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Alexander Trifanov

Publications and source records attributed to Alexander Trifanov.

5 recordsLinked to original sources
arXiv2026

Changing Pedagogical Paradigms: Integrating Generative AI in Mathematics to Enhance Digital Literacy through 'Mathematical Battles with AI'

This paper introduces `Math Battles with AI', an innovative competitive format designed at ITMO University to redefine the role of generative AI in mathematics education. Moving away from a purely defensive stance, the authors propose an AI agent with intentionally increased hallucination likelihood in specific modes to train verification skills. We describe the three-stage tournament structure and a specialized assessment system that rewards critical verification over blind reliance. Initial results indicate a significant shift in student mindsets, fostering essential skills in digital hygiene and prompt engineering. This work serves as a practical guide for academic institutions aiming to leverage AI for enhancing, rather than undermining, intellectual development.

cs.HC↗
arXiv2013

Reduced conditional dynamic of quantum system under indirect quantum measurement

In this report, we study the reduced conditional dynamics of a quantum system in the case of indirect quantum measurement. The detectors microscopic part (pointer) interacts with the measured system (target) and the environment, which results in a nonunitary interaction between target and pointer. The quantum state evolution conditioned by the measurement result is under investigation. Particularly, we are interested in explicit analytical expressions for the conditional evolution superoperators and basic information characteristics of this measurement process, which is applied to the cavity mode photodetection problem.

quant-ph↗
arXiv2013

Indirect Measurement Process Parameterized by Nonunitary System - Pointer Interaction

An indirect quantum state measurement process is under investigation. Common evolution of detector's microscopic part (pointer) and measured system (target) is considered to be nonunitary due to the interaction between pointer and environment. System of differential equations for superoperators, which map initial target state to it's conditional final state is obtained. Developed formalism is applied to the problem of cavity quantum mode photodetection to investigate basic information characteristics of this measurement process.

quant-ph↗
arXiv2012

The Photodetection Process under the Conditions of an Imperfect Measurement Device

The process of cavity mode quantum state photodetection subject to a nonideal measurement device is under consideration. A set of nonorthogonal probabilistic operator valued measures (POVMs) describing the photodetection process is suggested. The superoperators of conditional system evolution and their Kraus representations are obtained. Developed formalism is used to the quantum state reconstruction problem. We recalculate the probabilities of hypotheses about the initial state of cavity quantum mode in the case of unknown superposition of vacuum and single photon states.

quant-ph↗