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We demonstrate how to simulate both discrete and continuous stochasticevolution of a quantum many body system subject to measurements using matrixproduct states. A particular, but generally applicable, measurement model isanalyzed and a simple representation in terms of matrix product operators isfound. The technique is exemplified by numerical simulations of theanti-ferromagnetic Heisenberg spin-chain model subject to various instances ofthe measurement model. In particular we focus on local measurements with smallsupport and non-local measurements which induces long range correlations.

Simulating local measurements on a quantum many body system with stochastic matrix product states