Statistical uncertainty in quantum optical photodetection measurements

We present a complete statistical analysis of quantum optical measurement schemes based on photodetection. Statistical distributions of quantum observables determined from a finite number of experimental runs are characterized with the help of the generating function, which we derive using the exact statistical description of raw experimental outcomes. We use the developed formalism to point out that the statistical uncertainty results in substantial limitations of the determined information on the quantum state: though a family of observables characterizing the quantum state can be safely evaluated from experimental data, its further use to obtain the expectation value of some operators generates exploding statistical errors. These issues are discussed using the example of phase-insensitive measurements of a single light mode. We study reconstruction of the photon number distribution from photon counting and random phase homodyne detection. We show that utilization of the reconstructed distribution to evaluate a simple well-behaved observable, namely the parity operator, encounters difficulties due to accumulation of statistical errors. As the parity operator yields the Wigner function at the phase space origin, this example also demonstrates that transformation between various experimentally determined representations of the quantum state is a quite delicate matter.Comment: 18 pages REVTeX, 7 figures included using epsf. Few minor corrections made, clarified conclusion

C5AC_5^A axial form factor from bubble chamber experiments

A careful reanalysis of both Argonne National Laboratory and Brookhaven National Laboratory data for weak single pion production is done. We consider deuteron nuclear effects and normalization (flux) uncertainties in both experiments. We demonstrate that these two sets of data are in good agreement. For the dipole parametrization of $C_5^A(Q^2)$, we obtain $C_5^A(0)=1.19\pm 0.08$, $M_A=0.94\pm 0.03$ GeV. As an application we present the discussion of the uncertainty of the neutral current 1$\pi^0$ production cross section, important for the T2K neutrino oscillation experiment.Comment: 16 pages, 8 figures, 2 table

The light curve of a transient X-ray source

The Ariel-V satellite monitored the X-ray light curve of A1524-62 almost continuously from 40 days prior to maximum light until its disappearance below the effective experimental sensitivity. The source exhibited maximum light on approximately 4 December 1974, at a level of 0.9 the apparent magnitude of the Crab Nebula in the energy band 3-6 keV. Although similar to previously reported transient sources with a decay time constant of approximately 2 months, the source exhibited an extended, variable pre-flare on-state of about 1 month at a level of greater than approximately 0.1 maximum light. The four bright (greater than 0.2 of the Crab Nebula) transient sources observed during the first half-year of Ariel-V operation are indicative of a galactic disk distribution, and a luminosity at maximum in excess of 10 to the 37th power ergs/sec

Maximum likelihood estimation of photon number distribution from homodyne statistics

We present a method for reconstructing the photon number distribution from the homodyne statistics based on maximization of the likelihood function derived from the exact statistical description of a homodyne experiment. This method incorporates in a natural way the physical constraints on the reconstructed quantities, and the compensation for the nonunit detection efficiency.Comment: 3 pages REVTeX. Final version, to appear in Phys. Rev. A as a Brief Repor

A New Technique for Finding Needles in Haystacks: A Geometric Approach to Distinguishing Between a New Source and Random Fluctuations

We propose a new test statistic based on a score process for determining the statistical significance of a putative signal that may be a small perturbation to a noisy experimental background. We derive the reference distribution for this score test statistic; it has an elegant geometrical interpretation as well as broad applicability. We illustrate the technique in the context of a model problem from high-energy particle physics. Monte Carlo experimental results confirm that the score test results in a significantly improved rate of signal detection.Comment: 5 pages, 4 figure

Could psoralen plus ultraviolet A1 (“PUVA1”) work? Depth penetration achieved by phototherapy lamps

Funding: PhD Studentship UK EPRSC EP/N509759/1.Psoralen and ultraviolet A (PUVA) is useful in treating various hand and foot skin diseases.1 Most cases of psoriasis respond well to phototherapy or PUVA. However, for some diseases, such as palmoplantar pustular psoriasis, PUVA is not always sufficient to produce therapeutic effect. If PUVA fails, it is sometimes necessary to progress to other treatments such as Grenz ray therapy (where available),2 systemic retinoid or systemic immunosuppression. Could “PUVA1” (psoralen combined with ultraviolet A1 long wavelength ultraviolet A [UVA]) work in cases where conventional PUVA (psoralen plus broadband UVA) has been inadequate?PostprintPeer reviewe

Quantum homodyne tomography with a priori constraints

I present a novel algorithm for reconstructing the Wigner function from homodyne statistics. The proposed method, based on maximum-likelihood estimation, is capable of compensating for detection losses in a numerically stable way.Comment: 4 pages, REVTeX, 2 figure

Minimal, superficial DNA damage in human skin from filtered far-ultraviolet C

Funding: This study was funded in part by MR/P012248/1 to R.P.H. from the Medical Research Council.Publisher PDFPeer reviewe