Bulletin of the American Physical Society
38th Annual Meeting of the Division of Atomic, Molecular, and Optical Physics
Volume 52, Number 7
Tuesday–Saturday, June 5–9, 2007; Calgary, Alberta, Canada
Session W5: Quantum Measurement and Quantum Information |
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Chair: D. Uskov, Louisiana State University Room: TELUS Convention Centre Macleod A3-A4 |
Saturday, June 9, 2007 8:00AM - 8:12AM |
W5.00001: Measuring an unknown phase with quantum-limited precision using nonlinear beamsplitters Yuping Huang, Michael Moore High precision phase measurement is currently a central goal of quantum interferometry. In general, the precision is described by the phase estimation uncertainty $\Delta\theta$, which is characterized by two scaling behaviors, shot-noise limited with $\Delta\theta\sim 1/\sqrt{N}$ and Heisenberg limited with $\Delta\theta\sim 1/N$ (N the total particle number). According to Bayesian analysis, Heisenberg limited preciosion for $\theta=0$ can be achieved in a Mach-Zehnder interferometer with $(|N-1,N+1\rangle+|N+1,N-1\rangle)/\sqrt{2}$ as input state based and a single measurement or $|N,N\rangle$ input based on multiple measurements. As $\theta$ deviates from zero, both schemes degrade rapidly to worse than shot-noise-limited precision. In contrast, a Quantum Fourier Transform (QFT) based interferometer can measure an arbitrary $\theta$ at Heisenberg limited precision, but requires a quantum computer. To extend the range of precisely measurable $\theta$ without a quantum computer, we propose using nonlinear beam-spitters. We find that this can achieve nearly Heisenberg-limited precision over a wide range of $\theta$. This scheme can be implemented in a bimodal Bose-Einstein condensate (BEC) system with tunable scattering length. Numerical calculations show: i) at $\theta=0$, $\Delta\theta\sim 1/N$; and ii) as $\theta$ moves towards $\pm \pi/2$, the precision crosses over smoothly to $\Delta\theta\sim 1/\sqrt{N}$, providing a wide range over which the precision is nearly Heisenberg limited. [Preview Abstract] |
Saturday, June 9, 2007 8:12AM - 8:24AM |
W5.00002: Interaction- and measurement-free quantum information processing with single-atom and/or single-photon qubits Michael Moore, Yuping Huang Interaction-free measurement (IFM) uses quantum interference to allow a single photon to detect a perfectly absorbing object without the photon interacting with the object directly. In high-efficiency IFM, the Quantum Zeno Effect is employed to increase the success probability from the original 50\% to (N-a)/N, where N is the number of cycles the photon makes through the device and a~1. In principle IFM protocols allow the hyperfine state of a single atom to become entangled with the polarization of a single photon. To date, attempts to employ this entanglement to create universal atom-atom quantum logic gates, such as CNOT gates, have not succeeded in achieving (N-a)/N efficiency. In addition, they also require the detection of ancillary photons. At present, single-photon detection cannot be implemented experimentally with high efficiency. By making several key modications, we have developed a pair of complimentary Interaction-Free quantum gates that can be used to design high-efficiency atom-atom, atom-photon, and photon-photon CNOT and state-transfer protocols, which do not require the use of photodetectors or measurements of any kind. In addition, we have analyzed the effects of imperfect atomic selection rules due to tight-focussing of the photons and tight trapping of the atoms, and identified the scattering parameter on which the efficiency depends sensitively. [Preview Abstract] |
Saturday, June 9, 2007 8:24AM - 8:36AM |
W5.00003: Adaptive Quantum State Detection through Repetitive Mapping David Hume, Till Rosenband, David Wineland, Jim Bergquist State detection plays an important role in quantum information processing and quantum-limited metrology. In some quantum systems direct detection is impossible or inefficient. This can be overcome by coupling the primary quantum system to an ancillary system used for measurement [1]. The measurement process consists of mapping the primary state to the ancilla followed by ancilla detection. If the measurement does not affect the projected populations of the primary system, it may be repeated yielding higher fidelity. Using two trapped ion species ($\rm{^{27}Al^{+ }}$and $\rm{^{9}Be^{+}}$) as the primary and ancillary systems, we demonstrate high-fidelity measurement despite imperfect information transfer and ancilla detection. An adaptive measurement strategy allows for multiple qubit state discrimination with one ancilla. This opens the way for several applications in quantum information processing and advances our optical clock effort. [1] P.O. Schmidt, et. al. Science 309 749 (2005) [Preview Abstract] |
Saturday, June 9, 2007 8:36AM - 8:48AM |
W5.00004: Atom interferometry, microscopy, complementarity, and the perfect lens Barry Sanders, Karl-Peter Marzlin, Peter Knight Development of the `perfect lens' poses an interesting challenge to standard concepts of complementarity manifested in interferometric which-way vs fringe visibility experiments. We show that a `microscope' with a `perfect lens' provides the extremal point of maximum which-way information in atom interferometry, and our theory rigorously connects complementarity in interferometry with the standard position-momentum Heisenberg uncertainty relation. [Preview Abstract] |
Saturday, June 9, 2007 8:48AM - 9:00AM |
W5.00005: Distinguishability of a Tripartite Unextendible Product Basis using Local Operations and Classical Communication Michael Durocher, Barry C. Sanders, Jonathan Walgate Quantum states must be distinguished every time we need to obtain information from a system. Here, we quantify multi- partite state distiguishability with different measurement settings; this leads to important results in the case of an important tripartite system. Specifically, we analyze the smallest tripartite Unextendible Product Basis (UPB). This UPB has interesting symmetries and is not entangled, hence interesting here. Our work is an important step towards full quantitative analysis of local information available in locally indistinguishable sets of states. We consider the case in which the parties are restricted to Local Operations and Classical Communication (LOCC), which makes perfect distinguishability impossible in this situation. We also discuss our discovery of optimal (maximum extraction of information as given by the Shannon entropy decrease) protocols for distinguishing our UPB. [Preview Abstract] |
Saturday, June 9, 2007 9:00AM - 9:12AM |
W5.00006: ABSTRACT HAS BEEN MOVED TO J5.00012 |
Saturday, June 9, 2007 9:12AM - 9:24AM |
W5.00007: Three Undistinguished Quantum Radiators in Quantified Cavity Field Nicolae Enaki, Tudor Rosca In many problems of quantum information it is used the distinguished ensembles of qubits in the realization of quantum states of registers. On the other hand, the Bose-Einstein condensations of atomic ensembles give us the possibility to regard two-level atoms like an undistinguished ensemble. In this representation N two-level atoms have a more reduced number of collective states. In general case, N two-level atoms with the number of states 2$^{N}$ can be reduced to N+1 states in processes of coherent excitation in according with the undistinguished principle between the radiators. In this paper the behavior of ensemble consisted from three undistinguished atoms in interaction with one mode of microcavity is discussed. This problem is reduced to the solution of characteristic equation for the linear system, which contains N+1equations. We reduced the number of 2$^{3}$ states for three two-level radiators to four levels and solved exactly the system of linear equations. The application of cooperative effect of absorption and emission in micromasers is discussed. The condition for lasing and trapping effects is found. The quantum proprieties of cooperative generated field in the cavity are studied. [Preview Abstract] |
Saturday, June 9, 2007 9:24AM - 9:36AM |
W5.00008: Fundamental physics issues of multilevel logic in developing a parallel processor. Anirban Bandyopadhyay, Kazushi Miki In the last century, On and Off physical switches, were equated with two decisions 0 and 1 to express every information in terms of binary digits and physically realize it in terms of switches connected in a circuit. Apart from memory-density increase significantly, more possible choices in particular space enables pattern-logic a reality, and manipulation of pattern would allow controlling logic, generating a new kind of processor. Neumann's computer is based on sequential logic, processing bits one by one. But as pattern-logic is generated on a surface, viewing whole pattern at a time is a truly parallel processing. Following Neumann's and Shannons fundamental thermodynamical approaches we have built compatible model based on series of single molecule based multibit logic systems of 4-12 bits in an UHV-STM. On their monolayer multilevel communication and pattern formation is experimentally verified. Furthermore, the developed intelligent monolayer is trained by Artificial Neural Network. Therefore fundamental weak interactions for the building of truly parallel processor are explored here physically and theoretically. [Preview Abstract] |
Saturday, June 9, 2007 9:36AM - 9:48AM |
W5.00009: Spherical Geometry of Two Qubit Unitary Operators. Dmitry Uskov, Ravi Rau Geometric and algebraic properties of the SU(4) group of two-qubit transformations are much richer than corresponding properties of an arbitrary SU(N) group because there exists an accidental isomorphism between the SU(4) Lie group and the Spin(6) Lie group (a spinor form of orthogonal rotations in Euclidean 6-dimensional space). We exploit this property to construct a new set of [Spin(n+1)/Spin(n)]$\times $Spin(n) fiber bundles, embedded in the SU(4) manifold and to identify relevant holonomies. Geometrically these fiber bundles are even simpler than fiber bundles supporting Berry and Wilczek-Zee non-Abelian phases. It is well known that construction of the Bloch Sphere is based on the SU(2)=Spin(3) Lie group isomorphism. Since quotient spaces Spin(n+1)/Spin(n) are n-dimensional spheres S$^{n}$, the chain of embedded subgroups Spin(3), Spin(4), Spin(5) allows to complete the Bloch Sphere construction for the SU(4) case by a combination of spheres of higher dimensions S$^{3}$-S$^{4}$-S$^{5}$. As an example we derive a set of linear dynamic equation for generalized S$^{4}$ Bloch sphere, describing an evolution of a 4-level quantum system. [Preview Abstract] |
Saturday, June 9, 2007 9:48AM - 10:00AM |
W5.00010: The Spekkens Toy Model Revisited Michael Skotiniotis, Aidan Roy, Barry C. Sanders We review the toy model introduced by R.W. Spekkens, and show that the operations on a single toy bit belong to the group $S_3$ semi direct $Z_2^3$. The original group $S_4$ is shown to be a subgroup of this. We show that this group does not violate the basic principle of the toy model nor any quantum mechanics and we show its natural extension to the two toy bit case. [Preview Abstract] |
Saturday, June 9, 2007 10:00AM - 10:12AM |
W5.00011: De Broglie waves as a manifestation of clock desynchronization William Baylis De Broglie matter waves, such as used in atom optics or for interference in a BE condensate, can be viewed as the relativistic effect that spatially separated clocks that are synchronized in the rest frame become desynchronized when set in motion. The ``clocks'' here are the quantum oscillation of a stationary state. The usual de Broglie wavelength and superluminal wave velocity are easily derived. As simple and obvious as this picture is, I have not seen it described before. It is not only a nice example of clock desynchronization, it also has an interesting consequence: the oscillation of the stationary state must be at the Zitterbewegung frequency, that is, the corresponding energy must include the rest-mass energy. Of course most experiments are only sensitive to frequency differences. [Preview Abstract] |
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