A Tensor Version of the Quantum Wielandt Theorem

Mateusz Michałek,Frank Verstraete,Tim Seynnaeve

doi:10.1137/18m1227664

Abstract

We prove boundedness results for the injectivity regions for projected entangled pair states. Our result is a higher-dimensional generalization of the quantum Wielandt inequality.

Highlights

In [8], Sanz et al proved a quantum version of the Wielandt inequality
This theorem was motivated by the study of matrix product states (MPS) and conjectures stated in [5]
In quantum physics the data corresponding to a system is described by a vector in a Hilbert space, or tensor products of these spaces

Summary

Introduction

In [8], Sanz et al proved a quantum version of the Wielandt inequality. This theorem was motivated by the study of matrix product states (MPS) and conjectures stated in [5]. Grids without outgoing edges are used to represent tensors in v∈V Wv. This is done as follows.

Results

Conclusion