A classification of bisymmetric polynomial functions over integral domains of characteristic zero

We describe the class of n-variable polynomial functions that satisfy Acz\'el's bisymmetry property over an arbitrary integral domain of characteristic zero with identity

A new automated technique for the reconstitution of hydrophobic proteins into planar bilayer membranes. Studies of human recombinant uncoupling protein 1

AbstractElectrophysiological characterisation of the vast number of annotated channel and transport proteins in the postgenomic era would be greatly facilitated by the introduction of rapid and robust methods for the functional incorporation of membrane proteins into defined lipid bilayers. Here, we describe an automated technique for reconstitution of membrane proteins into lipid bilayer membranes, which substantially reduces both the reconstitution time and the amount of protein required for the membrane formation. The method allows the investigation of single protein channels as well as insertion of multiple copies (∼107) into a single bilayer. Despite a comparatively large membrane area (up to 300 μm diameter), the high stability of the membrane permits the application of transmembrane voltages up to 300 mV. This feature is especially important for studies of inner membrane mitochondrial proteins, since they act at potentials up to ∼200 mV under physiological conditions. It is a combination of these advantages that enables the detailed investigation of the minuscule single protein conductances typical for proton transporters. We have applied the new technique for the reconstitution and electrophysiological characterisation of human recombinant uncoupling protein 1, hUCP1, that has been overexpressed in E. coli and purified from inclusion bodies. We demonstrate that hUCP1 activity in the presence of fatty acids is comparable to the activity of UCP1 isolated from brown adipose tissue

Optimal discrimination of mixed quantum states involving inconclusive results

We propose a generalized discrimination scheme for mixed quantum states. In the present scenario we allow for certain fixed fraction of inconclusive results and we maximize the success rate of the quantum-state discrimination. This protocol interpolates between the Ivanovic-Dieks-Peres scheme and the Helstrom one. We formulate the extremal equations for the optimal positive operator valued measure describing the discrimination device and establish a criterion for its optimality. We also devise a numerical method for efficient solving of these extremal equations.Comment: 5 pages, 1 figur

Iterative algorithm for reconstruction of entangled states

An iterative algorithm for the reconstruction of an unknown quantum state from the results of incompatible measurements is proposed. It consists of Expectation-Maximization step followed by a unitary transformation of the eigenbasis of the density matrix. The procedure has been applied to the reconstruction of the entangled pair of photons.Comment: 4 pages, no figures, some formulations changed, a minor mistake correcte

Mixed quantum state detection with inconclusive results

We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a collection of mixed quantum states. We develop a sufficient condition for the scaled inverse measurement to maximize the probability of correct detection for the case in which the rate of inconclusive results exceeds a certain threshold. Using this condition we derive the optimal measurement for linearly independent pure-state sets, and for mixed-state sets with a broad class of symmetries. Specifically, we consider geometrically uniform (GU) state sets and compound geometrically uniform (CGU) state sets with generators that satisfy a certain constraint. We then show that the optimal measurements corresponding to GU and CGU state sets with arbitrary generators are also GU and CGU respectively, with generators that can be computed very efficiently in polynomial time within any desired accuracy by solving a semidefinite programming problem.Comment: Submitted to Phys. Rev.

Implementation of a Toffoli Gate with Superconducting Circuits

The quantum Toffoli gate allows universal reversible classical computation. It is also an important primitive in many quantum circuits and quantum error correction schemes. Here we demonstrate the realization of a Toffoli gate with three superconducting transmon qubits coupled to a microwave resonator. By exploiting the third energy level of the transmon qubit, the number of elementary gates needed for the implementation of the Toffoli gate, as well as the total gate time can be reduced significantly in comparison to theoretical proposals using two-level systems only. We characterize the performance of the gate by full process tomography and Monte Carlo process certification. The gate fidelity is found to be $68.5\pm0.5$%.Comment: 4 pages, 5figure