Pooling quantum states obtained by indirect measurements

We consider the pooling of quantum states when Alice and Bob both have one part of a tripartite system and, on the basis of measurements on their respective parts, each infers a quantum state for the third part S. We denote the conditioned states which Alice and Bob assign to S by alpha and beta respectively, while the unconditioned state of S is rho. The state assigned by an overseer, who has all the data available to Alice and Bob, is omega. The pooler is told only alpha, beta, and rho. We show that for certain classes of tripartite states, this information is enough for her to reconstruct omega by the formula omega \propto alpha rho^{-1} beta. Specifically, we identify two classes of states for which this pooling formula works: (i) all pure states for which the rank of rho is equal to the product of the ranks of the states of Alice's and Bob's subsystems; (ii) all mixtures of tripartite product states that are mutually orthogonal on S.Comment: Corrected a mistake regarding the scope of our original result. This version to be published in Phys. Rev. A. 6 pages, 1 figur

Practical quantum realization of the ampere from the electron charge

One major change of the future revision of the International System of Units (SI) is a new definition of the ampere based on the elementary charge \emph{e}. Replacing the former definition based on Amp\`ere's force law will allow one to fully benefit from quantum physics to realize the ampere. However, a quantum realization of the ampere from \emph{e}, accurate to within $10^{-8}$ in relative value and fulfilling traceability needs, is still missing despite many efforts have been spent for the development of single-electron tunneling devices. Starting again with Ohm's law, applied here in a quantum circuit combining the quantum Hall resistance and Josephson voltage standards with a superconducting cryogenic amplifier, we report on a practical and universal programmable quantum current generator. We demonstrate that currents generated in the milliampere range are quantized in terms of $ef_\mathrm{J}$ ($f_\mathrm{J}$ is the Josephson frequency) with a measurement uncertainty of $10^{-8}$. This new quantum current source, able to deliver such accurate currents down to the microampere range, can greatly improve the current measurement traceability, as demonstrated with the calibrations of digital ammeters. Beyond, it opens the way to further developments in metrology and in fundamental physics, such as a quantum multimeter or new accurate comparisons to single electron pumps.Comment: 15 pages, 4 figure

Quantum State Diffusion and Time Correlation Functions

In computing the spectra of quantum mechanical systems one encounters the Fourier transforms of time correlation functions, as given by the quantum regression theorem for systems described by master equations. Quantum state diffusion (QSD) gives a useful method of solving these problems by unraveling the master equation into stochastic trajectories; but there is no generally accepted definition of a time correlation function for a single QSD trajectory. In this paper we show how QSD can be used to calculate these spectra directly; by formally solving the equations which arise, we arrive at a natural definition for a two-time correlation function in QSD, which depends explicitly on both the stochastic noise of the particular trajectory and the time of measurement, and which agrees in the mean with the ensemble average definition of correlation functions.Comment: 16 pages standard LaTeX + 1 figure (uuencoded postscript) Numerous minor revisions and clarifications. To appear in J. Mod. Optic

The H.E.S.S. multi-messenger program

Based on fundamental particle physics processes like the production and subsequent decay of pions in interactions of high-energy particles, close connections exist between the acceleration sites of high-energy cosmic rays and the emission of high-energy gamma rays and high-energy neutrinos. In most cases these connections provide both spatial and temporal correlations of the different emitted particles. The combination of the complementary information provided by these messengers allows to lift ambiguities in the interpretation of the data and enables novel and highly sensitive analyses. In this contribution the H.E.S.S. multi-messenger program is introduced and described. The current core of this newly installed program is the combination of high-energy neutrinos and high-energy gamma rays. The search for gamma-ray emission following gravitational wave triggers is also discussed. Furthermore, the existing program for following triggers in the electromagnetic regime was extended by the search for gamma-ray emission from Fast Radio Bursts (FRBs). An overview over current and planned analyses is given and recent results are presented.Comment: In Proceedings of the 34th International Cosmic Ray Conference (ICRC2015), The Hague, The Netherland

The Population of Weak Mg II Absorbers I. A Survey of 26 QSO HIRES/Keck Spectra

We present a search for "weak" MgII absorbers [those with W_r(2796) < 0.3 A in the HIRES/Keck spectra of 26 QSOs. We found 30, of which 23 are newly discovered. The spectra are 80% complete to W_r(2796) = 0.02 A and have a cumulative redshift path of ~17.2 for the redshift range 0.4 < z < 1.4. The number of absorbers per unit redshift, dN/dz, is seen to increase as the equivalent width threshold is decreased; we obtained dN/dz = 1.74+/-0.10 for our 0.02 <= W_r(2796) < 0.3 A sample. The equivalent width distribution follows a power law with slope -1.0; there is no turnover down to W_r(2796) = 0.02 A at = 0.9. Weak absorbers comprise at least 65% of the total MgII absorption population, which outnumbers Lyman limit systems (LLS) by a factor of 3.8+/-1.1; the majority of weak MgII absorbers must arise in sub-LLS environments. Tentatively, we predict that ~5% of the Lyman-alpha forest clouds with W_r(1215) > 0.1 A will have detectable MgII absorption to W_r,min(2796) = 0.02 A and that this is primarily a high-metallicity selection effect (Z/Z_sun] > -1). This implies that MgII absorbing structures figure prominently as tracers of sub-LLS environments where gas has been processed by stars. We compare the number density of W_r(2796) > 0.02 A absorbers with that of both high and low surface brightness galaxies and find a fiducial absorber size of 35h^-1 to 63h^-1 kpc, depending upon the assumed galaxy population and their absorption properties. The individual absorbing "clouds" have W_r(2796) <= 0.15 A and their narrow (often unresolved) line widths imply temperatures of ~25,000 K. We measured W_r(1548) from CIV in FOS/HST archival spectra and, based upon comparisons with FeII, found a range of ionization conditions (low, high, and multi-phase) in absorbers selected by weak MgII.Comment: Accepted Version: 43 pages, PostScript figures embedded; accepted to ApJ; updated version includes analysis of CIV absorptio

Impingement of Cloud Droplets on a Cylinder and Procedure for Measuring Liquid-Water Content and Droplet Sizes in Supercooled Clouds by Rotating Multicylinder Method

No abstract availabl

The power of random measurements: measuring Tr(\rho^n) on single copies of \rho

While it is known that Tr(\rho^n) can be measured directly (i.e., without first reconstructing the density matrix) by performing joint measurements on n copies of the same state rho, it is shown here that random measurements on single copies suffice, too. Averaging over the random measurements directly yields estimates of Tr(\rho^n), even when it is not known what measurements were actually performed (so that one cannot reconstruct \rho)

NP-hardness of decoding quantum error-correction codes

Though the theory of quantum error correction is intimately related to the classical coding theory, in particular, one can construct quantum error correction codes (QECCs) from classical codes with the dual containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expect degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or non-degenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems, and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.Comment: 5 pages, no figure. Final version for publicatio