slope over six consecutive separations, not a statistical error (the bootstrap error on the published fit to the same data is 0.63); the plateau value was reproduced at 2.5921 by a separately written implementation run on the same recorded state (SIM-2026-073). This is a single geometry at a single size. On a 24-site periodic ring, analysed with chord distance as pre-registered, two probes that are both energy-density-like (Delta = 1) give 1.83 and 2.37 against a CFT two-point value of 2 (SIM-2026-074): one size, not converged, disagreeing with each other by 29 percent, and not attributable to a single operator channel. No corrected exponent is established. The exchange channel is an open question. Treat 2.6 +/- 0.2 as the provisional open-chain value, not as a result. Also withdrawn or voided alpha = 3.92 +/- 0.16 (24 sites) and alpha = 3.97 +/- 0.15 (16 sites, exact) from stress-tensor exchange. Was: headline result and its first corroboration. Now: withdrawn. Why: the same estimator artifact: both move in lockstep under it (3.92 to 2.56, 3.97 to 2.75 on dropping the contact point), because they share one observable, one fit window and one fitting routine. scalar exchange (alpha = 2) excluded. Was: stated as excluded at about 12 sigma. Now: withdrawn. Why: the 12 sigma used the covariance error 0.16; at the bootstrap error 0.63 computed before release the exclusion is about 2.2 sigma, and under any window starting at separation 3 the point estimate itself falls to about 2.56. alpha = 4 is universal; alpha = 4.00 at Ising, tricritical Ising and Potts. Was: confirmed at three classes. Now: withdrawn; the operator towers at all three classes stand. Why: the exponent was measured only at Ising and inherited by the other two; the towers are spectra, not forces. third independent evaluation alpha = 4.07 (chi = 3 MERA), and with it the statement that this was the first holographic force measurement from an optimized tensor network state. Was: supporting evidence and a priority claim. Now: both withdrawn. Why: the profile changes sign inside its own fit window and cannot be a fixed-sign power law; the priority claim rests on that evaluation alone and was never gated against prior work. the discriminating test: stress tensor (Z_j Z_j+1) versus spin primary (X_j). Was: registered killer test. Now: void. Why: at the critical point these are one operator, related by exact Kramers-Wannier self-duality. Measured on the periodic ring: identical expectation values to 1e-15 and identical force profiles to 1e-13 at 14 sites, 2.4e-9 at 24 sites (SIM-2026-074). Open boundaries break the duality, which is why the open-chain run of this test (SIM-2026-073) showed a spurious difference between the two arms. The test compared the energy density to itself. Neither label was correct: Z_j Z_j+1 is the energy density, not the stress tensor; X_j is its dual, not the spin primary. transport time T = (pi/2) l_AdS to 1.2 percent as a geometric prediction. Was: confirmed. Now: measurement stands (T = 2.239 at N = 16); geometric reading not established. Why: l_AdS cancels in the cited derivation, which also gives pi rather than the pi/2 the manuscript compares against; the chi = 3 estimate of l_AdS gives a 57 percent miss; the transport driver never applies a MERA. The true spin primary Z_j was never in the design, and the direct replacement test is blocked: Z_j is odd under the Z2 symmetry, so the energy-difference observable used throughout this work subtracts across symmetry sectors and is undefined for it. A replacement test using two Z2-even probes has been pre-registered (PREREGISTRATION-T.md, committed before its driver) and run; its result is deliberately not part of this correction and will appear in a later version. Not previously reported The published fit has a reduced chi-squared of 6.008 on 9 degrees of freedom, and a bootstrap standard deviation of 0.63 rather than the quoted 0.16. Both were computed before release and omitted. What is unaffected Of the claims in this record: the two-phase optimization method, the chi = 3 criticality threshold, the exact-diagonalization gates, the measured OPE coefficient C_sigma-sigma-epsilon = 0.50 +/- 0.03 against the exact 1/2, and the conformal towers at all three classes. Not part of this record, mentioned only because they are sometimes read together with it: the later C_TTT stress-tensor self-coupling measurements (SIM-2026-067/068/069, dated after this record) and the matched off-critical ring control (SIM-2026-074) are unaffected by this correction and make no claim about the force exponent. How the error was found and what this record contains The error was found by the author's own internal adversarial audit, not by a reviewer; the journal submission it was found after is closed, and no review of this work has taken place. Files in this record: the full re-analysis (SIM-2026-072.json, driver, figure), the pre-registered chain test (SIM-2026-073.json) and ring test (SIM-2026-074.json) with both pre-registrations as committed before the runs, the runnable drivers with their shared module and the negative test suite for their validation gates, and the error register (ERRATA.md). Concept DOI 10.5281/zenodo.19660302 always resolves to the current version. The abstract of the original manuscript follows unchanged, for the record. Every claim in it about the force exponent should be read against the correction above. We report results from classical simulation of critical spin chains that establish quantitative physical content in the MERA-AdS correspondence. First, the interaction energy between boundary-primary excitations follows a power law F(dr) ~ dr^(-alpha) with three consistent evaluations yielding alpha = 3.92 +/- 0.16 (24q), 3.97 +/- 0.15 (16q), and 4.07 +/- 0.18 (16q chi=3 MERA), all consistent with stress-tensor exchange (alpha = 2*Delta_T = 4) and inconsistent with scalar exchange (alpha = 2); the exponent is explained by the Ising CFT fusion rule eps x eps = [1]. Because Delta_T = 2 is fixed by conformal symmetry in every unitary 2D CFT, alpha = 4 is universal: we confirm this at two further fixed points - the tricritical Ising model (c = 7/10), where a scale-invariant MERA recovers the full M(4,5) primary spectrum (Delta_sigma = 0.092, Delta_eps = 0.204, Delta_T = 1.999), and the three-state Potts model (c = 4/5), where a Z3-symmetric MERA at chi = 12 recovers Delta_sigma = 0.134, Delta_eps = 0.805, Delta_T = 2.001 - giving alpha = 4.00 at all three universality classes. Second, the holographic transport time matches the AdS_3 null geodesic prediction T = (pi/2) l_AdS to 1.2% at N = 16 sites on a time-grid-converged measurement, with the residual shrinking from 2.8% at N = 12. Third, we introduce a two-phase optimization method (ALM + Z2 projection) for Z2-symmetric MERA ground states at 24 qubits. Fourth, extending the MERA bond dimension from chi=2 to chi=3 overcomes the expressibility barrier, achieving 0.15% energy error at 16 qubits and enabling the first holographic force measurement from an optimized tensor network state. The OPE coefficient is also measured directly from the fixed-point tensors: C_sigma-sigma-eps = 0.50 +/- 0.03 against the exact Ising value 1/2. A hardware path is designed for Quantinuum Helios (57 CNOTs, 0.57% logical error). Version 4 changes (relative to v3): Transport: N=16 residual restated as the time-grid-converged value of -1.21% (dt = 1e-3), with -2.78% at N=12 showing the finite-size trend; the 0.72% figure in v3 was an artifact of the dt = 0.05 integration grid and is now labeled as such. The N=24 transport point carries a new reliability caveat (double-lobe trace structure). The l_AdS comparison table is recomputed against the converged transport time (best fit 1.425, deviation 1.21%). Effective-mass derivation rewritten in a consistent AdS3 convention m^2 l^2 = Delta(Delta-2); m_eff = 0.693 = 1/l_AdS follows from Delta = 1 exactly. NEW: universality section extended to a third fixed point - a Z3-symmetric MERA at chi = 12 recovers the three-state Potts (c = 4/5) tower, giving alpha = 4.00 at all three universality classes (c = 1/2, 7/10, 4/5). NEW: the OPE coefficient C_sigma-sigma-eps = 0.50 +/- 0.03 measured directly from the fixed-point tensors, with C_sigma-sigma-sigma = 0 at machine precision as the Z2 structural check. Supplemental table row SIM-007 annotated (record lost; script preserved); data availability expanded; Zenodo DOI added to the front matter.