Extraction of product and higher moment weak values: Applications in quantum state reconstruction and entanglement detection

Abstract

Weak values of product observables or higher moments of an observable are informationally significant because of their ability to solve some paradoxes, realise strange quantum effects, reconstruct density matrices, etc. In this work, we demonstrate that pairwise orthogonal post-selections can be used to obtain higher moment weak values. By measuring only local weak values (defined as single system weak values in a multipartite scenario), product weak values can be obtained. As applications, we use product and higher moment weak values to reconstruct quantum states showing advantages over previous works in terms of number of required measurement operators and experimental feasibility. Additionally, a necessary separability criteria is given using product weak values to detect entanglement. For some classes of entangled states, positive partial transpose (PPT) criteria is achieved by cleverly choosing product observables and post selections. Robustness of our method against inappropriate choices of observables and noisy post-selections is also discussed.