Relating quantum information aspects of quantum mechanics and gravity
ABSTRACT :
This seminar is a part of the activities of Center for Quantum Information Theory of Spacetime and Matter of IIT Madras
I will present two recent works of our Wuerzburg group on this subject. First, I will present a relation between entanglement in simple quantum mechanical qubit systems and in wormhole physics as considered in the context of the AdS/CFT correspondence. In both cases, states with the same entanglement structure, indistinguishable by any local measurement, nevertheless are characterized by a different Berry phase. This feature is experimentally accessible in coupled qubit systems. I will also give a group-theory argument highlighting the different factorisation properties of the two-qubit system and the wormhole. The second project is devoted to extending the Nielsen geometric approach operator complexity to the SU(N) group and considering the large N limit. This is motivated by the aim of constructing a gravity dual for computational complexity. We implement the Euler-Arnold approach to identify incompressible inviscid hydrodynamics on the two-torus as a novel effective theory for the evaluation of operator complexity for large qudits. I will discuss the ergodicity properties of our result. Based on 2109.01152 and 2109.06190