Criteria for reliable entanglement quantification with finite data

We propose one and a half criteria for determining how many measurements are needed to quantify entanglement reliably. We base these criteria on Bayesian analysis of measurement results, and apply our methods to four-qubit entanglement, but generalizations to more qubits are straightforward.Comment: >4

Entanglement verification with finite data

Suppose an experimentalist wishes to verify that his apparatus produces entangled quantum states. A finite amount of data cannot conclusively demonstrate entanglement, so drawing conclusions from real-world data requires statistical reasoning. We propose a reliable method to quantify the weight of evidence for (or against) entanglement, based on a likelihood ratio test. Our method is universal in that it can be applied to any sort of measurements. We demonstrate the method by applying it to two simulated experiments on two qubits. The first measures a single entanglement witness, while the second performs a tomographically complete measurement.Comment: 4 pages, 3 pretty picture

Entanglement and purity of single- and two-photon states

Whereas single- and two-photon wave packets are usually treated as pure states, in practice they will be mixed. We study how entanglement created with mixed photon wave packets is degraded. We find in particular that the entanglement of a delocalized single-photon state of the electro-magnetic field is determined simply by its purity. We also discuss entanglement for two-photon mixed states, as well as the influence of a vacuum component.Comment: 11 pages, 10 figures, 1 debuting autho

Critical phenomena in exponential random graphs

The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence between particle states in a grand canonical ensemble of statistical physics. By adjusting the specific values of these subgraph densities, one can analyze the influence of various local features on the global structure of the network. Loosely put, a phase transition occurs when a singularity arises in the limiting free energy density, as it is the generating function for the limiting expectations of all thermodynamic observables. We derive the full phase diagram for a large family of 3-parameter exponential random graph models with attraction and show that they all consist of a first order surface phase transition bordered by a second order critical curve.Comment: 14 pages, 8 figure

Nuclear magnetism in silver at positive and negative absolute temperatures in the low nanokelvin range

We have investigated the susceptibility and entropy in the thermally isolated system of silver nuclei down to 0.8 nK and, at negative temperatures, up to -4.3 nK. Low-frequency SQUID-NMR techniques were employed to measure the dynamic sysceptibility. Curie-Weiss behavior was observed for the static susceptibility both at T>0 and T<0; for FTHETA we deduce -4.4±1.0 nK. Our results show directly that antiferromagnetic nuclear alignment at positive temperatures transforms into ferromagnetic orientation at T<0 in the nuclear-spin system of silver, dominated by exchange interaction.Peer reviewe

Information criteria for efficient quantum state estimation

Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to be estimated is reduced by tentatively introducing certain simplifying assumptions on the form of the quantum state, and subsequently using the data to rigorously verify these assumptions. The simplifying assumptions considered so far were (i) the state can be well approximated to be of low rank, or (ii) the state can be well approximated as a matrix product state. We add one more method in that same spirit: we allow in principle any model for the state, using any (small) number of parameters (which can, e.g., be chosen to have a clear physical meaning), and the data are used to verify the model. The proof that this method is valid cannot be as strict as in above-mentioned cases, but is based on well-established statistical methods that go under the name of "information criteria." We exploit here, in particular, the Akaike Information Criterion (AIC). We illustrate the method by simulating experiments on (noisy) Dicke states

Anomalous Soft Photons in Hadron Production

Anomalous soft photons in excess of what is expected from electromagnetic bremsstrahlung have been observed in association with the production of hadrons, mostly mesons, in high-energy (K+)p, (pi+)p, (pi-)p, pp, and (e+)(e-) collisions. We propose a model for the simultaneous production of anomalous soft photons and mesons in quantum field theory, in which the meson production arises from the oscillation of color charge densities of the quarks of the underlying vacuum in the flux tube. As a quark carries both a color charge and an electric charge, the oscillation of the color charge densities will be accompanied by the oscillation of electric charge densities, which will in turn lead to the simultaneous production of soft photons during the meson production process. How the production of these soft photons may explain the anomalous soft photon data will be discussed. Further experimental measurements to test the model will be proposed.Comment: 19 pages, 2 figures, to be published in Physical Review

124-Color Super-resolution Imaging by Engineering DNA-PAINT Blinking Kinetics

Optical super-resolution techniques reach unprecedented spatial resolution down to a few nanometers. However, efficient multiplexing strategies for the simultaneous detection of hundreds of molecular species are still elusive. Here, we introduce an entirely new approach to multiplexed super-resolution microscopy by designing the blinking behavior of targets with engineered binding frequency and duration in DNA-PAINT. We assay this kinetic barcoding approach in silico and in vitro using DNA origami structures, show the applicability for multiplexed RNA and protein detection in cells, and finally experimentally demonstrate 124-plex super-resolution imaging within minutes.We thank Martin Spitaler and the imaging facility of the MPI of Biochemistry for confocal imaging support

Constraining conformal field theories with a slightly broken higher spin symmetry

We consider three dimensional conformal field theories that have a higher spin symmetry that is slightly broken. The theories have a large N limit, in the sense that the operators separate into single trace and multitrace and obey the usual large N factorization properties. We assume that the spectrum of single trace operators is similar to the one that one gets in the Vasiliev theories. Namely, the only single trace operators are the higher spin currents plus an additional scalar. The anomalous dimensions of the higher spin currents are of order 1/N. Using the slightly broken higher spin symmetry we constrain the three point functions of the theories to leading order in N. We show that there are two families of solutions. One family can be realized as a theory of N fermions with an O(N) Chern-Simons gauge field, the other as a N bosons plus the Chern-Simons gauge field. The family of solutions is parametrized by the 't Hooft coupling. At special parity preserving points we get the critical O(N) models, both the Wilson-Fisher one and the Gross-Neveu one. Our analysis also fixes the on shell three point functions of Vasiliev's theory on AdS_4 or dS_4.Comment: 54 pages, 3 figure