arXiv subjects

Andrés Macho Ortiz

Publications and source records attributed to Andrés Macho Ortiz.

4 recordsLinked to original sources

arXiv2026

Emergence of the Partial Trace from Classical Probability Theory

The partial trace is commonly introduced in quantum mechanics as an algebraic operation used to define reduced states of composite systems. However, the probabilistic origin of this operation goes systematically unnoticed in the literature. Here, we show that the partial trace emerges naturally from the requirement of consistency between the Born rule for measurement probabilities and the classical marginalization of probability mass functions. Starting from the classical marginalization rule relating joint and marginal probability distributions, we impose that the reduced density operator of a subsystem must reproduce the local measurement statistics derived from the global state. We show that this requirement directly leads to the standard expression of the partial trace. From this perspective, the reduced density operator appears not as an ad hoc algebraic construction, but as a natural consequence of the probabilistic structure of quantum mechanics.

quant-ph↗

arXiv2025

Analog Programmable-Photonic Information

The limitations of digital electronics in handling real-time matrix operations for emerging computational tasks - such as artificial intelligence, drug design, and medical imaging - have prompted renewed interest in analog computing. Programmable Integrated Photonics (PIP) has emerged as a promising technology for scalable, low-power, and high-bandwidth analog computation. While prior work has explored PIP implementations of quantum and neuromorphic computing, both approaches face significant limitations due to misalignments between their mathematical models and the native capabilities of photonic hardware. Building on the recently proposed Analog Programmable-Photonic Computation (APC) - a computation theory explicitly matched to the technological features of PIP - we introduce its critical missing component: an information theory. We present Analog Programmable-Photonic Information (API), a mathematical framework that addresses fundamental concepts beyond APC by examining the amount of information that can be generated, computed and recovered in a PIP platform. API also demonstrates the robustness of APC against errors arising from system noise and hardware imperfections, enabling scalable computation without the extensive error-correction overhead required in quantum computing. Together, APC and API provide a unified foundation for on-chip photonic computing, offering a complementary alternative to digital, quantum and neuromorphic paradigms, and positioning PIP as a cornerstone technology for next-generation information processing.

physics.optics↗

arXiv2019

Optical Supersymmetry in the Time Domain

Originally emerged within the context of string and quantum field theory, and later fruitfully extrapolated to photonics, the algebraic transformations of quantum-mechanical supersymmetry were conceived in the space realm. Here, we introduce a paradigm shift, demonstrating that Maxwell's equations also possess an underlying supersymmetry in the time domain. As a result, we obtain a simple analytic relation between the scattering coefficients of a large variety of time-varying optical systems and uncover a wide new class of reflectionless, three dimensional, all-dielectric, isotropic, omnidirectional, polarization-independent, non-complex media. Temporal supersymmetry is also shown to arise in dispersive media supporting temporal bound states, which allows engineering their momentum spectra and dispersive properties. These unprecedented features define a promising design platform for free-space and integrated photonics, enabling the creation of a number of novel reconfigurable reflectionless devices, such as frequency-selective, polarization-independent and omnidirectional invisible materials, compact frequency-independent phase shifters, broadband isolators, and versatile pulse-shape transformers.

physics.optics↗

arXiv2018

Ultra-short Pulse Propagation in Nonlinear Optics

In this work, we perform a detailed review about the theoretical modeling of the optical propagation of ultra-short pulses in different scenarios of nonlinear optics. In particular, we focus our efforts on optical fibers and uniform media, with special attention on the white light continuum generation by using gases.

physics.optics↗