arXiv subjects

José J. Gil

Publications and source records attributed to José J. Gil.

14 recordsLinked to original sources

arXiv2026

Intrinsic Pointer Basis and Irreversible Classicality from Coherence Contraction

This work analyzes an operational route to classical behavior for reduced quantum states using the intrinsic reference basis (IRB). Relative to a fixed physical conjugation, the IRB separates intrinsic populations from a real antisymmetric cohesion sector. A globally bounded cohesion index is defined and its exponential contraction is proved for phase-free dephasing dynamics aligned with the IRB; for general aligned dephasing, the corresponding modulus-based coherence functional contracts at the same computable rates. The results provide distance bounds to the IRB-diagonal description and a logarithmic upper bound on the time required to reach a prescribed experimental tolerance. The IRB projectors constitute state-derived candidate pointer sectors, and they become dynamically stable pointer sectors when the effective dephasing generator is aligned with them and damps the relevant inter-sector coherences. Degenerate population sectors lead naturally to block-classicality and protected intra-block coherence. In a two-level active sector, the cohesion index equals fringe visibility, giving a direct interferometric test of the contraction law. The construction is independent of any spacetime- or unification-emergence hypothesis and is intended as a channel-level complement to environment-induced einselection.

quant-ph↗

arXiv2026

Cohesion accounting of complementarity in path--polarization interferometry

Two-path complementarity in polarized interferometric fields is reconsidered by retaining the complete path--polarization density matrix instead of reducing the description to the path degree of freedom from the outset. The familiar relation connecting the Cartesian visibility components, path predictability, and reduced-state mixedness is recovered as a marginal consequence of the reduced path state and is not interpreted as a new complementarity law. Attention is focused instead on the full path--polarization description in a real reference basis adapted to the path and linear-polarization degrees of freedom. Within this framework, the normalized purity separates naturally into path, polarization, and path--polarization-correlation contributions, while the antisymmetric sector provides a sector-resolved measure of cohesion. The resulting decomposition identifies which parts of the complete state store phase-sensitive interferometric coherence and which contributions are removed when polarization is traced out. The formalism therefore provides a sector-resolved accounting of complementarity within the full path--polarization state and clarifies the connection between reduced visibility loss, polarization marking, path--polarization correlations, and quantum-eraser recovery. The present article establishes the framework and associated purity decomposition; a more detailed exploration of full path--polarization complementarity and its dynamical aspects is left for future work.

quant-ph↗

arXiv2026

Electromagnetic polarization matrix and its physical interpretation

Despite the intrinsic coupling between electric and magnetic fields in random stationary light, their polarization properties are not mutually determined. A complete second-order description thus necessitates a joint electromagnetic treatment. The 6x6 electromagnetic polarization matrix introduced here generalizes the conventional electric 3x3 matrix by incorporating both electric and magnetic contributions together with their mutual correlations. It consists of diagonal 3x3 blocks, representing the electric and magnetic polarization matrices, and off-diagonal 3x3 blocks that encode the full structure of electric-magnetic cross-correlations. The information contained in this matrix can be interpreted through physically meaningful quantities such as active and reactive energy fluxes, in-phase and quadrature alignment matrices, and global indices describing electric-magnetic coupling. The formalism is applied to a field composed of two orthogonally propagating plane waves sharing a common linear electric polarization (a simple yet physically realizable configuration) that demonstrates the need for a general combined electric-magnetic representation even in free space. This approach provides a comprehensive and unified framework for characterizing electromagnetic polarization beyond the electric-field description alone, bridging classical statistical optics with quantum-like density-matrix interpretations.

physics.optics↗

arXiv2026

Population-coherence routes to purity in Page-type models of black-hole evaporation

We revisit the black-hole information problem from the viewpoint of a population-coherence decomposition of density-matrix purity. Building on a previously developed formalism for ndimensional density matrices, we characterize each state by a normalized global purity index and two complementary indices, which quantify the contributions of level populations and coherences. This yields a simple quadratic relation and a geometric representation in a population-coherence plane, where different routes to purity can be distinguished. In the two-level case we construct explicit families of states with identical spectra and global purity but opposite internal structure, realizing population-dominated and coherence-dominated routes. We then apply this framework to a standard Page-type evaporation model without an explicit Hamiltonian, in which a black hole and its Hawking radiation form a bipartite pure state with varying Hilbert-space dimensions. Using known results for typical reduced states in large dimensions, we analyze the behavior of population and coherence components of purity along the evaporation process. Under the physically motivated requirement that, in this energy-free setting, the radiation populations remain nearly uniform in the chosen basis, we show that the late-time recovery of purity must be coherence-dominated: the global purity of the radiation approaches unity while the population index stays small and the coherence index carries essentially all the purity.

gr-qc↗

arXiv2026

Antisymmetric Mueller generator as the universal origin of geometric phase in classical polarization and quantum two-level systems

We show that the antisymmetric Mueller generator provides a universal algebraic kernel for geometric phase in classical polarization optics and in quantum two-level systems. For any ideal retarder, the antisymmetric 3x3 block of its Mueller matrix (the antisymmetric generator of the adjoint SU(2) action on the Stokes vector) encodes the angular-velocity vector that drives the tangential motion on the Poincaré sphere and fully determines the Pancharatnam-Berry phase, while the symmetric block is geometrically neutral. The same antisymmetric generator governs the evolution of pure qubit states on the Bloch sphere. This unified viewpoint yields operational criteria to identify and control geometric-phase contributions from measured Mueller matrices and from qubit process tomography.

physics.gen-ph↗

arXiv2025

Spectral Bounds on Entropy and Ergotropy via Statistical Effective Temperature in Classical Polarization and Quantum Thermal States

We formulate a unified definition of the statistical effective temperature (SET) for finite-dimensional classical and quantum systems using dimension-dependent indices of purity derived from the eigenvalue spectrum. This spectral approach bypasses the need for Hamiltonians or energy gaps and remains applicable to both quantum density matrices and classical polarization coherency matrices. The SET framework naturally describes the divergence of inverse temperature near pure, non-degenerate states, consistent with the third law. Using entropy-SET diagrams, we explore spectral bounds in two-, three-, and four-level systems, which reveal physically realizable entropy regions, rank-dependent constraints, and cusp-like features. A Hamiltonian-free parametric spectrum ansatz provides a universal reference curve within these bounds. Furthermore, we derive spectral bounds on ergotropy as a function of entropy and SET, which quantify the maximum extractable work under passive constraints and introduce the notion of structured-states, engineered spectral configurations that saturate these bounds. Our analysis shows that SET serves as a thermodynamically meaningful and operationally relevant quantity for bounding entropy and ergotropy in both classical polarization systems and quantum thermal states.

quant-ph↗

arXiv2021

Information structure and general characterization of Mueller matrices

Linear polarimetric transformations of light polarization states by the action of material media are fully characterized by the corresponding Mueller matrices, which contain in an implicit and intricate manner all measurable information on such transformations. The general characterization of Mueller matrices relies on the nonnegativity of the associated coherency matrix, which can be mathematically formulated through the nonnegativity of its eigenvalues. The enormously involved explicit algebraic form of such formulation prevents its interpretation in terms of simple physical conditions. In this work, a general and simple characterization of Mueller matrices is presented based on their statistical structure. The concepts associated with the retardance, enpolarization and depolarization properties as well as the essential coupling between the two latter are directly described in the light of the new approach.

physics.optics↗

arXiv2020

Coherency vector formalism for polarimetric transformations

Despite the virtues of Jones and Mueller formalisms for the representation of the polarimetric properties, for some purposes in both Optics and SAR Polarimetry, the concept of coherency vector associated with a nondepolarizing medium has proven to be an useful mathematical structure that inherits certain symmetries underlying the nature of linear polarimetric transformations of the states of polarization of light caused by its interaction with material media. While the Jones and Mueller matrices of a serial combination of devices are given by the respective conventional matrix products, the composition of coherency vectors of such serial combinations requires a specific and unconventional mathematical rule. In this work, a vector product of coherency vectors is presented that satisfies, in a meaningful and consistent manner, the indicated requirements. As a result, a new algebraic formalism is built where the representation of polarization states of electromagnetic waves through Stokes vectors is preserved, while nondepolarizing media are represented by coherency vectors and general media are represented by coherency matrices generated by partially coherent compositions of the coherency vectors of the components.

physics.optics↗

arXiv2020

Polarimetric characterization of light and media

An analysis of the matrix models representing the polarimetric properties of light and material media is carried out by using the concept of the coherency matrix, which leads to the identification and definition of their corresponding physical quantities. For light, cases of homogeneous and inhomogeneous wavefront are analyzed, and a model for 3D polarimetric purity is formulated. For linear passive material media, a general model is developed on the basis that any physically realizable linear transformation of Stokes vectors is equivalent to an ensemble average of passive, deterministic, nondepolarizing transformations. Through this framework, the relevant physical quantities, including the indices of polarimetric purity, are identified and decoupled. Some decompositions of the whole system into a set of well-defined components are considered, as well as techniques for isolating the unknown components by means of new procedures for subtracting coherency matrices. These results and methods constitute a powerful tool for analyzing and exploiting experimental and industrial polarimetry. Some particular application examples are indicated.

physics.optics↗

arXiv2020

Degrees of mutual coherence of a 3D polarization state

The absolute values of the three degrees of mutual coherence between the analytic signals representing the components of the electric field of a given three-dimensional (3D) polarization state are relative quantities that depend on the laboratory reference frame considered. The extremal values for the said absolute values are determined and analyzed. The reduction to the well-known conventional 2D case is retrieved in a natural way.

physics.optics↗

arXiv2020

Arbitrary decomposition of a Mueller matrix

Mueller polarimetry involves a variety of instruments and technologies whose importance and scope of applications are rapidly increasing. The exploitation of these powerful resources depends strongly on the mathematical models that underlie the analysis and interpretation of the measured Mueller matrices and, very particularly, on the theorems for their serial and parallel decompositions. In this letter, the most general formulation for the parallel decomposition of a Mueller matrix is presented, which overcomes certain critical limitations of the previous approaches. In addition, the results obtained lead to a generalization of the polarimetric subtraction procedure and allow for a formulation of the arbitrary decomposition that integrates, in a natural way, the passivity criterion.

physics.optics↗

arXiv2019

Retarding parallel components of a Mueller matrix

Mueller matrix polarimetry constitutes a nondestructive powerful tool for the analysis of material samples that is used today in an enormous variety of applications. Depolarizing samples exhibit, in general, a complicated physical behavior that requires appropriate mathematical formulation through models involving decomposition theorems in terms of simpler components. In this work, the general conditions for identifying retarding incoherent components of a given Mueller matrix M are obtained. It is found that when the coherency matrix C associated with M has rank C = 3,4 it is always possible to identify one or two retarding incoherent components respectively, while in the case where rank C =2, such retarding component only can be achieved if and only if the diattenuation and the polarizance of M are equal. Since the Mueller matrices associated with retarders have a simple structure, the results obtained open new perspectives for the exploitation of polarimetric techniques in optics, remote sensing and other areas.

physics.optics↗

arXiv2019

Characterization of passivity in Mueller matrices

Except for very particular and artificial experimental configurations, linear transformations of the state of polarization of an electromagnetic wave result in a reduction of the intensity of the exiting wave with respect to the incoming one. This natural passive behavior imposes certain mathematical restrictions on the corresponding Mueller matrices associated to the said transformations. Although the general conditions for passivity in Mueller matrices were presented in a previous paper [J. J. Gil, J. Opt. Soc. Am. A 17, 328-334 (2000)], the demonstration was incomplete. In this paper, the set of two necessary and sufficient conditions for a Mueller matrix to represent a passive medium are determined and demonstrated on the basis of its arbitrary decomposition as a convex combination of nondepolarizing and passive pure Mueller matrices. The procedure followed to solve the problem provides also an appropriate framework to identify the Mueller matrix that, among the family of proportional passive Mueller matrices, exhibits the maximal physically achievable intensity transmittance. Beyond the theoretical interest on the rigorous characterization of passivity, the results obtained, when applied to absolute Mueller polarimetry, also provide a criterion to discard those experimentally measured Mueller matrices that do not satisfy the passivity criterion.

physics.optics↗

arXiv2016

Two-vector representation of a nondepolarizing Mueller matrix

A geometric view of the polarimetric properties of a nondepolarizing medium is presented by means of a pair of vectors in the Poincaré sphere. An alternative representation constituted by a set of vectors contained in the equatorial plane of the Poincaré sphere is also defined and interpreted. The analyses of the magnitudes and relative orientations of the constitutive vectors of such simple representations allow for a classification of nondepolarizing media.

physics.optics↗