Two methods for measuring Bell nonlocality via local unitary invariants of two-qubit systems in Hong-Ou-Mandel interferometers

We describe a direct method to experimentally determine local two-qubit invariants by performing interferometric measurements on multiple copies of a given two-qubit state. We use this framework to analyze two different kinds of two-qubit invariants of Makhlin and Jing et. al. These invariants allow to fully reconstruct any two-qubit state up to local unitaries. We demonstrate that measuring 3 invariants is sufficient to find, e.g., the optimal Bell inequality violation. These invariants can be measured with local or nonlocal measurements. We show that the nonlocal strategy that follows from Makhlin's invariants is more resource-efficient than local strategy following from the invariants of Jing et al. To measure all of the Makhlin's invariants directly one needs to use both two-qubit singlet and three-qubit W-state projections on multiple copies of the two-qubit state. This problem is equivalent to a cordinate system handness measurement. We demonstrate that these 3-qubit measurements can be performed by utilizing Hong-Ou-Mandel interference which gives significant speedup in comparison to the classical handness measurement. Finally, we point to potential application of our results in quantum secret sharing.Comment: 11 pages, 7 figures, 3 table

Optimal cloning of qubits given by arbitrary axisymmetric distribution on Bloch sphere

We find an optimal quantum cloning machine, which clones qubits of arbitrary symmetrical distribution around the Bloch vector with the highest fidelity. The process is referred to as phase-independent cloning in contrast to the standard phase-covariant cloning for which an input qubit state is a priori better known. We assume that the information about the input state is encoded in an arbitrary axisymmetric distribution (phase function) on the Bloch sphere of the cloned qubits. We find analytical expressions describing the optimal cloning transformation and fidelity of the clones. As an illustration, we analyze cloning of qubit state described by the von Mises-Fisher and Brosseau distributions. Moreover, we show that the optimal phase-independent cloning machine can be implemented by modifying the mirror phase-covariant cloning machine for which quantum circuits are known.Comment: 8 pages, 6 figure

On 2D integro-differential systems. Stability and sensitivity analysis

In the paper a two-dimensional integro-differential system is considered. Using some variational methods we give sufficient conditions for the existence and uniqueness of a solution to the considered system. Moreover, we show that the system is stable and robust

Experimental measurement of the collectibility of two-qubit states

We present a proof-of-principle experiment demonstrating measurement of the collectibility, a nonlinear entanglement witness proposed by Rudnicki et al. [Phys. Rev. Lett. 107, 150502 (2011)]. This entanglement witness works for both mixed and pure two-qubit states. In the later case it can be used to measure entanglement in terms of the negativity. We measured the collectibility for three distinct classes of photonic polarization-encoded two-qubit states, i.e., maximally entangled, separable and maximally mixed states. We demonstrate that the measurement procedure is feasible and robust against typical experimental shortcomings such as imperfect two-photon indistinguishability.Comment: 7 pages, 4 figure

Discovery of four periodic methanol masers and updated light curve for a further one

We report the discovery of 6.7 GHz methanol maser periodic flares in four massive star forming regions and the updated light curve for the known periodic source G22.357+0.066. The observations were carried out with the Torun 32 m radio telescope between June 2009 and April 2014. Flux density variations with period of 120 to 245 d were detected for some or all spectral features. A variability pattern with a fast rise and relatively slow fall on time-scale of 30-60 d dominated. A reverse pattern was observed for some features of G22.357+0.066, while sinusoidal-like variations were detected in G25.411+0.105. A weak burst lasting ~520 d with the velocity drift of 0.24 km/s/yr occurred in G22.357+0.066. For three sources for which high resolution maps are available, we found that the features with periodic behaviour are separated by more than 500 au from those without any periodicity. This suggests that the maser flares are not triggered by large-scale homogeneous variations in either the background seed photon flux or the luminosity of the exciting source and a mechanism which is able to produce local changes in the pumping conditions is required.Comment: 12 pages, 15 figures. Accepted in MNRA

EVN observations of an OH maser burst in OH17.7-2.0

We have observed the OH 1612-MHz maser emission towards the proto-planetary nebula candidate OH17.7-2.0 that underwent a very strong and unusual outburst in 2003. Phase-referencing data were obtained with the EVN in order to localize the outburst and to examine its possible causes. The majority of the emission comes from an incomplete spherical shell with inner and outer radii of 220 and 850 mas, respectively. There is a strong evidence for maser components that arise due to the interaction of a jet-like post-AGB outflow with the remnant outer AGB shell. The most prominent signature of such an interaction is the strongly bursting polarized emission near 73.3km/s coming from two unresolved components of brightness temperature up to 10^11K located at the edge of the biconal region 2500 AU from the central star. It is remarkable that this OH biconal region is well-aligned with the polar outflow inferred from the near-infrared image.Comment: 6 pages, 3 figures, Proceedings of the 8th European VLBI Network Symposium, Torun, Poland, 26-29 Sep. 200

Scheme for a linear-optical controlled-phase gate with programmable phase shift

We present a linear-optical scheme for a controlled-phase gate with tunable phase shift programmed by a qubit state. In contrast to all previous tunable controlled-phase gates, the phase shift is not hard-coded into the optical setup, but can be tuned to any value from 0 to pi by the state of a so-called program qubit. Our setup is feasible with current level of technology using only linear-optical components. We provide an experimental feasibility study to assess the gate's implementability. We also discuss options for increasing the success probability up to 1/12 which approaches the success probability of a optimal non-programmable tunable controlled-phase gate.Comment: 7 pages, 3 figure

Direct method for measuring of purity, superfidelity, and subfidelity of photonic two-qubit mixed states

The Uhlmann-Jozsa fidelity (or, equivalently, the Bures distance) is a basic concept of quantum communication and quantum information, which however is very difficult to measure efficiently without recourse to quantum tomography. Here we propose a direct experimental method to estimate the fidelity between two unknown two-qubit mixed states via the measurement of the upper and lower bounds of the fidelity, which are referred to as the superfidelity and subfidelity, respectively. Our method enables a direct measurement of the first- and second-order overlaps between two arbitrary two-qubit states. In particular, the method can be applied to measure the purity (or linear entropy) of a single two-qubit mixed state in a direct experiment. We also propose and critically compare several experimental strategies for measuring the sub- and superfidelities of polarization states of photons in various linear-optical setups.Comment: 9 pages, 5 figure

State-dependent linear-optical qubit amplifier

We propose a linear-optical setup for heralded qubit amplification with tunable output qubit fidelity. We study its success probability as a function of output qubit fidelity showing that at the expense of lower fidelity, the setup can considerably increase probability of successful operation. These results are subsequently applied in a proposal for state dependent qubit amplification. Similarly to state-dependent quantum cloning, the a priori information about the input state allows to optimize the qubit amplification procedure to obtain better fidelity versus success probability trade-off.Comment: 8 pages, 7 figure

Measuring distances in Hilbert space by many-particle interference

The measures of distances between points in a Hilbert space are one of the basic theoretical concepts used to characterize properties of a quantum system with respect to some etalon state. These are not only used in studying fidelity of signal transmission and basic quantum phenomena but also applied in measuring quantum correlations, and also in quantum machine learning. The values of quantum distance measures are very difficult to determine without completely reconstructing the state. Here we demonstrate an interferometric approach to measuring distances between quantum states that in some cases can outperform quantum state tomography. We propose a direct experimental method to estimate such distance measures between two unknown two-qubit mixed states as Uhlmann-Jozsa fidelity (or the Bures distance), the Hilbert-Schmidt distance, and the trace distance. The fidelity is estimated via the measurement of the upper and lower bounds of the fidelity, which are referred to as the superfidelity and subfidelity, respectively. Our method is based on the multiparticle interactions (i.e., interference) between copies of the unknown pairs of qubits.Comment: 9 pages, 1 figure, 3 table