Quantum entanglement and its applications in gravitational physics

Abstract

In this work, the definitions and basics of quantum complexities are followed and various works which are done in regards of circuit and Kolmogorov com plexity are studied. Based on these works, calculations with respect to fi delity susceptibility, capacity of entanglement, expected Kolmogorov complex ity have been performed. First law of circuit complexity is calculated by using SYK model Hamiltonian which is also used in calculation of expected Kol mogorov complexity and infinitesimal change in Kolmogorov complexity. So in this way, we tried to build a relation between these two kinds of complex ities. Nielsen’s approach has been followed for the calculation of first law of circuit complexity. In this work we also tried to look for a relation between first law of thermodynamics and Kolmogorov complexity and hence tried to build first law of Kolmogorov complexity. Some open questions have been discussed at the end.