Certification of classical and quantum processes with information theory: Markovianity and Causality

• Grant number: 24/06972-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: November 01, 2024
• End date: October 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Celso Jorge Villas-Bôas
• Grantee: Matheus Capela
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 22/00209-6 - Second generation quantum technologies, AP.TEM

Abstract

The certification of properties of temporal processes is crucial for the development and use of new quantum technologies. This project will develop techniques for the analysis and witness of classical and quantum processes incompatible with Markovian and causal models.Quantum processes can have non-trivial temporal correlations through interactions between system and environment, these processes being called non-Markovian. However, the possibility of the existence of quantum processes that are not compatible with a well-defined causal structure is also currently considered.The proposed research project aims to develop techniques for detecting processes incompatible with Markovianity and well-defined causal order through local interventions on quantum systems. Given the recent technological developments in quantum computing devices, this project is of fundamental relevance and can serve as an application for detecting time-correlated errors in the implementation of quantum algorithms.Specifically, given access to local action in a classical or quantum temporal process, we intend to determine necessary conditions for the Markov model, and also for processes with a defined causal order. In this way, such conditions can be used as witnesses of non-Markovianity, and respectively, witnesses of non-causality.In this project we propose to develop techniques based on information theory methods to analyze the aforementioned problem.