An uncertainty relation based study of quantum correlations

Abstract

Quantum mechanics has long been a subject of fascination and intense study, chal lenging our classical intuition and offering unique insights into the behavior of particles at the smallest scales. Among its fundamental principles, the uncertainty principle, as articulated by Heisenberg, lays the groundwork for understanding the limitations of si multaneous measurements of complementary observables. Quantum correlations, such as entanglement, and the emerging concept of quantum synchronization, represent intriguing phenomena that transcend classical boundaries and have the potential to revolutionize information processing and communication technologies. This thesis delves into the mul tifaceted world of quantum correlations, entanglement and quantum synchronization, us ing the framework of uncertainty relations as a guiding light. The first part of this study explores the effect of linear and quadratic coupling on the entanglement and quantum synchronization between two indirectly coupled mechanical oscillators in a double cavity optomechanical system. Our investigation revealed that the quadratic coupling, in partic ular, plays a pivotal role in preserving both entanglement and quantum synchronization simultaneously. Following this findings, in the second part of the thesis, we do a similar analysis in a more generic optomechanical system. This analysis is expected to provide some insight into correlated behavior of synchronization and entanglement. By employ ing uncertainty-based synchronization measure and entanglement criterion, we probed the generalized relation between entanglement and quantum synchronization. This ap proach unveils the intricate connections between the two independent phenomena, offering insights into how the presence of entanglement can facilitate the complete quantum syn chronization. The final part of our research delves into generalized uncertainty relations that extend beyond the traditional position-momentum pair. These extended uncertainty inequalities serve as a foundational tool in understanding the inherent limitations gov erning quantum systems. Moreover, we employ these relations to formulate a stronger uncertainty-based entanglement criterion, providing a fresh perspective on the character ization of entangled bipartite mixed states.