QUROPE Quantum Information Processing and Communication in Europe

We analyze the error of approximating Gibbs states of local quantum spin Hamiltonians on lattices with Projected Entangled Pair States (PEPS) as a function of the bond dimension (D), temperature (&#946;&#8722;1), and system size (N). First, we introduce a compression method in which the bond dimension scales as D=eO(log2(N/&#1013;)) if &#946;<O(log(N)).

It is commonly believed that area laws for entanglement entropies imply that a quantum many-body state can be faithfully represented by efficient tensor network states - a conjecture frequently stated in the context of numerical simulations and analytical considerations. In this work, we show that this is in general not the case, except in one dimension.

We show how to measure the order-two Renyi entropy of many-body states of spinful fermionic atoms in an optical lattice in equilibrium and non-equilibrium situations. The proposed scheme relies on the possibility to produce and couple two copies of the state under investigation, and to measure the occupation number in a site- and spin-resolved manner, e.g. with a quantum gas microscope.