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In the Ψ-space limiting procedure limits of expectation values, rather than operator or states, are found as the state space dimensionality tends to infinity. This approach has been applied successfully to the calculation of the phase properties of various states of light, but its status as a valid quantum mechanical thory equivalent to the usual infinite Hilbert space (H-space) approach has not yet been fully accepted. Here we address this issue by investigating the formal relationship between the two approaches. We establish the consistency between the Ψ-space and H-space approaches for observables which are amenable to an H-space treatment. Such observables are represented in H by operators which are strong limits of Ψ-space operators and which obey the same algebra as the corresponding Ψ-space operators. The phase operator, however, exists in H only as a weak limit of a Ψ-space operator. For such limits the Ψ-space operator algebra is not preserved, which is the fundamental reason for the difficulties in constructing a consistent quantum description of phase in H. We show that for the phase observable the Ψ-space approach is consistent with the probability-operator measure (POM) method with the important distinction that, whereas the relation between non-orthogonal POMs and probability has to be accepted in the latter method as a postulate, the corresponding relation is derived in the Ψ-space approach. We conclude that the Ψ-space approach is not only equivalent to, but is also more fundamental than both the H-space and POM approaches.

We report a case of renal leiomyosarcoma arising from the renal pelvis with immunohistochemical confirmation of the diagnosis. Treatment was extirpative surgery for both primary and metastatic lung lesions as well as adjunctive radiation and chemotherapy. This patient remains disease free twelve months following treatment.

We investigate the relationship between squeezing and reduced phase fluctuations for various states of the single-mode electromagnetic field, including the strongly-squeezed vacuum and phase states. We find that, although squeezing the fluctuations of the electric field that arise from the vacuum guarantees a more well-defined phase, reducing phase fluctuations does not guarantee a squeezed electric field. We also investigate the evolution of the electric field and its fluctuations for a phase state. Our results show that even though the electric field fluctuations never vanish for a phase state, the times when the electric field changes sign are precisely defined. We also discuss why it is not always possible to attribute physical properties to certain states, such as simple superpositions of phase states.

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/

We show that the physically absurd state obtained by Vorontsov and Rembovsky [Phys. Lett. A 254 (1999) 7] results from an unphysical choice of approximate phase measurement and not from the phase formalism itself as claimed. Thus their assertion that it is impossible to perform even an approximate measurement of phase is unfounded.

Superselection rules (SSRs) limit the mechanical and quantum processing resources represented by quantum states. However, SSRs can be violated using reference systems to break the underlying symmetry. We show that there is a duality between the ability of a system to do mechanical work and to act as a reference system. Further, for a bipartite system in a globally symmetric pure state, we find a triality between the system's ability to do local mechanical work, its ability to do ``logical work'' due to its accessible entanglement, and its ability to act as a shared reference system.

Global conservation laws imply superselection rules (SSR) which restrict the operations that are possible on any given state. Imposing the additional constraint of local operations and classical communication (LOCC) forbids the transfer of quantum systems between spatially separated sites. In the case of particle conservation this imposes a SSR for local particle number. That is, the coherences between subspaces of fixed particle number at each site are not accessible and any state is therefore equivalent to its projection onto these subspaces. The accessible entanglement under the SSR is less than (or equal to) that available in the absence of the SSR. An ancilla can be used as a reference system to increase the amount of accessible entanglement. We examine the relationship between local particle number uncertainty and the accessible entanglement and consider the optimal reference states for recovering entanglement from certain systems. In particular we derive the optimal ancilla state for extracting entanglement for a single shared particle and make steps towards the optimum for general systems., Comment: 14 pages, 6 figures, clarified a key result but otherwise mostly minor changes

We use a new limiting procedure, developed to study quantum-optical phase, to examine canonically conjugate operators in general. We find that Dirac's assumption that photon number and phase should be canonically conjugate variables, similar to momentum and position, is essentially correct. The difficulties with Dirac's approach are shown to arise through use of a form of the canonical commutator which, although the only possible form in the usual infinite Hilbert space approach, is not sufficiently general to be used as a model for a number-phase commutator. The approach in this paper unifies the theory of conjugate operators, which include photon number and phase, angular momentum and angle, and momentum and position as particular cases. The usual position-momentum commutator is regained from a more generally applicable expression by means of a domain restriction which cannot be used for the phase-number commutator.

SUMMARY Urologic endoscopic resectoscopes greatly simplify electrofulguration and resection of rectal tumors. The most important advantage is the enhanced visibility that allows determination of the depth of resection and good hemostasis. The indications for this procedure are otherwise-poor surgical candidates, palliation, excision of locally aggressive tumors such as villous adenomas, and bowel diversion prior to definitive therapy. Bleeding, peritoneal perforation requiring colostomy, and postoperative infection have all been reported, but the complication rate appears to be acceptable. Further clinical studies are necessary to determine if, indeed, this can be considered a curative procedure. Finally, because the practicing urologist is intimately aware of the technical aspects of the urologic resectoscope, he will probably be called on to perform, and should be aware of, this procedure.

The recently introduced Hermitian phase operator allows a phase-state representation of the single-mode light field. We find the requirement that a light field is in a physical state, that is, has finite energy moments, imposes strict and simple continuity conditions on the phase-amplitude distribution. We exploit these conditions to examine the physical intelligent and minimum-uncertainty states associated with the number-phase uncertainty relations, including those involving the Hermitian phase operator and its sine and cosine forms. The single number-state is found to be the only physical exact intelligent state and also the only physical exact minimum-uncertainty state for all the uncertainty relations considered. We construct states which are both physical states and approximately intelligent states. Under certain conditions coherent states, ideal squeezed states and the number-phase intelligent states associated with the Susskind-Glogower cosine and sine operators are found to be both physi...

Describing the phase of an electromagnetic field mode or harmonic oscillator has been an obstacle since the early days of modern quantum theory. The quantum phase operator was even more problematic with the invention of the maser and laser in the 1950s and 1960s. This problem was not solved until the Pegg-Barnett formalism was developed in the 1980s. Edited by one of the scientists who created this key solution, The Quantum Phase Operator: A Review charts the development of phase and angle operators from their first appearance to modern theory. Bringing together vital works that have been published on the subject, the book presents the ideas that led to the current theory of the phase operator and provides a complete picture of the progress that has followed since then. With introductions by the editors to put the papers in context and unify the content of the book, each section focuses on a different aspect of phase operators. The editors also chronologically organize the papers within the sections to highlight how scientific thought has evolved, if at all, over time. A collection of important relevant material that is scattered throughout the literature, this volume chronicles the history of the various facets of the quantum phase operator, promoting a solid foundation in quantum theory.

This paper concentrates on a particular example of a constraint imposed by superselection rules (SSRs): that which applies when the parties (Alice and Bob) cannot distinguish among certain quantum objects they have. This arises naturally in the context of ensemble quantum information processing such as in liquid NMR. We discuss how a SSR for the symmetric group can be applied, and show how the extractable entanglement can be calculated analytically in certain cases, with a maximum bipartite entanglement in an ensemble of N Bell-state pairs scaling as log(N) as N goes to infinity . We discuss the apparent disparity with the asymptotic (N >> 1) recovery of unconstrained entanglement for other sorts of superselection rules, and show that the disparity disappears when the correct notion of applying the symmetric group SSR to multiple copies is used. Next we discuss reference frames in the context of this SSR, showing the relation to the work of von Korff and Kempe [Phys. Rev. Lett. 93, 260502 (2004)]. The action of a reference frame can be regarded as the analog of activation in mixed-state entanglement. We also discuss the analog of distillation: there exist states such that one copy can act as an imperfect reference frame for another copy. Finally we present an example of a stronger operational constraint, that operations must be non-collective as well as symmetric. Even under this stronger constraint we nevertheless show that Bell-nonlocality (and hence entanglement) can be demonstrated for an ensemble of N Bell-state pairs no matter how large N is. This last work is a generalization of that of Mermin [Phys. Rev. D 22, 356 (1980)]., 16 pages, 6 figures. v2 updated version published in Phys Rev A

The stationary solution ρ of a quantum master equation can be represented as an ensemble of pure states in a continuous infinity of ways. Here we suggest a definition of the the “most natural” ensemble. The first requirement is that the ensemble be physically realizable through monitoring the system’s environment. We call this an ’unraveling’ of the master equation. The second requirement is that it be the most robust of such ensembles. Robustness of an ensemble is defined in terms of the survival probability S(t) which is the average probability for one of its elements to remain unchanged after a time t. The most natural ensemble can thus be said to be the one produced by the maximally robust unraveling. An application of interest is the atom laser. We show that the nature of the maximally robust unraveling is closely related to the question of whether the output beam satisfies the conditions required to be a true laser beam.

Summary form only given. We show that the atomic field of an atom laser is best characterized as being in amplitude-squeezed states. We derive scaling laws for these states and examine parameter regimes corresponding to recent experimental work.

Introduces tensor-product neural networks, composed of a layer of univariate neurons followed by a net of polynomial post-processing. We look at the general approximation problem by these networks observing in particular their relationship to the Stone-Weierstrass theorem for uniform function algebras. The implementation of the post-processing as a two-layer network with logarithmic and exponential neurons leads to potentially important 'generalised' product networks which, however, require a complex approximation theory of the Mu/spl uml/ntz-Szasz-Ehrenpreis type. A backpropagation algorithm for product networks is presented and used in three computational experiments. In particular, approximation by a sigmoid product network is compared to that of a single-layer radial basis network and a multiple-layer sigmoid network.

We describe quantum protocols for voting and surveying. A key feature of our schemes is the use of entangled states to ensure that the votes are anonymous and to allow the votes to be tallied. The entanglement is distributed over separated sites; the physical inaccessibility of any one site is sufficient to guarantee the anonymity of the votes. The security of these protocols with respect to various kinds of attack is discussed. We also discuss classical schemes and show that our quantum voting protocol represents a N-fold reduction in computational complexity, where N is the number of voters., 8 pages. V2 includes the modifications made for the published version

We have recently introduced a measure of the bipartite entanglement of identical particles, E_P, based on the principle that entanglement should be accessible for use as a resource in quantum information processing. We show here that particle entanglement is limited by the lack of a reference phase shared by the two parties, and that the entanglement is constrained to reference-phase invariant subspaces. The super-additivity of E_P results from the fact that this constraint is weaker for combined systems. A shared reference phase can only be established by transferring particles between the parties, that is, with additional nonlocal resources. We show how this nonlocal operation can increase the particle entanglement., 8 pages, no figures. Invited talk given at EQIS'03, Kyoto, September, 2003. Minor typos corrected, 1 reference added

Interest in lossless nonlinearities has focussed on the the dispersive properties of $\Lambda $ systems under conditions of electromagnetically induced transparency (EIT). We generalize the lambda system by introducing further degenerate states to realize a `Chain $ \Lambda $' atom where multiple coupling of the probe field significantly enhances the intensity dependent dispersion without compromising the EIT condition., Comment: 6 pages, 7 figures, revtex 4, Two errors corrected (|D_0^{(7)}> and R^{(7)}, Replaced with version accepted in Phys. Rev. A

Spectra illustrating the doubly driven N system are presented with accompanying dressed state analysis. The spectra show a three-photon absorption peak in addition to the normal EIT profile, due to the second coupling field.

Entanglement is a resource central to quantum information (QI). In particular, entanglement shared between two distant parties allows them to do certain tasks that would otherwise be impossible. In this context, we study the effect on the available entanglement of physical restrictions on the local operations that can be performed by the two parties. We enforce these physical restrictions by generalized superselection rules (SSRs), which we define to be associated with a given group of physical transformations. Specifically the generalized SSR is that the local operations must be covariant with respect to that group. Then we operationally define the entanglement constrained by a SSR, and show that it may be far below that expected on the basis of a naive (or ``fluffy bunny'') calculation. We consider two examples. The first is a particle number SSR. Using this we show that for a two-mode BEC (with Alice owning mode $A$ and Bob mode $B$), the useful entanglement shared by Alice and Bob is identically zero. The second, a SSR associated with the symmetric group, is applicable to ensemble QI processing such as in liquid-NMR. We prove that even for an ensemble comprising many pairs of qubits, with each pair described by a pure Bell state, the entanglement per pair constrained by this SSR goes to zero for a large ensemble., Comment: 8 pages, proceedings paper for an invited talk at 16th International Conference on Laser Spectroscopy (2003)

In elementary presentations of quantum optics it is more or less an axiom that lasers produce coherent light. However, theoretical models for typical laser processes imply that the state of the cavity mode for a laser has no mean coherent amplitude at all. Rather, far above threshold, it is a Poissonian mixture of number states, or, equivalently, a mixture of coherent states of all phases [1, 2] Equation $$ {\psi^8}(x,t) = 2|c{|^{{ - \frac{1}{2}}}}\eta (\exp i\Phi (x,t))\sec h[2\eta (x - {x_0}) + 8\xi \eta t] $$ (1) The existence of these two representations warns against believing that the laser really is in a coherent state |{√μ} e(sui〉 of definite but unknown phase .

This work studies the lossless intensity-dependent dispersion in coherently prepared multi-state atoms using electromagnetically induced transparency (EIT). This study also describes the chain /spl Lambda/ atoms, identifies realistic conditions for observing chain /spl Lambda/ atoms, presents extended results where propagation effects are taken into account and explores the prospects for using such atoms in novel quantum devices.

A new multiresolution SAR image formation algorithm called planar subarray processing, PSAP, is presented. The PSAP provides the capability to perform intermediate decisions using lower resolution image data to redirect the remaining processing functions. These intermediate decisions can include, target detection, change detection, super resolution, and moving target parameter estimation. The PSAP algorithm has a tree like flow structure using small cascaded FFT stages making it suitable for parallel processor implementation.

A laser, be it an optical laser or an atom laser, is an open quantum system that produces a coherent beam of bosons (photons or atoms, respectively). Far above threshold, the stationary state rho(ss) of the laser mode is a mixture of coherent-field states with random phase, or, equivalently, a Poissonian mixture of number states. This paper answers the question: can descriptions such as these, of rho(ss) as a stationary ensemble of pure states, be physically realized? Here physical realization is as defined previously by us [H. M. Wiseman and J. A. Vaccaro, Phys. Lett. A 250, 241 (1998)]: an ensemble of pure states for a particular system can be physically realized if, without changing the dynamics of the system, an experimenter can (in principle) know at any time that the system is in one of the pure-state members of the ensemble. Such knowledge can be obtained by monitoring the baths to which the system is coupled, provided that coupling is describable by a Markovian master equation. Using a family of master equations for the (atom) laser, we solve for the physically realizable (PR) ensembles. We find that for any finite self-energy chi of the bosons in the laser mode, the coherent-state ensemble is not PR; the closest one can come to it is an ensemble of squeezed states. This is particularly relevant for atom lasers, where the self-energy arising from elastic collisions is expected to be large. By contrast, the number-state ensemble is always PR. As the self-energy chi increases, the states in the PR ensemble closest to the coherent-state ensemble become increasingly squeezed. Nevertheless, there are values of chi for which states with well-defined coherent amplitudes are PR, even though the atom laser is not coherent (in the sense of having a Bose-degenerate output). We discuss the physical significance of this anomaly in terms of conditional coherence (and hence conditional Bose degeneracy).

As discussed in Wiseman and Vaccaro [quant-ph/9906125], the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of $\rho_{ss}$, is more natural. In the preceding paper we concentrated upon whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy $\chi$ of the bosons in the laser mode, and the excess phase noise $\nu$. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit ($\nu=\chi=0$), the most robust states are coherent states. As the phase noise $\nu$ or phase dispersion $\chi$ is increased, the most robust states become increasingly amplitude-squeezed. We find scaling laws for these states. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR states having a well-defined coherent amplitude. This lends support to the idea that robust PR ensembles are the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large., Comment: 16 pages, 9 figures included. To be published in Phys. Rev. A, as Part II of a two-part paper. The original version of quant-ph/9906125 is shortly to be replaced by a new version which is Part I of the two-part paper. This paper (Part II) also contains some material from the original version of quant-ph/9906125

Using an operational definition we quantify the entanglement, $E_P$, between two parties who share an arbitrary pure state of $N$ indistinguishable particles. We show that $E_P \leq E_M$, where $E_M$ is the bipartite entanglement calculated from the mode-occupation representation. Unlike $E_M$, $E_P$ is {\em super-additive}. For example, $E_P =0$ for any single-particle state, but the state $\ket{1}\ket{1}$, where both modes are split between the two parties, has $E_P = 1/2$. We discuss how this relates to quantum correlations between particles, for both fermions and bosons., Comment: 4 + epsilon pages. No figures. This published version is slightly modified from the original

We have observed clear Rabi oscillations of a weak probe in a strongly driven three-level lambda system in laser-cooled rubidium for the first time. When the coupling field is non-adiabatically switched on using a Pockels cell, transient probe gain without population inversion is obtained in the presence of uncoupled absorptions. Our results are supported by three-state computations., Comment: 4 pages, 4 figures, experimental results

Observations of a doubly driven V system probed to a fourth level in an N configuration are reported. A dressed state analysis is also presented. The expected three-peak spectrum is explored in a cold rubidium sample in a magneto-optic trap. Good agreement is found between the dressed state theory and the experimental spectra once light shifts and uncoupled absorptions in the rubidium system are taken into account., Comment: 8 pages, 8 figures, Replaced with version scheduled to appear in 1 July 2001 issue of Physical Review A

We consider the implementation of an arbitrary unitary operation U upon a distant quantum system. This teleportation of U can be viewed as a quantum remote control. We investigate protocols which achieve this using local operations, classical communication and shared entanglement (LOCCSE). Lower bounds on the necessary entanglement and classical communication are determined using causality and the linearity of quantum mechanics. We examine in particular detail the resources required if the remote control is to be implemented as a classical black box. Under these circumstances, we prove that the required resources are, necessarily, those needed for implementation by bidirectional state teleportation., Comment: 5 pages, 2 figures Typographical erros in formulas have been corrected. Conclusions unchanged

Certain quantum gates, such as the controlled-NOT gate, are symmetric in terms of the operation of the control system upon the target system and vice versa. However, no operational criteria yet exist for establishing whether or not a given quantum gate is symmetrical in this sense. We consider a restricted, yet broad, class of two-party controlled gate operations for which the gate transforms a reference state of the target into one of an orthogonal set of states. We show that for this class of gates it is possible to establish a simple necessary and sufficient condition for the gate operation to be symmetric., 8 pages

An open quantum system in steady state $\hat\rho_{ss}$ can be represented by a weighted ensemble of pure states $\hat\rho_{ss}=\sum_{k}\wp_{k}\ket{\psi_k} \bra{\psi_k}$ in infinitely many ways. A physically realizable (PR) ensemble is one for which some continuous measurement of the environment will collapse the system into a pure state $\ket{\psi(t)}$, stochastically evolving such that the proportion of time for which $\ket{\psi(t)} = \ket{\psi_{k}}$ equals $\wp_{k}$. Some, but not all, ensembles are PR. This constitutes the preferred ensemble fact, with the PR ensembles being the preferred ensembles. We present the necessary and sufficient conditions for a given ensemble to be PR, and illustrate the method by showing that the coherent state ensemble is not PR for an atom laser., Comment: 5 pages, no figures

We study the remote implementation of a unitary transformation on a qubit. We show the existence of non-trivial protocols (i.e., using less resources than bidirectional state teleportation) which allow the perfect remote implementation of certain continuous sets of quantum operations. We prove that, up to a local change of basis, only two subsets exist that can be implemented remotely with a non-trivial protocol: Arbitrary rotations around a fixed direction $\vec{n}$ and rotations by a fixed angle around an arbitrary direction lying in a plane orthogonal to $\vec{n}$. The overall classical information and distributed entanglement cost required for the remote implementation depends on whether it is a priori known to which of the two teleportable subsets the transformation belongs to. If it is so, the optimal protocol consumes one e-bit of entanglement and one c-bit in each direction. If the subset is not known, two e-bits of entanglement need to be consumed while the classical channel becomes asymmetric, two c-bits are conveyed from Alice to Bob but only one from Bob to Alice.

This paper presents a wide-ranging theoretical and experimental study of non-adiabatic transient phenomena in a $\Lambda $ EIT system when a strong coupling field is rapidly switched on or off. The theoretical treatment uses a Laplace transform approach to solve the time-dependent density matrix equation. The experiments are carried out in a Rb$^{87}$ MOT. The results show transient probe gain in parameter regions not previously studied, and provide insight into the transition dynamics between bare and dressed states., Comment: 19 Pages, 9 Figures, 1 in colour. RevTex 4.0 Submitted to Physical Review A

Twenty-six individuals with Stage A1 carcinoma of the prostate (less than or equal to 5%, Gleason score less than or equal to 4) diagnosed from 1969 to 1980 were evaluated with digital rectal examination (DRE) and prostate-specific antigen (PSA). This unique cohort, sixty-one to eight-two years of age (median 72 years), had a mean interval from diagnosis of thirteen years (median 12.5 years). Abnormal findings on DRE were found in 6 individuals, whereas only one elevated PSA was detected. Ninety-six percent of the PSA levels were less than 3.0 ng/mL and nearly 60 percent of the group had 1.0 ng/mL or less. These levels compare favorably with healthy control subjects under forty years of age and with the limited data available for PSA in healthy men over seventy years of age (87% and 26%, respectively). While biopsy showed persistent or recurrent carcinoma in 2 of 5 individuals, further evaluation disclosed only localized disease. Though the PSA provided little additional information to DRE in the individual patient, it appears from an overview of this group that a low level of PSA in Stage A1 prostatic carcinoma may be associated with long-term survival.

We show that for appropriate choices of parameters it is possible to achieve photon blockade in idealised one, two and three atom systems. We also include realistic parameter ranges for rubidium as the atomic species. Our results circumvent the doubts cast by recent discussion in the literature (Grangier et al Phys. Rev Lett. 81, 2833 (1998), Imamoglu et al Phys. Rev. Lett. 81, 2836 (1998)) on the possibility of photon blockade in multi-atom systems., 8 page, revtex, 7 figures, gif. Submitted to Journal of Optics B: Quantum and Semiclassical Optics

Eosinophilic infiltrate of the urinary tract is rare. We report on a patient with eosinophilic cholangitis who later had eosinophilic ureteritis. This case emphasizes the potential serious nature of eosinophilic ureteritis, which often presents with complete ureteral obstruction. The literature pertaining to eosinophilic ureteritis and eosinophilic biliary disease is reviewed.

The stationary solution \rho of a quantum master equation can be represented as an ensemble of pure states in a continuous infinity of ways. An ensemble which is physically realizable through monitoring the system's environment we call an `unraveling'. The survival probability S(t) of an unraveling is the average probability for each of its elements to be unchanged a time t after cessation of monitoring. The maximally robust unraveling is the one for which S(t) remains greater than the largest eigenvalue of \rho for the longest time. The optical parametric oscillator is a soluble example., Comment: 4 pages, LaTeX, 2 figures, Submitted to Phys. Rev. Lett

We define a quasiprobability distribution ${\mathit{S}}_{\mathrm{NP}}$(n,\ensuremath{\theta}) which describes the quantum statistics of the photon number and phase observables of a single-mode field (or, equivalently, a harmonic oscillator). The properties of ${\mathit{S}}_{\mathrm{NP}}$(n,\ensuremath{\theta}) are the photon number and phase analogies of the properties of Wigner's original function, which describes the position and momentum observables. For example, the marginals of ${\mathit{S}}_{\mathrm{NP}}$(n,\ensuremath{\theta}) are the continuous phase and the discrete photon-number probability distributions. We give examples of the ${\mathit{S}}_{\mathrm{NP}}$(n,\ensuremath{\theta}) representation of various states and show, in particular, that ${\mathit{S}}_{\mathrm{NP}}$(n,\ensuremath{\theta}) displays the quantum interference associated with Schr\"odinger cat states. We also describe how ${\mathit{S}}_{\mathrm{NP}}$(n,\ensuremath{\theta}) can be determined from quantities that are, in principle, measurable.

We examine the operator \ensuremath{\Phi}${\mathrm{^}}_{12}$ proposed by Luis and S\'anchez-Soto [Phys. Rev. A 48, 4702 (1993)] as a possible description of the phase difference between two electromagnetic fields. We show that there is a difficulty in directly representing the phase difference between arbitrary fields by this operator, but conclude that the incorporation of the operator into an alternative definition of phase difference constitutes a valuable alternative approach to the quantum description of phase.

A highly regular and computationally efficient SAR image formation processor architecture has been developed for wide-area ground surveillance systems. The architecture is based on the repetitive use of a very simple small FFT kernel (instead of a large 2D FFT) providing a variable resolution capability. The first stage of the planar subarray processor (PSAP) forms coarse images and constructs polar formatted, pseudo spotlight SARs. The second stage evaluates the requisite 2D transforms in a multiple- stage block FFT, providing variable resolution images. The fold- FFT is paramount to the computational efficiency of the approach.

We discuss a simple and readily acceptable operational approach to defining quantum optical phase, and examine possible ways of measuring the resulting phase probability density.

The physical nature of time has been an enigma for centuries. Despite the progress made in linking various arrows of time together, the underlying reason for the observed direction of time has remained a deep mystery. However, an increasing number of experiments are confirming a violation of time reversal invariance (T) in meson decay processes. T violation represents a fundamental break in the symmetry between the past and future. I show here that such processes 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. These results illustrate that there are previously-unknown large-scale physical effects arising from the T violation processes in meson decay. Moreover these effects offer a solution to the age-old problem of the cause of the unidirectionality of time.

Replacement of a percutaneous nephrostomy tube can be a difficult task. The often time-consuming procedure involves replacement of a guide wire blindly or under fluoroscopic control, or by using ultrasound after decompression of hydronephrosis. A rigid 8.5F ureteroscope was used successfully to replace nephrostomy tubes in 3 patients with obstructive uropathy secondary to prostate carcinoma and in 1 with an ileoureteral anastomotic leak following radical cystectomy.

A programmable, reconfigurable DSP array has been designed in response to the need for a real-time adaptive sidelobe canceller to support wide bandwidth high frequency radar concepts. These concepts incorporate multiple (up to 128) mainbeams and many degrees of freedom using many auxiliary antenna elements, and employ frequency sub-banding to partition a 1 MHz instantaneous bandwidth. The real-time sidelobe canceller is based on the Gram-Schmidt orthogonalization procedure and uses concurrent block adaptation to derive an optimal solution for the available data. The sidelobe canceller implementation configures the modular DSP array into a two-dimensional Gram-Schmidt processor. A proof-of-concept sidelobe canceller implementation will provide the capability to perform sidelobe cancellation on two simultaneous mainbeams using eight auxiliary channels. The DSP array sidelobe canceller can be expanded to support more than 128 mainbeams using auxiliary channels. The array consists of TMS320C30 based processing nodes providing four independent data ports (two inputs and two outputs) connected via high speed serial data links supporting two megawords-per-second sustained throughput rates (8 megawords-per-second burst rates). These manually configured data connections are separated from the control structure, allowing a variety of interconnect strategies (one-dimensional, two-dimensional, etc.). A host processor is used to download application code and control the system. This programmable, reconfigurable array processor can also be used for a variety of other applications including the singular value decomposition, matrix-matrix multipliers, and FFTs.

A technique for digitally-directed core biopsy using the Biopty device and prospective comparison of accuracy and comfort, using this technique simultaneously with transrectal needle aspiration, are presented. To better estimate the true prevalence of carcinoma in the study population, a repeat combined procedure was performed on all subjects who did not have carcinoma confirmed on the initial core biopsies. All procedures were done by one investigator and all pathology reviewed by one senior pathologist. A total of 180 combined procedures were performed on 100 consecutive patients with palpably abnormal prostates; 30 carcinomas were detected. Digitally-directed Biopty biopsy yielded a sensitivity rate of 87 percent compared with 57 percent for needle aspiration (p less than 0.05). Using a numerical comfort scale, the Biopty device was also rated less painful than needle aspiration (p = 0.0001). The morbidity of the combined procedure was minimal, with a minor complication rate of 2.2 percent. No infections occurred.

Various quasiprobability distributions have been developed in the past using the Hilbert space of the single-mode light field. The development of a quasiprobability distribution associated with a phase operator has previously been impossible because of the absence of a unique Hermitian phase operator defined on the Hilbert space. Recently, however, Pegg and Barnett [Europhys. Lett. 6, 483 (1988); Phys. Rev. A 39, 1665 (1989)] and Barnett and Pegg [J. Mod. Optics 36, 7 (1989)] introduced a new formalism that does allow the construction of a Hermitian phase operator and associated phase eigenstates. In this paper we develop a quasiprobability distribution associated with the number and phase operators of the single-mode light field in the new formalism. The new distribution, which we call the number-phase Wigner function, has properties analogous to the Wigner function. We also derive the number-phase Wigner representation of number states, phase states, general physical states, coherent states, and the squeezed vacuum. We find this new representation has features that are related to the number and phase properties of states. For example, the number-phase Wigner representation of a number state is nonzero only on a circle, while the representation of a phase state is only nonzero along a radial line.