All Abstracts | Poster Abstracts | Talk Abstracts

A generalization of Schur-Weyl duality with applications in quantum estimation

Iman Marvian, University of Southern California

(Session 5 : Thursday from 5:00pm - 7:00pm)

Schur-Weyl duality is a powerful tool in representation theory which has many applications to quantum information theory. We provide a generalization of this duality and demonstrate some of its applications. In particular, we use it to develop a general framework for the study of a family of quantum estimation problems wherein one is given n copies of an unknown quantum state according to some prior and the goal is to estimate certain parameters of the given state. In particular, we are interested to know whether collective measurements are useful and if so to find an upper bound on the amount of entanglement which is required to achieve the optimal estimation. In the case of pure states, we show that commutativity of the set of observables that define the estimation problem implies the sufficiency of unentangled measurements.

Symmetry-Protected Topological Entanglement

Iman Marvian, University of Southern California

(Session 9b : Friday from 5:30pm - 6:00pm)

We propose an order parameter for the Symmetry-Protected Topological (SPT) phases which are protected by an Abelian on-site symmetry. This order parameter, called the SPT entanglement, is defined as the entanglement between A and B, two distant regions of the system, given that the total charge (associated with the symmetry) in a third region C is measured and known, where C is a connected region surrounded by A and B and the boundaries of the system. In the case of 1-dimensional systems we prove that at the limit where A and B are large and far from each other compared to the correlation length, the SPT entanglement remains constant throughout a SPT phase, and furthermore, it is zero for the trivial phase while it is nonzero for all the non-trivial phases. Moreover, we show that the SPT entanglement is invariant under the low-depth local quantum circuits which respect the symmetry, and hence it remains constant throughout a SPT phase in the higher dimensions as well. Finally, we show that the concept of SPT entanglement leads us to a new interpretation of the string order parameters and based on this interpretation we propose an algorithm for extracting the relevant information about the SPT phase of the system from the string order parameters.