arXiv subjects

E. A. Ramirez Trino

Publications and source records attributed to E. A. Ramirez Trino.

4 recordsLinked to original sources

arXiv2026

The Pauli Probability Spectrum Carries the Pure-State Quantum Fisher Metric

How a quantum state responds to small parameter changes underlies state distinguishability, many-body response, and metrological sensitivity. The Pauli probability spectrum provides a natural description of many-body quantum states, but it is not evident how much of this response survives in the corresponding classical distribution. Here we show that, for pure states, the complete labeled Pauli distribution retains the full local metric of the pure-state manifold, reproducing the quantum Fisher metric up to a fixed normalization. This correspondence has a direct measurement realization: preparing a state together with its complex conjugate and performing pairwise Bell measurements between corresponding degrees of freedom converts the quantum response into an ordinary classical distribution without losing any of the sensitivity available in the two inputs. The readout is fixed, factorizes into local pairwise measurements even for strongly entangled many-body states, and preserves the response along all parameter directions simultaneously. We trace this correspondence to the reality of the underlying operator amplitudes and show that the same mechanism extends beyond qubits. When the correspondence fails, we identify explicitly where the missing information resides: part of the response can remain hidden in phases for identical-copy and complex-coordinate readouts, while mixed states develop transverse operator-space motion that is invisible to the Bell probabilities. These results provide a direct link between Pauli/Bell statistics, many-body response, nonstabilizerness, and quantum geometry.

quant-ph↗

arXiv2026

Equivalence of Stabilizer and Shannon Rényi Entropies: Exact Results for Quantum Critical Chains

Shannon-Rényi and stabilizer entropies are key diagnostics of structure, ``nonstabilizerness,'' phase transitions, and universality in quantum many-body states. We establish an exact correspondence for quadratic fermions: for any Gaussian eigenstate, the stabilizer Rényi entropy equals the Shannon-Rényi entropy of a number-conserving free-fermion eigenstate on a doubled system, evaluated in the computational basis. Specializing to the transverse-field Ising (TFI) chain, the TFI ground-state stabilizer entropies map to the Shannon-Rényi entropies of the XX-chain ground state of length $2L$. Building on this correspondence, together with other exact identities we prove, we derive closed expressions for the stabilizer entropy at indices $α=\tfrac{1}{2},2,4$ for a broad class of critical closed free-fermion systems. Each of these can be written with respect to the universal functions of the TFI chain. We further derive conformal-field-theory scaling laws for the stabilizer entropy at arbitrary Rényi index under both periodic and open boundary conditions. At $α=4$, these scaling forms display a discontinuity for both open and periodic boundary conditions.

quant-ph↗

arXiv2026

Universal Crossovers of Stabilizer Entropy Beyond Criticality

Stabilizer Rényi entropy has emerged as a probe of nonstabilizerness in quantum many-body systems, but its scaling structure beyond critical points remains poorly understood compared with entanglement entropy. Recent field-theory approaches indicate that stabilizer entropy contains universal critical data and boundary-sensitive terms, raising the question of how these structures extend into massive and crossover regimes. We address this problem for a broad class of finite-range spin chains at Rényi index one-half. We derive exact finite-size formulas for both full periodic chains and finite intervals of the infinite chain, making the universal crossover from critical to noncritical behavior analytically accessible. In periodic geometry, the entropy obeys a volume law away from criticality and exhibits a universal finite-size crossover controlled by the competition between system size and correlation length. We also show that the large-scale SRE density develops a cusp across the field-tuned critical line, while the XX endpoint is governed by a distinct scaling regime associated with the saturation point. In the subsystem geometry, the interval entropy separates bulk critical behavior from boundary contributions generated by the way the finite region cuts the infinite chain. The crossover from critical to massive behavior is then encoded in boundary constants and universal functions controlled by the correlation length. Through exact stabilizer-entropy correspondences, the scaling theory extends to internal XY reductions, Finite-range spin chains, and Cluster--Ising representatives. Our results provide an exact lattice benchmark for the emerging QFT description of stabilizer entropy beyond isolated conformal points.

quant-ph↗

arXiv2025

A Generalized Grassmann-Pfaffian Framework for Monomer-Dimer and Spanning Trees

We develop a unified framework for Berezin integrals over Grassmann variables that establishes master identities for exponential quadratic fermionic forms and linear fermionic forms coupled to both bosonic and fermionic sources. The construction is rigorous for both real and complex fermions in arbitrary dimensions and remains well-defined even when the underlying matrices are singular. Our main mathematical results appear in two master theorems. Theorem 12 provides a comprehensive identity for Berezin integrals over Grassmann variables for real fermions with mixed bosonic-fermionic sources, applicable to any antisymmetric matrix. Its complex analogue, Theorem 13, yields corresponding determinant-based representations. Together, they serve as generating functionals for a wide range of combinatorial and physical models. Key applications include the dimer, monomer-dimer, matching, and almost-matching problems. We revisit the Kasteleyn theorem for planar dimers using Berezin integrals. We construct monomer-dimer systems through the \textit{Monobisyzexant (Mbsz)} function, which generalizes the Hafnian to incorporate monomer contributions and admits a Pfaffian-sum representation for planar graphs (Theorem 5); and practical techniques for handling singular matrices via unitary block decomposition (Theorem 6) and spectral analysis. We further present explicit mappings between Hafnians and Pfaffians and their submatrix generalizations (Hafnianinhos and Pfaffianinhos); an alternative source-ordered Berezin integral representation for spanning trees and forests using complex bosonic sources that regularizes the Laplacian zero mode (Theorem 10). Overall, this work offers a flexible toolkit for the theoretical analysis and computational implementation of graph-based models and lattice field theories using Berezin integrals over Grassmann variables .

cond-mat.stat-mech↗