Exponential Separation of Quantum and Classical Online Space Complexity

Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we study, for the first time explicitly, space-bounded quantum algorithms for computational problems where the input is given not as a whole, but bit by bit. We show that there exist such problems that a quantum computer can solve using exponentially less work space than a classical computer. More precisely, we introduce a very natural and simple model of a space-bounded quantum online machine and prove an exponential separation of classical and quantum online space complexity, in the bounded-error setting and for a total language. The language we consider is inspired by a communication problem (the set intersection function) that Buhrman, Cleve and Wigderson used to show an almost quadratic separation of quantum and classical bounded-error communication complexity. We prove that, in the framework of online space complexity, the separation becomes exponential.Comment: 13 pages. v3: minor change

Molecular prediction of lytic vs lysogenic states for Microcystis phage: Metatranscriptomic evidence of lysogeny during large bloom events

Microcystis aeruginosa is a freshwater bloom-forming cyanobacterium capable of producing the potent hepatotoxin, microcystin. Despite increased interest in this organism, little is known about the viruses that infect it and drive nutrient mobilization and transfer of genetic material between organisms. The genomic complement of sequenced phage suggests these viruses are capable of integrating into the host genome, though this activity has not been observed in the laboratory. While analyzing RNA-sequence data obtained from Microcystis blooms in Lake Tai (Taihu, China), we observed that a series of lysogeny-associated genes were highly expressed when genes involved in lytic infection were down-regulated. This pattern was consistent, though not always statistically significant, across multiple spatial and temporally distinct samples. For example, samples from Lake Tai (2014) showed a predominance of lytic virus activity from late July through October, while genes associated with lysogeny were strongly expressed in the early months (June–July) and toward the end of bloom season (October). Analyses of whole phage genome expression shows that transcription patterns are shared across sampling locations and that genes consistently clustered by co-expression into lytic and lysogenic groups. Expression of lytic-cycle associated genes was positively correlated to total dissolved nitrogen, ammonium concentration, and salinity. Lysogeny-associated gene expression was positively correlated with pH and total dissolved phosphorous. Our results suggest that lysogeny may be prevalent in Microcystis blooms and support the hypothesis that environmental conditions drive switching between temperate and lytic life cycles during bloom proliferation

An entanglement monotone derived from Grover's algorithm

This paper demonstrates that how well a state performs as an input to Grover's search algorithm depends critically upon the entanglement present in that state; the more entanglement, the less well the algorithm performs. More precisely, suppose we take a pure state input, and prior to running the algorithm apply local unitary operations to each qubit in order to maximize the probability P_max that the search algorithm succeeds. We prove that, for pure states, P_max is an entanglement monotone, in the sense that P_max can never be decreased by local operations and classical communication.Comment: 7 page

Experimental requirements for Grover's algorithm in optical quantum computation

The field of linear optical quantum computation (LOQC) will soon need a repertoire of experimental milestones. We make progress in this direction by describing several experiments based on Grover's algorithm. These experiments range from a relatively simple implementation using only a single non-scalable CNOT gate to the most complex, requiring two concatenated scalable CNOT gates, and thus form a useful set of early milestones for LOQC. We also give a complete description of basic LOQC using polarization-encoded qubits, making use of many simplifications to the original scheme of Knill, Laflamme, and Milburn.Comment: 9 pages, 8 figure

Radiative Correction to the Dirichlet Casimir Energy for λϕ4\lambda\phi^{4} Theory in Two Spatial Dimensions

In this paper, we calculate the next to the leading order Casimir energy for real massive and massless scalar fields within $\lambda\phi^{4}$ theory, confined between two parallel plates with the Dirichlet boundary condition in two spatial dimensions. Our results are finite in both cases, in sharp contrast to the infinite result reported previously for the massless case. In this paper we use a renormalization procedure introduced earlier, which naturally incorporates the boundary conditions. As a result our radiative correction term is different from the previously calculated value. We further use a regularization procedure which help us to obtain the finite results without resorting to any analytic continuation techniques.Comment: 8 pages, 3 figure

A Measurement of Time-Averaged Aerosol Optical Depth using Air-Showers Observed in Stereo by HiRes

Air fluorescence measurements of cosmic ray energy must be corrected for attenuation of the atmosphere. In this paper we show that the air-showers themselves can yield a measurement of the aerosol attenuation in terms of optical depth, time-averaged over extended periods. Although the technique lacks statistical power to make the critical hourly measurements that only specialized active instruments can achieve, we note the technique does not depend on absolute calibration of the detector hardware, and requires no additional equipment beyond the fluorescence detectors that observe the air showers. This paper describes the technique, and presents results based on analysis of 1258 air-showers observed in stereo by the High Resolution Fly's Eye over a four year span.Comment: 7 pages, 3 figures, accepted for publication by Astroparticle Physics Journa

Classical and Quantum Integrable Systems in \wt{\gr{gl}}(2)^{+*} and Separation of Variables

Classical integrable Hamiltonian systems generated by elements of the Poisson commuting ring of spectral invariants on rational coadjoint orbits of the loop algebra \wt{\gr{gl}}^{+*}(2,{\bf R}) are integrated by separation of variables in the Hamilton-Jacobi equation in hyperellipsoidal coordinates. The canonically quantized systems are then shown to also be completely integrable and separable within the same coordinates. Pairs of second class constraints defining reduced phase spaces are implemented in the quantized systems by choosing one constraint as an invariant, and interpreting the other as determining a quotient (i.e., by treating one as a first class constraint and the other as a gauge condition). Completely integrable, separable systems on spheres and ellipsoids result, but those on ellipsoids require a further modification of order \OO(\hbar^2) in the commuting invariants in order to assure self-adjointness and to recover the Laplacian for the case of free motion. For each case - in the ambient space ${\bf R}^{n}$, the sphere and the ellipsoid - the Schr\"odinger equations are completely separated in hyperellipsoidal coordinates, giving equations of generalized Lam\'e type.Comment: 28 page

Winterberg's conjectured breaking of the superluminal quantum correlations over large distances

We elaborate further on a hypothesis by Winterberg that turbulent fluctuations of the zero point field may lead to a breakdown of the superluminal quantum correlations over very large distances. A phenomenological model that was proposed by Winterberg to estimate the transition scale of the conjectured breakdown, does not lead to a distance that is large enough to be agreeable with recent experiments. We consider, but rule out, the possibility of a steeper slope in the energy spectrum of the turbulent fluctuations, due to compressibility, as a possible mechanism that may lead to an increased lower-bound for the transition scale. Instead, we argue that Winterberg overestimated the intensity of the ZPF turbulent fluctuations. We calculate a very generous corrected lower bound for the transition distance which is consistent with current experiments.Comment: 7 pages, submitted to Int. J. Theor. Phy

f0(980) meson as a K bar K molecule in a phenomenological Lagrangian approach

We discuss a possible interpretation of the f0(980) meson as a hadronic molecule - a bound state of K and bar K mesons. Using a phenomenological Lagrangian approach we calculate the strong f0(980) to pi pi and electromagnetic f0(980) to gamma gamma decays. The compositeness condition provides a self-consistent method to determine the coupling constant between f0 and its constituents, K and bar K. Form factors governing the decays of the f0(980) are calculated by evaluating the kaon loop integrals. The predicted f0(980) to pi pi and f0(980) to gamma gamma decay widths are in good agreement with available data and results of other theoretical approaches.Comment: 21 pages, 11 figures, revised version accepted for publication in Eur. Phys. J.