A discourse on entanglement and its detection in finite dimensions

Abstract

We explore procedures to detect entanglement of unknown mixed states, which can be experimentally viable. The heart of the method is a hierarchy of semi-definite programs, which provides sufficient conditions to entanglement. Our numerical investigations indicate that the entanglement is detected with a cost which is much lower than full state tomography. The procedure is applicable to both free and bound entanglements and involves only single copy measurements. The discourse involves density matrices and its properties, quantum manipulations, entanglement and its detection.