Quantum-state filtering applied to the discrimination of Boolean functions

Quantum state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs.The simplest case, when the N given states are divided into two subsets and the first set consists of one state only while the second consists of all of the remaining states, is termed quantum state filtering. We derived previously the optimal strategy for the case of N non-orthogonal states, {|\psi_{1} >, ..., |\psi_{N} >}, for distinguishing |\psi_1 > from the set {|\psi_2 >, ..., |\psi_N >} and the corresponding optimal success and failure probabilities. In a previous paper [PRL 90, 257901 (2003)], we sketched an appplication of the results to probabilistic quantum algorithms. Here we fill in the gaps and give the complete derivation of the probabilstic quantum algorithm that can optimally distinguish between two classes of Boolean functions, that of the balanced functions and that of the biased functions. The algorithm is probabilistic, it fails sometimes but when it does it lets us know that it did. Our approach can be considered as a generalization of the Deutsch-Jozsa algorithm that was developed for the discrimination of balanced and constant Boolean functions.Comment: 8 page

The African Lungfish (\u3cem\u3eProtopterus dolloi\u3c/em\u3e): Ionoregulation and Osmoregulation in a Fish out of Water

Although urea production and metabolism in lungish have been thoroughly studied, we have little knowledge of how internal osmotic and electrolyte balance are controlled during estivation or in water. We tested the hypothesis that, compared with the body surface of teleosts, the slender African lungfish (Protopterus dolloi) body surface was relatively impermeable to water, Na+ and Cl- due to its greatly reduced gills. Accordingly, we measured the tritiated water (3H-H2O) flux in P. dolloi in water and during air exposure. In water, 3H-H2O efflux was comparable with the lowest measurements reported in freshwater teleosts, with a rate constant (K) of 17.6% body water h-1. Unidirectional ion fluxes, measured using 22Na+ and 36Cl-, indicated that Na+ and Cl- influx was more than 90% lower than values reported in most freshwater teleosts. During air exposure, a cocoon formed within 1 wk that completely covered the dorsolateral body surface. However, there were no disturbances to blood osmotic or ion (Na+, Cl-) balance, despite seven- to eightfold increases in plasma urea after 20 wk. Up to 13-fold increases in muscle urea (on a dry-weight basis) were the likely explanation for the 56% increase in muscle water content observed after 20 wk of air exposure. The possibility that muscle acted as a “water reservoir” during air exposure was supported by the 20% decline in body mass observed during subsequent reimmersion in water. This decline in body mass was equivalent to 28 mL water in a 100-g animal and was very close to the calculated net water gain (approximately 32 mL) observed during the 20-wk period of air exposure. Tritiated water and unidirectional ion fluxes on air-exposed lungfish revealed that the majority of water and ion exchange was via the ventral body surface at rates that were initially similar to aquatic rates. The 3H-H2O flux declined over time but increased upon reimmersion. We conclude that the slender lungfish body surface, including the gills, has relatively low permeability to water and ions but that the ventral surface is an important site of osmoregulation and ionoregulation. We further propose that an amphibian-like combination of ventral skin water and ion permeability, plus internal urea accumulation during air exposure, allows P. dolloi to extract water from its surroundings and to store water in the muscle when the water supply becomes limited

Pulsed squeezed light: simultaneous squeezing of multiple modes

We analyze the spectral properties of squeezed light produced by means of pulsed, single-pass degenerate parametric down-conversion. The multimode output of this process can be decomposed into characteristic modes undergoing independent squeezing evolution akin to the Schmidt decomposition of the biphoton spectrum. The main features of this decomposition can be understood using a simple analytical model developed in the perturbative regime. In the strong pumping regime, for which the perturbative approach is not valid, we present a numerical analysis, specializing to the case of one-dimensional propagation in a beta-barium borate waveguide. Characterization of the squeezing modes provides us with an insight necessary for optimizing homodyne detection of squeezing. For a weak parametric process, efficient squeezing is found in a broad range of local oscillator modes, whereas the intense generation regime places much more stringent conditions on the local oscillator. We point out that without meeting these conditions, the detected squeezing can actually diminish with the increasing pumping strength, and we expose physical reasons behind this inefficiency

Distinguishing between optical coherent states with imperfect detection

Several proposed techniques for distinguishing between optical coherent states are analyzed under a physically realistic model of photodetection. Quantum error probabilities are derived for the Kennedy receiver, the Dolinar receiver and the unitary rotation scheme proposed by Sasaki and Hirota for sub-unity detector efficiency. Monte carlo simulations are performed to assess the effects of detector dark counts, dead time, signal processing bandwidth and phase noise in the communication channel. The feedback strategy employed by the Dolinar receiver is found to achieve the Helstrom bound for sub-unity detection efficiency and to provide robustness to these other detector imperfections making it more attractive for laboratory implementation than previously believed

Unified Treatment of Heterodyne Detection: the Shapiro-Wagner and Caves Frameworks

A comparative study is performed on two heterodyne systems of photon detectors expressed in terms of a signal annihilation operator and an image band creation operator called Shapiro-Wagner and Caves' frame, respectively. This approach is based on the introduction of a convenient operator $\hat \psi$ which allows a unified formulation of both cases. For the Shapiro-Wagner scheme, where $[\hat \psi, \hat \psi^{\dag}] =0$, quantum phase and amplitude are exactly defined in the context of relative number state (RNS) representation, while a procedure is devised to handle suitably and in a consistent way Caves' framework, characterized by $[\hat \psi, \hat \psi^{\dag}] \neq 0$, within the approximate simultaneous measurements of noncommuting variables. In such a case RNS phase and amplitude make sense only approximately.Comment: 25 pages. Just very minor editorial cosmetic change

Operational Theory of Homodyne Detection

We discuss a balanced homodyne detection scheme with imperfect detectors in the framework of the operational approach to quantum measurement. We show that a realistic homodyne measurement is described by a family of operational observables that depends on the experimental setup, rather than a single field quadrature operator. We find an explicit form of this family, which fully characterizes the experimental device and is independent of a specific state of the measured system. We also derive operational homodyne observables for the setup with a random phase, which has been recently applied in an ultrafast measurement of the photon statistics of a pulsed diode laser. The operational formulation directly gives the relation between the detected noise and the intrinsic quantum fluctuations of the measured field. We demonstrate this on two examples: the operational uncertainty relation for the field quadratures, and the homodyne detection of suppressed fluctuations in photon statistics.Comment: 7 pages, REVTe

First-Principles Approach to Electrorotation Assay

We have presented a theoretical study of electrorotation assay based on the spectral representation theory. We consider unshelled and shelled spheroidal particles as an extension to spherical ones. From the theoretical analysis, we find that the coating can change the characteristic frequency at which the maximum rotational angular velocity occurs. The shift in the characteristic frequency is attributed to a change in the dielectric properties of the bead-coating complex with respect to those of the uncoated particles. By adjusting the dielectric properties and the thickness of the coating, it is possible to obtain good agreement between our theoretical predictions and the assay data.Comment: 17 pages, 4 eps figures; minor revisions, accepted for publications by J. Phys.: Condens. Matte

Cosmological Perturbations of Quantum-Mechanical Origin and Anisotropy of the Microwave Background

Cosmological perturbations generated quantum-mechanically (as a particular case, during inflation) possess statistical properties of squeezed quantum states. The power spectra of the perturbations are modulated and the angular distribution of the produced temperature fluctuations of the CMBR is quite specific. An exact formula is derived for the angular correlation function of the temperature fluctuations caused by squeezed gravitational waves. The predicted angular pattern can, in principle, be revealed by the COBE-type observations.Comment: 9 pages, WUGRAV-92-17 Accepted for Publication in Phys. Rev. Letters (1993

Measuring the quantum statistics of an atom laser beam

We propose and analyse a scheme for measuring the quadrature statistics of an atom laser beam using extant optical homodyning and Raman atom laser techniques. Reversal of the normal Raman atom laser outcoupling scheme is used to map the quantum statistics of an incoupled beam to an optical probe beam. A multimode model of the spatial propagation dynamics shows that the Raman incoupler gives a clear signal of de Broglie wave quadrature squeezing for both pulsed and continuous inputs. Finally, we show that experimental realisations of the scheme may be tested with existing methods via measurements of Glauber's intensity correlation function.Comment: 4 pages, 3 figure

Effects of geometric anisotropy on local field distribution: Ewald-Kornfeld formulation

We have applied the Ewald-Kornfeld formulation to a tetragonal lattice of point dipoles, in an attempt to examine the effects of geometric anisotropy on the local field distribution. The various problems encountered in the computation of the conditionally convergent summation of the near field are addressed and the methods of overcoming them are discussed. The results show that the geometric anisotropy has a significant impact on the local field distribution. The change in the local field can lead to a generalized Clausius-Mossotti equation for the anisotropic case.Comment: Accepted for publications, Journal of Physics: Condensed Matte