arXiv subjects

Mateo Cárdenes Wuttig

Publications and source records attributed to Mateo Cárdenes Wuttig.

6 recordsLinked to original sources

arXiv2026

More mutually unbiased bases

Mutually unbiased bases (MUBs) describe quantum measurements for which certainty in one basis gives uniform outcomes in the others. Their maximum number remains unknown in dimensions that are not powers of a prime. We introduce an ansatz that, in many dimensions, allows us to construct more MUBs than have previously been found. Each basis in the ansatz consists of a diagonal phase matrix applied to a fixed unitary, which is a tensor product of Fourier matrices and, optionally, any real Hadamard matrix. This construction yields five MUBs in dimension 12, six in dimensions 48, 96, and 192, seven in dimensions 36 and 108, and ten in dimension 648. These bases can then be extended to exceed the tensor product bound, asymptotically, in every eighteenth dimension. Moreover, we show that Paley's real Hadamard matrix can be used to construct $q+1$ bases in dimension $d = q(q+1)$ for every prime power $q\equiv3\pmod4$. This count grows as $\sqrt d$ and cannot be exceeded by tensor products of smaller sets.

quant-ph↗

arXiv2026

How Good Are Frontier Models at Physics? Expert Re-Grading Reveals Broken Evaluations and Near-Saturation of Leading Benchmarks

Low reported scores on leading physics benchmarks, including those featured in the Artificial Analysis Intelligence Index (2026), suggest that frontier language models still struggle with advanced physics, a demanding test of their scientific reasoning and quantitative problem-solving abilities. Yet this impression does not always align with domain experts' experiences using these models in their work. We revisit these reported findings by evaluating frontier models on six widely used physics benchmarks and auditing them with experts, focusing on text-only problems with verifiable final answers. For each subfield of physics, faculty and graduate researchers with relevant expertise carefully review problem statements, reference solutions, and model responses to distinguish genuine model errors from grader errors, incorrect reference solutions, and ambiguous or underspecified questions. Most audited cases initially evaluated as incorrect reflect these benchmarking issues rather than errors in the models' physics reasoning. We then ask experts to address these benchmarking issues by correcting erroneous reference solutions and repairing or excluding flawed questions. We find that GPT-5.6-Sol's measured mean@4 rises from 47.3% to 78.7% on HLE-Physics and from 61.0% to 87.2% on CMT-Benchmark, while its corrected pass@4 reaches 94.4% on the 54 retained CritPt challenges. Corrected scores are computed on the retained evaluation subsets following expert review. Scores on the audited subsets of UGPhysics, PRISM-Physics, and PHYBench also rise substantially after correction. These findings suggest that current benchmarks substantially understate frontier models' ability to solve well-posed physics problems. Near-saturation on these closed-ended tasks highlights the need for more demanding, expert-validated evaluations.

cs.AI↗

arXiv2026

A Complete Classification of Complex Hadamard Matrices of Order Six

Complex Hadamard matrices encode perfectly balanced unitary transformations. Their classification is complete through order five, but order six -- the first dimension in which several continuous families coexist with an isolated solution -- has remained open for decades. Here, we give a complete and exact finite-incidence classification of order-six complex Hadamard matrices up to standard equivalence. We supply the global step missing from Szöllősi's dilation method, which allows us to prove an even stronger version of his conjecture: every complex Hadamard matrix of order six can be recovered algebraically from a suitable, dephased $3 \times 3$ corner defined by four initial phases. We then describe the geometry of the reconstruction from these phases and show that, except for Tao's isolated matrix and a single explicit Karlsson matrix, every class admits a representative obtained by solving one quadratic and one cubic equation in both the horizontal and vertical directions. Our work resolves the classification problem and provides a rigorous framework for further investigating order-six Hadamards, with applications to balanced six-mode interferometers and the study of mutually unbiased bases.

quant-ph↗

arXiv2026

Probing Impurity Quantum Criticality with Entanglement Witnesses

Entanglement is a defining feature of quantum mechanics, and its relation to quantum criticality is of considerable current interest. Here we show that measurable spin and charge fluctuations provide an entanglement witness of quantum criticality in the two-impurity Kondo model, which has experimental realizations in terms of coupled quantum dots and magnetic impurities added to surfaces. We use density-matrix renormalization group and numerical renormalization group calculations to resolve the non-Fermi-liquid critical point separating two independently Kondo-screened impurities from an inter-impurity singlet and interpret it as a change in the dominant entanglement partner of each local moment: from entanglement of the local moment with an extended set of conduction-electron degrees of freedom to entanglement with the other impurity. This reorganization is accompanied by a singular response of the impurity-bath entanglement and the inter-impurity susceptibility. We show how the same structure is encoded in the quantum Fisher information of collective spin and charge operators at zero and finite temperatures, connecting the entanglement picture to experimentally accessible dynamical response functions. Our results establish impurity systems as controlled settings in which quantum-critical entanglement can be detected through measurable correlations, and provide further insight into the possibility of understanding heavy-fermion physics in terms of entanglement.

cond-mat.str-el↗

arXiv2026

Machine Learning Green's Functions of Strongly Correlated Hubbard Models

We demonstrate that a machine learning framework based on kernel ridge regression can encode and predict the self-energy of one-dimensional Hubbard models using only mean-field features such as static and dynamic Hartree-Fock quantities and first-order GW calculations. This approach is applicable across a wide range of on-site Coulomb interaction strengths $U/t$, ranging from weakly interacting systems ($U/t \ll 1$) to strong correlations ($U/t > 8$). The predicted self-energy is transformed via Dyson's equation and analytic continuation to obtain the real-frequency Green's function, which allows access to the spectral function and density of states. This method can be used for nearest-neighbor interactions $t$ and long-range hopping terms $t'$, $t''$, and $t'''$.

cond-mat.str-el↗

arXiv2026

From One to Two Dimensions: Magnetic Phases in Weakly Coupled Spin Ladders

A large variety of materials can be approximately described by means of spin-1/2 Heisenberg ladders. Here, the Density Matrix Renormalization Group (DMRG) algorithm together with a previously established numerical self-consistent mean-field approximation is used to investigate the magnetic properties of spin ladders coupled in a second dimension. The full ground state phase diagram including spin-gapped, antiferromagnetic, ferrimagnetic and fully polarized phases is presented as a function of interladder and intraladder coupling and magnetic field. Measurement of the dependence of magnetization on applied magnetic field is shown to enable location of a material on the phase diagram and determination of the Hamiltonian parameters. These results provide a practical route toward identifying and characterizing magnetic materials composed of coupled spin ladders.

cond-mat.str-el↗