Certified boundary-magic witness for state-dependent proto-area in a holographic code

• URL: http://arxiv.org/abs/2607.10663v1
• Date: Sun, 12 Jul 2026 09:16:46 GMT
• Title: Certified boundary-magic witness for state-dependent proto-area in a holographic code
• Abstract summary: We study a four-qubit product-EPR holographic code whose reconstructing region contains matter and one leg of a geometry bond.<n>We show that only matter-controlled bond motion produces a leading quadratic logical-state dependence of the boundary entropy.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study a four-qubit product-EPR holographic code whose reconstructing region contains matter and one leg of a geometry bond. Seven deformations compare local, bipartite, bond-stabilizing, and bond-moving operators. Exact spectra show that only matter-controlled bond motion produces a leading quadratic logical-state dependence of the boundary entropy. We select one state-independent physical recovery by optimizing coherent information of the channel Choi state. A separate semidefinite program maximizes entanglement fidelity over all channels. At fixed coupling the physical recovery attains that optimum to numerical precision, while recovered-entropy subtraction leaves a nonzero variational proto-area response. Total stabilizer Renyi magic is also nonzero for deformations with no boundary response, so it does not characterize the effect. Projecting the exact stabilizer-Renyi quadratic form away from pairwise Pauli tangents defines a leading-order boundary witness. Its global convex minimum is positive for the bond-moving deformation and zero for the six comparisons. For the reference-matter-geometry resource partition, however, pairwise tangents span the full projective tangent space at the product-EPR base, so the witness vanishes for every Hermitian deformation. A two-bound extension retains this degeneracy but exhibits a split-geometry structural residual and a logical-state-dependent cut switch. These results establish a finite-code witness, not a universal magic law or continuum gravitational dynamics.

Related papers

• CyclOT: Learning Quadratic Optimal Transport Maps via Synchronized Forward-Backward Interpolants [20.064386074670605]
  We introduce a bidirectional neural framework in which the learned maps induce forward and backward displacement interpolants.<n>Experiments on Swiss roll, MNIST, CelebA, single-cell data, and chest X-ray images evaluate endpoint fidelity, transport cost inverse, consistency, and the geometry of the induced inverts.
  arXiv  Detail & Related papers  (2026-09-12T11:31:53Z)
• Why Learning Rediscovers the Closed-Form Diagonal Regularizer [3.1822873305165618]
  When truncation noise is isotropic, Tikhonov shape is a closed-form power law Gamma_k proportional to where exponential_k|s| set by the prior alone.<n>Berry's random-wave conjecture decorrelates the truncation noise across modes, and Weyl's eigenvalue counting law supplies enough modes for the conclusion to survive empirical Berry violations.<n>On FEM-simulated acoustic rooms, the closed form is near-optimal relative to perroom tuning across observation windows, and three diagonal architectures trained on the same data match its oracle error within 1
  arXiv  Detail & Related papers  (2026-09-09T03:10:42Z)
• Interior skin focusing and directional mirror transfer in a graded non-Hermitian Krawtchouk network [0.0]
  We study a finite open Krawtchouk network with oppositely graded directed hoppings.<n>For a broad intermediate range of asymmetries, their local imaginary gauge field changes sign in the bulk.
  arXiv  Detail & Related papers  (2026-08-19T10:56:53Z)
• Universal Frame Potential Hierarchy in Critical Projected Ensembles [0.0]
  We show that the projected ensemble of a Tomonaga-Luttinger liquid exhibits a universal nonlinear hierarchy of state overlap moments.<n>Remarkably, the leading scaling exponents are independent of the continuously varying Luttinger parameter.
  arXiv  Detail & Related papers  (2026-08-16T01:23:04Z)
• Floquet-Resolved Dissipation Selects Entanglement Beyond Population Spectroscopy [41.99844472131922]
  We show that two dissipative descriptions of the same parametrically coupled qubits can yield closely similar period-averaged populations.<n>Both retain the complete periodically driven Hamiltonian, the same microscopic bath couplings, and the same physical observables.
  arXiv  Detail & Related papers  (2026-08-12T15:33:26Z)
• Frame-Dependent Traces and the Third-Particle Paradox [45.88028371034407]
  We show that the Paradox of the Third Particle arises when comparing subsystem descriptions across Quantum Reference Tracing perspectives.<n>We argue that our condition captures the Paradox content: rather than imposing consistency on the whole state space, we reproduce exactly the states on which it holds.
  arXiv  Detail & Related papers  (2026-07-23T18:00:01Z)
• CoCurve: Cross-Module Co-Pruning Curvature for Training-Free Structured LLM Pruning [47.406985340436925]
  CoCurve is a calibration-only, fine-tuning-free method that prunes attention and FFN units jointly.<n>It reduces to one budgeted quadratic program, solved in a single shot under a shared attention--FFN budget, with no labels, fine-tuning, or recovery.
  arXiv  Detail & Related papers  (2026-07-20T05:27:57Z)
• Static entanglement structure and adiabatic Bell-state preparation in the tripartite quantum Rabi model [20.740233476359148]
  tripartite quantum Rabi model couples two qubits to a bosonic mode through a collective spin-oscillator interaction.<n>In the zero-detuning limit, the triplet part of the spectrum splits into branches with zero and maximal entanglement.<n>We show how collective spin-oscillator coupling reorganizes spectral entanglement and connects static branch structure to finite-time Bell-state preparation.
  arXiv  Detail & Related papers  (2026-07-11T14:24:18Z)
• Stability Annealing Selects the Implicit Bias of Smoothed Sign Descent: A Rate-Indexed Barrier Path on Separable Data [3.7437735326653883]
  This paper studies the rate-controlled middle case for full-batch linear classification on separable data.<n>For memoryless stability-annealed smoothed-sign descent with weighted exponential loss, we prove that the normalized iterates converge to the minimizer of a convex Burg-type barrier over a margin slice.
  arXiv  Detail & Related papers  (2026-07-07T08:55:35Z)
• The Double Well Done Doubly-Well [0.17188280334580197]
  symmetric double-well potential is one of the simplest quantum-mechanical systems in which perturbative and non-perturbative physics are deeply entangled.<n>Resurgence ties the two features together, organizing the exact spectrum into a single tightly-constrained trans-series.<n>This paper gives a self-contained account of this trans-series from two complementary approaches.
  arXiv  Detail & Related papers  (2026-06-03T18:00:01Z)
• Defect Holonomy Near Rank-Deficient Mixed States [2.679171884680826]
  We investigate the geometry of mixed quantum states near rank-changing points.<n>We show that rank-deficient states form singular boundary strata where the bundle structure degenerates.<n>By restricting to a punctured state manifold that excludes the singular set, we obtain a well-defined gauge structure.
  arXiv  Detail & Related papers  (2026-06-01T14:51:19Z)
• Deforming the Trail: Baseline Quantum Circuitry for $\text{SU(2)}_k$ Lattice Gauge Theory [0.0]
  We provide a strategy of gauge-variant completions to extend unitarity to the entire computational Hilbert space.<n>We show that the physical Hilbert space dimension of the deformed plaquette operator scales equivalently to its non-deformed counterpart with a constant factor.<n>Q-deformation continues to pass scrutiny as a reliable truncation offering advantages in quantum circuit synthesis.
  arXiv  Detail & Related papers  (2026-05-14T17:01:35Z)
• Reasoning on the Manifold: Bidirectional Consistency for Self-Verification in Diffusion Language Models [30.607422839762553]
  Bidirectional Manifold Consistency (BMC) is a training-free, unsupervised metric.<n>BMC serves as a robust discriminator of solution validity without ground truth answer.<n>Our results establish intrinsic geometric stability as a robust indicator of correctness for dLLMs.
  arXiv  Detail & Related papers  (2026-04-17T10:17:16Z)
• Kinematic budget of quantum correlations [0.0]
  We introduce a local-unitary-invariant budget split of symmetrised second moments into local and nonlocal sectors.<n>By coarse-graining over gauge-like first moments, the budget geometry acts as a thermodynamic phase diagram.
  arXiv  Detail & Related papers  (2026-03-04T09:40:02Z)
• Hinge Regression Tree: A Newton Method for Oblique Regression Tree Splitting [18.562483381753804]
  We present the Hinge Regression Tree (HRT), which reframes each split as a non-linear least-squares problem over two linear predictors.<n>We analyze this node-level optimization and, for a backtracking line-search variant, prove that the local objective decreases monotonically and converges.<n>We show on synthetic and real-world benchmarks that HRT matches or outperforms single-tree baselines with more compact structures.
  arXiv  Detail & Related papers  (2026-02-05T06:49:01Z)
• Deterministic Zeroth-Order Mirror Descent via Vector Fields with A Posteriori Certification [45.85698554568285]
  We develop a deterministic zeroth-order mirror descent framework by replacing gradients with a general vector field.<n>Our analysis provides an evaluation template for last-rate inequality evaluations.<n>Together, these results expose a hidden geometric linking Bregman identities, deterministic certification, and robust conic geometry in zeroth-order mirror descent.
  arXiv  Detail & Related papers  (2026-01-31T10:05:05Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.