Detecting a stochastic background of gravitational radiation: Signal processing strategies and sensitivities

We analyze the signal processing required for the optimal detection of a stochastic background of gravitational radiation using laser interferometric detectors. Starting with basic assumptions about the statistical properties of a stochastic gravity-wave background, we derive expressions for the optimal filter function and signal-to-noise ratio for the cross-correlation of the outputs of two gravity-wave detectors. Sensitivity levels required for detection are then calculated. Issues related to: (i) calculating the signal-to-noise ratio for arbitrarily large stochastic backgrounds, (ii) performing the data analysis in the presence of nonstationary detector noise, (iii) combining data from multiple detector pairs to increase the sensitivity of a stochastic background search, (iv) correlating the outputs of 4 or more detectors, and (v) allowing for the possibility of correlated noise in the outputs of two detectors are discussed. We briefly describe a computer simulation which mimics the generation and detection of a simulated stochastic gravity-wave signal in the presence of simulated detector noise. Numerous graphs and tables of numerical data for the five major interferometers (LIGO-WA, LIGO-LA, VIRGO, GEO-600, and TAMA-300) are also given. The treatment given in this paper should be accessible to both theorists involved in data analysis and experimentalists involved in detector design and data acquisition.Comment: 81 pages, 30 postscript figures, REVTE

Collective versus local measurements on two parallel or antiparallel spins

We give a complete analysis of covariant measurements on two spins. We consider the cases of two parallel and two antiparallel spins, and we consider both collective measurements on the two spins, and measurements which require only Local Quantum Operations and Classical Communication (LOCC). In all cases we obtain the optimal measurements for arbitrary fidelities. In particular we show that if the aim is determine as well as possible the direction in which the spins are pointing, it is best to carry out measurements on antiparallel spins (as already shown by Gisin and Popescu), second best to carry out measurements on parallel spins and worst to be restricted to LOCC measurements. If the the aim is to determine as well as possible a direction orthogonal to that in which the spins are pointing, it is best to carry out measurements on parallel spins, whereas measurements on antiparallel spins and LOCC measurements are both less good but equivalent.Comment: 4 pages; minor revision

Optimal estimation of quantum dynamics

We construct the optimal strategy for the estimation of an unknown unitary transformation $U\in SU(d)$. This includes, in addition to a convenient measurement on a probe system, finding which is the best initial state on which $U$ is to act. When $U\in SU(2)$, such an optimal strategy can be applied to estimate simultaneously both the direction and the strength of a magnetic field, and shows how to use a spin 1/2 particle to transmit information about a whole coordinate system instead of only a direction in space.Comment: 4 pages, REVTE

Parametrization of projector-based witnesses for bipartite systems

Entanglement witnesses are nonpositive Hermitian operators which can detect the presence of entanglement. In this paper, we provide a general parametrization for orthonormal basis of ${\mathbb C}^n$ and use it to construct projector-based witness operators for entanglement detection in the vicinity of pure bipartite states. Our method to parameterize entanglement witnesses is operationally simple and could be used for doing symbolic and numerical calculations. As an example we use the method for detecting entanglement between an atom and the single mode of quantized field, described by the Jaynes-Cummings model. We also compare the detection of witnesses with the negativity of the state, and show that in the vicinity of pure stats such constructed witnesses able to detect entanglement of the state.Comment: 12 pages, four figure

The quantum cryptographic switch

We illustrate using a quantum system the principle of a cryptographic switch, in which a third party (Charlie) can control to a continuously varying degree the amount of information the receiver (Bob) receives, after the sender (Alice) has sent her information. Suppose Charlie transmits a Bell state to Alice and Bob. Alice uses dense coding to transmit two bits to Bob. Only if the 2-bit information corresponding to choice of Bell state is made available by Charlie to Bob can the latter recover Alice's information. By varying the information he gives, Charlie can continuously vary the information recovered by Bob. The performance of the protocol subjected to the squeezed generalized amplitude damping channel is considered. We also present a number of practical situations where a cryptographic switch would be of use.Comment: 7 pages, 4 Figure

On the distinguishability of random quantum states

We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of their Gram matrix. We use the latter to lower bound the asymptotic distinguishability of ensembles of n random quantum states in d dimensions, where n/d approaches a constant. In particular, for almost all ensembles of n states in n dimensions, p>0.72. An application to distinguishing Boolean functions (the "oracle identification problem") in quantum computation is given.Comment: 20 pages, 2 figures; v2 fixes typos and an error in an appendi

T violation and the unidirectionality of time

An increasing number of experiments at the Belle, BNL, CERN, DA{\Phi}NE and SLAC accelerators are confirming the violation of time reversal invariance (T). The violation signifies a fundamental asymmetry between the past and future and calls for a major shift in the way we think about time. Here we show that processes which violate T symmetry induce destructive interference between different paths that the universe can take through time. The interference eliminates all paths except for two that represent continuously forwards and continuously backwards time evolution. Evidence from the accelerator experiments indicates which path the universe is effectively following. This work may provide fresh insight into the long-standing problem of modeling the dynamics of T violation processes. It suggests that T violation has previously unknown, large-scale physical effects and that these effects underlie the origin of the unidirectionality of time. It may have implications for the Wheeler-DeWitt equation of canonical quantum gravity. Finally it provides a view of the quantum nature of time itself.Comment: 24 pages, 5 figures. Final version accepted for publishing in Foundations of Physics. The final publication is available at http://www.springerlink.com/content/y3h4174jw2w78322

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

A Binary Lensing Event Toward the LMC: Observations and Dark Matter Implications

The MACHO collaboration has recently analyzed 2.1 years of photometric data for about 8.5 million stars in the Large Magellanic Cloud (LMC). This analysis has revealed 8 candidate microlensing events and a total microlensing optical depth of $\tau_{meas} = 2.9 +1.4/-0.9 \times 10^{-7}$. This significantly exceeds the number of events (1.1) and the microlensing optical depth predicted from known stellar populations: $\tau_{back} = 5.4\times 10^{-8}$, but it is consistent with models in which about half of the standard dark halo mass is composed of Machos of mass \sim 0.5 \msun. One of these 8 events appears to be a binary lensing event with a caustic crossing that is partially resolved which allows us to estimate the distance to the lenses. If the source star is not a short period binary star, then we show that the lens system is very likely to reside in the LMC. However, if we assume that the optical depth for LMC-LMC lensing is large enough to account for our entire lensing signal, then the binary event does not appear to be consistent with lensing of a single LMC source star by a binary residing in the LMC. Thus, while the binary lens may indeed reside in the LMC, there is no indication that most of the lenses reside in the LMC.Comment: 5 pages, 3 postscript figures included; To appear in the Proceedings of the Dark Matter '96 Conference held in Santa Monica, CA, Feb., 199