Removing a common displacement from a gravitational channel test need not preserve its ability to exclude classical communication between quantum laboratories. We give a quantitative construction for four oscillators in a passive Newtonian rotating-wave model, using independent unknown coherent inputs, local heterodyne measurements, and classical subtraction of the common mode. An analytic bound on a bounded score holds for every normal local-operations-and-classical-communication (LOCC) channel, without an output-energy or Gaussian restriction. The ideal quantum mean is 0.125, whereas the LOCC mean is below 0.124068. With residual gain errors of 0.1%, phase errors of 0.01 radians, and an independently bounded common displacement, the respective bounds remain above 0.124581 and below 0.124438. We exhibit a common-noise regime in which the original vacuum-outcome criterion loses its guarantee while the relative score retains one. A conservative fixed-sample test controls false exclusion with memory in the null. The result assumes quantum local matter and trusted measurement structure; it neither excludes all classical phase-space models nor establishes experimental feasibility. This record contains the preprint, editable LaTeX source, and an offline reproducibility archive with exact-arithmetic certificates and 26 computational tests. One project-history test requiring undistributed literature copies is explicitly excluded from the public runner. Substantial use of generative AI is disclosed in the manuscript. This preprint has not undergone journal peer review. Licensing: the manuscript, LaTeX source, documentation and numerical records are licensed under CC BY 4.0; Python software and tests are licensed under MIT. These licences apply to separate file categories, as specified in the archive.
Removing a common displacement from a gravitational channel test need not preserve its ability to exclude classical communication between quantum laboratories. We give a quantitative construction for four oscillators in a passive Newtonian rotating-wave model, using independent unknown coherent inputs, local heterodyne measurements, and classical subtraction of the common mode. An analytic bound on a bounded score holds for every normal local-operations-and-classical-communication (LOCC) channel, without an output-energy or Gaussian restriction. The ideal quantum mean is 0.125, whereas the LOCC mean is below 0.124068. With residual gain errors of 0.1%, phase errors of 0.01 radians, and an independently bounded common displacement, the respective bounds remain above 0.124581 and below 0.124438. We exhibit a common-noise regime in which the original vacuum-outcome criterion loses its guarantee while the relative score retains one. A conservative fixed-sample test controls false exclusion with memory in the null. The result assumes quantum local matter and trusted measurement structure; it neither excludes all classical phase-space models nor establishes experimental feasibility. This record contains the preprint, editable LaTeX source, and an offline reproducibility archive with exact-arithmetic certificates and 26 computational tests. One project-history test requiring undistributed literature copies is explicitly excluded from the public runner. Substantial use of generative AI is disclosed in the manuscript. This preprint has not undergone journal peer review. Licensing: the manuscript, LaTeX source, documentation and numerical records are licensed under CC BY 4.0; Python software and tests are licensed under MIT. These licences apply to separate file categories, as specified in the archive.
We study classical-communication simulation of the joint source and probe statistics of a qubit-controlled momentum kick. Competitors retain quantum local matter, arbitrary causal classical memory and two-way communication, but no shared entanglement or quantum communication. For fixed Gaussian probe preparation and specified source preparations and readouts, an explicit local instrument approximates the complete continuous momentum statistics arbitrarily well while preserving branch-control distributions exactly. An independently bounded full output position second moment gives a strictly positive total-variation lower bound against the entire competitor class; the explicit simulator attains the same asymptotic order. At fixed nonzero kick separation, the minimum RMS spatial resource for error d scales as Theta(d^(-1/2)); at fixed relative size greater than one, the minimum error scales as Theta(eta^2) in the weak-kick parameter eta. Fixed finite bins admit exact simulation at sufficiently large finite resource. These are statements about specified readout statistics, not full-channel approximation, a Newtonian realization of the simulator, or demonstrated experimental feasibility. The manuscript discusses conditional routes to independent resource certification. This record contains the preprint, editable LaTeX source and an offline reproducibility archive. The archive reproduces Table 1 and runs 22 computational tests; three project-history tests requiring undistributed materials are explicitly excluded. The preprint has not undergone external peer review. Licensing: the manuscript, documentation and numerical records are licensed under CC BY 4.0; the Python software and tests are licensed under MIT. The archive specifies these separate scopes.
For a fixed optical receiver, optimizing the classical modulation of Gaussian signals need not reach the best communication rate. This work gives a rigorous way to certify the advantage of a non-Gaussian signal constellation against every one-mode Gaussian alphabet, and to quantify how much of that advantage survives specified receiver and preparation errors. What is compared The receiver is the displacement-covariant phase-space measurement generated by a single-photon ancillary state. It is not a binary photon-click detector. The cost is the actual mean transmitted photon number E; the receiver is fixed, and ancillary preparation and local-oscillator overhead are not included in that signal budget. Let C(E) be the unrestricted capacity and CG(E) the optimum over Gaussian letters with arbitrary Borel modulation, displacement, squeezing and mixedness. For the ideal receiver, CG(E) < C(E), for every 0 < E < ∞. The comparison is global: it does not restrict the Gaussian competitor to a finite constellation or a locally optimized ansatz. A finite-energy certificate with a calibration interval For the actual unflagged receiver seed σv = (1 − v)|1⟩⟨1| + v|0⟩⟨0|, the paper constructs four equiprobable phase-rotated signals supported on photon numbers 0–3. Each signal has exactly 0.1 mean photons. Write I4,v for their mutual information and CG(0.1,v) for the Gaussian optimum of that same receiver. At v = 0.01, in nats per use, I4,0.01 > 0.0839244, CG(0.1,0.01) < 0.0839162,so the certified excess is greater than 8.2 × 10−6. The same constellation obeys I4,v − CG(0.1,v) > 5 × 10−6 for every 0.009 ≤ v ≤ 0.011. This is a continuum guarantee, obtained from a supporting line for the same-source information and a convex upper chord for the Gaussian optimum. It is not interpolation between sampled advantages. The proof retains the full photon tail of Gaussian competitors. Phase tolerance at unchanged energy Suppose all four signals share static photon-number phases θn while retaining their exact amplitudes. After removing irrelevant constant and linear phases, the two residual errors are ε2 = θ2 − 2θ1 + θ0 and ε3 = θ3 − 3θ1 + 2θ0, modulo 2π. If both residual magnitudes are at most δ, their information loss is at most Kδ², with K < 0.132762313267. Thus δ = 0.004 radians (about 0.229°) leaves a certified excess above 2.8 × 10−6 nat/use throughout the receiver interval, with photon cost still exactly 0.1. This phase guarantee concerns a common static source error. A separate trace-distance preparation bound requires an independent check of actual mean energy. Independent phase jitter and arbitrary detector noise are different error models. Collective encodings and interpretation For the ideal receiver, every fixed finite entangled Gaussian block retains a total deficit, and uniformly bounded common blocks retain a per-use deficit. Exact correlation and covariance-repair estimates identify necessary extensive resources for a Gaussian sequence to approach capacity. These results do not settle arbitrary growing-block Gaussian encodings. The quantitative advantage is small—about 0.01% of the rate at the certified point. Its significance is a robust, globally certified separation with explicit resource and error accounting, rather than a large throughput improvement or an experimental demonstration. The article contains the complete proofs, figures, exact reference data and error bounds.
An unknown optical phase can hide quantum non-Gaussianity in every individual mode while leaving it certifiable in the joint light. This paper shows when Gaussian measurements can exclude the complete Gaussian convex hull without knowing the source's common phase, and gives explicit finite-sample tests. The results guide whether to preserve phase relations between emissions and how to process the resulting measurement records. 1. Certification against the full Gaussian model. Let Gn be the trace-norm-closed convex hull of all physical n-mode Gaussian states. For a fixed known ρ∈/G1, form the common-phase state Ωn=∫02π(UϕρUϕ†)⊗n2πdϕ,Uϕ=e−iϕN. Finite Gaussian measurements with a laboratory phase reference and bounded classical scores achieve arbitrarily small false-positive and missed-detection probabilities. The null includes arbitrary Gaussian entanglement and classical correlations, with unrestricted displacement, squeezing and energy. In particular, infσn∈Gn∥Ωn−σn∥1⟶2. The norm is the full, unhalved trace norm. An unavailable common phase therefore differs operationally from independently randomising the phase of each emission. 2. An exact coherence boundary and a joint-only resource. For the displaced two-Gaussian-packet family, centred by its actual mean before pure loss, the Gaussian-hull boundary is ρη,ν∈G1⟺ν≤νc,νc=exp[−2(1−η)(v−1/2)2v2R]. Here v>1/2 is the packet quadrature variance, R the momentum displacement, 0<τ,η<1 the packet weight and transmissivity, and 0≤ν≤1 the coherence visibility. The same membership boundary holds after common-phase averaging for every n≥3. At (v,R,τ,ν,η)=(20,2/9,9/50,1,1/2), each phase-averaged single mode is a Gaussian mixture, while the joint common-phase state lies outside Gn for n≥3. Independent phase averaging instead gives a Gaussian mixture at every block size. These states are separable and Wigner-positive: their difference is carried by phase relations across emissions. 3. The same two-packet source has an explicit finite certificate. Heterodyne phase training, a finite homodyne score and an eight-direction bounded tail test provide a complete certificate for the preceding parameter choice. With ideal Gaussian readout, the sufficient raw acquisition budget and certified errors are nraw=1015+2(4×1015)=9×1015,PFP<3.86×10−22,PFN<0.002068. This conservative budget establishes finite-sample certification of the joint-only resource; it is not an optimised experimental acquisition requirement. The PDF contains the measurement coefficients and complete proof. 4. A complementary two-million-trial implementation. For a displaced lossy single-photon source with unknown common phase, the target conditional state is ωφ=D(eiφ)2∣0⟩⟨0∣+∣1⟩⟨1∣D†(eiφ). A bounded homodyne score uses the full-Gaussian one-photon benchmark 33/(4e), 128 phase candidates and decision threshold 0.490. Including the specified source and readout tolerances, n=2×106,PFP<1.86×10−4,PFN<7.908×10−3. All vacuum emissions, loss events and measurement outcomes count towards the raw budget. This is a separate source family from the two-packet example. Together, the results distinguish unknown common phase from destructive phase randomisation and connect full-model exclusion to explicit Gaussian-measurement scores, error bounds and acquisition costs. The 15-page PDF includes the manuscript, two figures and complete supplementary proofs.
Joint force and coherence constraints are implemented for one specified Gaussian Diósi–Penrose generator in a fixed finite-time protocol. The analysis retains kinetic energy, correlated two-body noise, three-dimensional wave packets, and local decoding followed by tracing out motion. A trusted normalized initial-force bound of 0.995 restricts the common smearing scale from above. Uniformly over the remaining positive scales, the local statistic has Newton mean greater than 0.9965 and DP absolute mean less than 0.4581. An entanglement witness from the same measurement record also has a positive prediction gap greater than 0.03761, but entanglement is not necessary for this model exclusion. The small-smearing argument bounds full coherence blocks by an early completely positive instrument and includes subsequent interacting evolution in the bound. The general force–decoherence principle is known; the contribution is the controlled finite-readout implementation. This is a conditional nonrelativistic theoretical result with trusted ideal preparation, force calibration, and readout, not an empirical exclusion or a general certification of quantum gravity. The companion archive includes the full LaTeX source, standalone Python checks, exact rational certificates, and reproducibility instructions. The work has undergone internal checks, not independent peer review. Generative-AI assistance is disclosed in the paper. Licensing: the manuscript PDF, LaTeX source, documentation and numerical records are licensed under CC BY 4.0. The Python software and its embedded tests are licensed under MIT. These licenses apply to separate file categories, as specified in the companion archive; they are not alternative licenses for every file.
This repository contains the computational reproducibility and verification package accompanying the frozen Version v1.0 manuscript: “Phase Curvature and Assumption-Budgeted Certification in Gravity-Mediated Entanglement.” The associated manuscript develops an operational certification framework for gravity-mediated entanglement experiments. Its central aim is to quantify when an observed entanglement signal excludes a specified neighborhood of local classical-mediator models under explicit assumptions and separately controlled nuisance channels. The package supports the manuscript’s analytical and numerical results concerning: gauge-invariant nonseparable phase curvature for diagonal two-path interactions; exact concurrence and separability-distance formulas for pure two-qubit outputs; assumption-budgeted exclusion bounds around the classical-mediator free class; primal and dual PPT/semidefinite-program certification; finite-shot confidence bounds for experimentally accessible Pauli correlators; certified residual bounds for physically compensated coherent nuisance interactions; stochastic geometry and Casimir–Polder uncertainty budgets; matter-bypass and common-auxiliary-channel bookkeeping; circular-shield mode analysis, including the azimuthal matched-null obstruction; thermal shield-channel factorization; finite-footprint high-mode suppression; an analytic positive high-mode tail bound for the shield benchmark; and a conservative outward-rounded audit of the finite numerical mode block. The frozen manuscript does not claim that a particular experimental apparatus has already closed every systematic-error channel. Quantities such as preparation error, matter-channel leakage, shield-model discrepancy, control error, and readout error remain apparatus-dependent inputs to the certification framework. Package contents The archive includes: the frozen Version v1.0 manuscript source; deterministic verification scripts for the theorem-core identities; finite-shot and Casimir–Polder statistical/geometry checks; shield-mode and analytic-tail verification; conservative floating-point interval/audit checks; submission-interface regression checks; machine-readable verification reports; and a SHA256 manifest for file-integrity verification. All verification scripts distributed with the Version v1.0 package return PASS under the documented software environment. The numerical audit is intended as a transparent reproducibility layer for the stated model calculations. It should not be interpreted as a formal interval-special-function proof or as certification of a realized experimental apparatus.
Given a unitary evolution U on a multipartite quantum system and an ensemble of initial states, how well can U be simulated by local operations and classical communication (LOCC) on that ensemble? We answer this question by establishing a general, efficiently computable upper bound on the maximal LOCC simulation fidelity—what we call an “LOCC inequality.” We then apply our findings to the fundamental setting where U implements a quantum Newtonian Hamiltonian over a gravitationally interacting system. Violation of our LOCC inequality can rule out the LOCCness of the underlying evolution, thereby establishing the nonclassicality of the gravitational dynamics, which can no longer be explained by a local classical field. As a prominent application of this scheme we study systems of quantum harmonic oscillators initialized in coherent states following a normal distribution and interacting via Newtonian gravity, and discuss a possible physical implementation with torsion pendula. One of our main technical contributions is the analytical calculation of the above LOCC inequality for this family of systems. As opposed to existing tests based on the detection of gravitationally mediated entanglement, our proposal works with coherent states alone, and thus it does not require the generation of largely delocalized states of motion nor the detection of entanglement, which is never created at any point in the process. Published by the American Physical Society 2024