Downloads & Free Reading Options - Results

How efficiently can the ground state of a local Hamiltonian be computed? This is a question that lies at the heart of an emerging area called quantum Hamiltonian complexity, that addresses fundamental issues in both quantum complexity theory and condensed matter physics. Of particular importance are 1D Hamiltonians. We give a new combinatorial approach to proving the area law for 1D systems via the detectability lemma, in the process exponentially improving on Hastings' bounds in the frustration free case. We also give an efficient algorithm for finding an MPS approximation to the ground state, in the case of constant bond dimension. Entanglement is a fundamental feature of quantum systems, and understanding its nature is a basic challenge in quantum computation. We study it in a number of basic contexts, including the complexity of parallel repetition of entangled games, and Bell-inequalities distinguishing non-locality versus entanglement. We show how to use entanglement to give a way of generating certifiably random numbers which are provably secure even against a quantum adversary. The method is based on an earlier paper in which we report an implementation of optimal extractors against quantum storage.