Energy-based entanglement detection and the thermodynamic significance of quantum Fisher information

Abstract

Abstract Establishing a concrete link between quantum information measures and thermodynamic quantities remains a significant challenge in contemporary research. This paper presents novel contributions exploring three key aspects. First, we investigate the relationship between quantum Fisher information (QFI) and work and heat exchange during a feedback control measurement cycle, unveiling a quantitative interplay between energy and information. Second, we demonstrate the behavior of heat exchange with the environment at the point of maximum estimation precision, and a direct relation that links the von Neumann entropy in systems with a large number of microstates with the precision of the estimation through QFI, shedding light on the thermodynamic signature of optimal quantum parameter estimation, bridging quantum metrology, and statistical thermodynamics in the context of high-dimensional stochastic systems. Finally, we propose a method for detecting entanglement based on thermodynamic work, introducing a framework to identify entanglement through energy considerations in a quantum system. Together, these findings advance our understanding of the intersection between quantum information theory and quantum thermodynamics, providing an additional foundation for future research.