Dr. Hastings has a body of work based on Lieb-Robinson bounds for the dynamics of quantum spin systems and lattice fermions that has been transformative in the sense that it has opened up new approaches to make progress on important problems in condensed matter physics. His work provides new insights in the (classical) computability of ground states and equilibrium states of standard Hamiltonians of condensed matter physics. His ideas of using Lieb-Robinson bounds to mathematically replace locality in QFT and to use it to prove exponential decay of correlations and a higher dimensional Lieb-Schultz-Mattis theorem are also examples of his ability to bring important new insights to bear on old quesions.

His proof of what is known as the area law for the local entropy in the ground state of gapped spin chains is another piece of work in the interface between quantum information, computation, and basic questions in many-body physics.

In September 2008, he literally stunned the quantum information community with a very different piece of work that solved a long standing question about additivity of certain quantities under tensor products of quantum channels. This question (or, more properly, a group of conjectures shown to be equivalent by Shor in 2003) was open despite concerted efforts by such luminaries as Shor, Holevo, King, and many others during the past 10-15 years. Hastings showed that the conjectures are false not by constructing explicit counter-examples, but by showing the existence of counter-examples by a very delicate probabilistic argument. Rather than ending the question, Hastings results show that there are pairs of quantum channels for which entangled inputs can improve the transmission of classical information, raising interesting new questions.

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