Dynamics of the entanglement spectrum in spin chains

We study the dynamics of the entanglement spectrum, that is the time evolution of the eigenvalues of the reduced density matrices after a bipartition of a one-dimensional spin chain. Starting from the ground state of an initial Hamiltonian, the state of the system is evolved in time with a new Hamiltonian. We consider both instantaneous and quasi adiabatic quenches of the system Hamiltonian across a quantum phase transition. We analyse the Ising model that can be exactly solved and the XXZ for which we employ the time-dependent density matrix renormalisation group algorithm. Our results show once more a connection between the Schmidt gap, i.e. the difference of the two largest eigenvalues of the reduced density matrix and order parameters, in this case the spontaneous magnetisation.Comment: 16 pages, 8 figures, comments are welcome! Version published in JSTAT special issue on "Quantum Entanglement In Condensed Matter Physics

Corner entanglement of a resonating valence bond wavefunction

We perform a quantum Monte Carlo simulation of the resonating valence bond wavefunction on a two-dimensional square lattice with periodic boundary conditions. Using two replicas of the system, we calculate the second Renyi entropy on a spatial bipartition with a square geometry. Through a finite-size scaling analysis, we extract the logarithmic correction to the area law due to the presence of the sharp corners in the entangling surface. We find that the coefficient of this logarithm is positive with a value of 0.073 for a single $90^{\circ}$ corner.Comment: 4 pages, 5 figure

Integrating Neural Networks with a Quantum Simulator for State Reconstruction

We demonstrate quantum many-body state reconstruction from experimental data generated by a programmable quantum simulator, by means of a neural network model incorporating known experimental errors. Specifically, we extract restricted Boltzmann machine (RBM) wavefunctions from data produced by a Rydberg quantum simulator with eight and nine atoms in a single measurement basis, and apply a novel regularization technique to mitigate the effects of measurement errors in the training data. Reconstructions of modest complexity are able to capture one- and two-body observables not accessible to experimentalists, as well as more sophisticated observables such as the R\'enyi mutual information. Our results open the door to integration of machine learning architectures with intermediate-scale quantum hardware.Comment: 15 pages, 13 figure

Violation of Bell's inequalities with preamplified homodyne detection

We show that the use of probabilistic noiseless amplification in entangled coherent state-based schemes for the test of quantum nonlocality provides substantial advantages. The threshold amplitude to falsify a Bell-CHSH nonlocality test, in fact, is significantly reduced when amplification is embedded into the test itself. Such a beneficial effect holds also in the presence of detection inefficiency. Our study helps in affirming noiseless amplification as a valuable tool for coherent information processing and the generation of strongly nonclassical states of bosonic systems