### Abstract

Measuring an entangled state of two particles is crucial to many quantum communication protocols. Yet Bell- state distinguishability using a finite apparatus obeying linear evolution and local measurement is theoretically limited. We extend known bounds for Bell-state distinguishability in one and two variables to the general case of entanglement in *n* two-state variables. We show that at most :mil:2^{n+1} - 1 classes out of :mil:4^{n} hyper-Bell states can be distinguished with one copy of the input state. With two copies, complete distinguishability is possible. We present optimal schemes in each case.

### Abstract

In single-qubit quantum secret sharing, a secret is shared between *N* parties via manipulation and measurement of one qubit at a time. Each qubit is sent to all *N* parties in sequence; the secret is encoded in the first participant’s preparation of the qubit state and the subsequent participants’ choices of state rotation or measurement basis. We present a protocol for single-qubit quantum secret sharing using polarization entanglement of photon pairs produced in type-I spontaneous parametric downconversion. We investigate the protocol’s security against eavesdropping attack under common experimental conditions: a lossy channel for photon transmission, and imperfect preparation of the initial qubit state. A protocol which exploits *entanglement* between photons, rather than simply polarization *correlation*, is more robustly secure. We implement the entanglement-based secret-sharing protocol with 87% secret-sharing fidelity, limited by the purity of the entangled state produced by our present apparatus. We demonstrate a photon-number splitting eavesdropping attack, which achieves no success against the entanglement-based protocol while showing the predicted rate of success against a correlation-based protocol.

### Abstract

A new method of direct, rapid nano- to micro-scale patterning of high purity cobalt is presented. The method utilizes a combination of electron beam induced deposition (EBID) and seeded growth at elevated temperatures below the temperature of spontaneous thermal decomposition. Dicobalt octacarbonyl $$\mathrm{Co_{2}(CO)_{8}}$$ is used as the precursor and carbon as a seed layer. Seeded deposition is carried out in the substrate temperature range from 55 to 75°C. Deposition yield is significantly higher than conventional EBID and magnetotransport measurements indicate that resistivity, $$22~\mu\Omega~\mathrm{cm}$$, and saturation magnetization, 1.55 T, are much closer to the corresponding values for bulk Co than those for standard EBID.

### Abstract

A popular method for generating micron-sized aerosols is to submerge ultrasonic ( *ω* ~ MHz) piezoelectric oscillators in a water bath. The submerged oscillator atomizes the fluid, creating droplets with radii proportional to the wavelength of the standing wave at the fluid surface. Classical theory for the Faraday instability predicts a parametric instability driving a capillary wave at the subharmonic (*ω*/2) frequency. For many applications it is desirable to reduce the size of the droplets; however, using higher frequency oscillators becomes impractical beyond a few MHz. Observations are presented that demonstrate that smaller droplets may also be created by increasing the driving amplitude of the oscillator, and that this effect becomes more pronounced for large driving frequencies. It is shown that these observations are consistent with a transition from droplets associated with subharmonic ( *ω*/2) capillary waves to harmonic (*ω*) capillary waves induced by larger driving frequencies and amplitudes, as predicted by a stability analysis of the capillary waves.

### Abstract

In ion trap quantum information processing, efficient fluorescence collection is critical for fast, high-fidelity qubit detection and ion–photon entanglement. The expected size of future many-ion processors requires scalable light collection systems. We report on the development and testing of a microfabricated surface-electrode ion trap with an integrated high-numerical aperture (NA) micromirror for fluorescence collection. When coupled to a low-NA lens, the optical system is inherently scalable to large arrays of mirrors in a single device. We demonstrate the stable trapping and transport of 40Ca+ ions over a 0.63 NA micromirror and observe a factor of 1.9 enhancement of photon collection compared to the planar region of the trap.

### Abstract

Being able to distinguish light-quark jets from gluon jets on an event-by-event basis could significantly enhance the reach for many new physics searches at the Large Hadron Collider. Through an exhaustive search of existing and novel jet substructure observables, we find that a multivariate approach can filter out over 95% of the gluon jets while keeping more than half of the light-quark jets. Moreover, a combination of two simple variables, the charge track multiplicity and the $$p_T$$-weighted linear radial moment (girth), can achieve similar results. Our study is only Monte Carlo based, so other observables constructed using different jet sizes and parameters are used to highlight areas that deserve further theoretical and experimental scrutiny. Additional information, including distributions of around 10 000 variables, can be found at http://jets.physics.harvard.edu/qvg/.

### Abstract

The role of petal spurs and specialized pollinator interactions has been studied since Darwin. Aquilegia petal spurs exhibit striking size and shape diversity, correlated with specialized pollinators ranging from bees to hawkmoths in a textbook example of adaptive radiation. Despite the evolutionary significance of spur length, remarkably little is known about Aquilegia spur morphogenesis and its evolution. Using experimental measurements, both at tissue and cellular levels, combined with numerical modelling, we have investigated the relative roles of cell divisions and cell shape in determining the morphology of the Aquilegia petal spur. Contrary to decades-old hypotheses implicating a discrete meristematic zone as the driver of spur growth, we find that Aquilegia petal spurs develop via anisotropic cell expansion. Furthermore, changes in cell anisotropy account for 99 per cent of the spur-length variation in the genus, suggesting that the true evolutionary innovation underlying the rapid radiation of Aquilegia was the mechanism of tuning cell shape.

#### From the Cover…

.. epigraph:: “Townsend has written an excellent book that someone needed to write for the modern physics textbook market. He has given it the same care that he gave to his excellent quantum mechanics book.” -- Jeff Dunham, Middlebury College .. epigraph:: “When I read this book I immediately adopted it for my sophomore modern physics class. This is the best introduction to quantum mechanics available.” -- B. Paul Padley, Rice University

# Recent Publications

Student authorFaculty author

61. Donna Phu, Lindsay S. Wray, Robert V. Warren, Richard C. Haskell, and Elizabeth Orwin Effect of Substrate Composition and Alignment on Corneal Cell Phenotype Tissue Engineering A 17 (2011) 799–807. Neal C. Pisenti, Carl Philipp E. Gaebler, and Theresa W. Lynn Distinguishability of hyperentangled Bell states by linear evolution and local projective measurement Physical Review A 84 (2011) 022340. David A. Berryrieser, Peter J. Scherpelz, Rudolph W. Resch, and Theresa W. Lynn Entanglement-secured single-qubit quantum secret sharing Physical Review A 84 (2011) 032303. L. M. Belova, James C. Eckert, J. J. L. Mulders, C. Christophersen, E. D. Dahlberg, and A. Riazanova Rapid electron beam assisted patterning of pure cobalt at elevated temperatures via seeded growth Nanotechnology 22 (2011) 145305. Andrew P. Higginbotham, Andrew J. Bernoff, Aaron M. Guillen, Thomas D. Donnelly, and Nathan Jones Evidence of the harmonic Faraday instability in ultrasonic atomization experiments with a deep, inviscid fluid Journal of the Acoustical Society of America 130 (2011) 2694-2699. J. T. Merrill, C. Volin, D. W. Landgren, J. M. Amini, K. Wright, Charlie Doret, C. -S. Pai, H. Hayden, T. Killian, D. L. Faircloth, K. R. Brown, A. W. Harter, and R. E. Slusher Demonstration of integrated microscale optics in surface-electrode ion traps New Journal of Physics 13 (2011) 103005. Jason Gallicchio and Matthew D Schwartz Pure samples of quark and gluon jets at the LHC Journal of High Energy Physics 2011 (2011) . Jason Gallicchio and Matthew D Schwartz Quark and Gluon Tagging at the LHC Physical Review Letters 107 (2011) 172001. Joshua R. Puzey, Sharon Gerbode, Scott A. Hodges, Elena M. Kramer, and L. Mahadevan Evolution of spur-length diversity in Aquilegia petals is achieved solely through cell-shape anisotropy Proceedings of the Royal Society B 279 (2011) 1640-1645. John S. Townsend Quantum Physics: a Fundamental Approach to Modern Physics University Science Books, Sausalito, 2010.