TY - JOUR T1 - Efficient Direct Tomography for Matrix Product States Y1 - 2010 A1 - Olivier Landon-Cardinal A1 - Yi-Kai Liu A1 - David Poulin AB - In this note, we describe a method for reconstructing matrix product states from a small number of efficiently-implementable measurements. Our method is exponentially faster than standard tomography, and it can also be used to certify that the unknown state is an MPS. The basic idea is to use local unitary operations to measure in the Schmidt basis, giving direct access to the MPS representation. This compares favorably with recently and independently proposed methods that recover the MPS tensors by performing a variational minimization, which is computationally intractable in certain cases. Our method also has the advantage of recovering any MPS, while other approaches were limited to special classes of states that exclude important examples such as GHZ and W states. UR - http://arxiv.org/abs/1002.4632v1 ER -