The Optimal Single Copy Measurement for the Hidden Subgroup Problem

The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient new quantum algorithms for the non-abelian hidden subgroup problem. Previous work has identified the optimal single copy measurement for the hidden subgroup problem over abelian groups as well as for the non-abelian problem in the setting where the subgroups are restricted to be all conjugate to each other. Here we describe the optimal single copy measurement for the hidden subgroup problem when all of the subgroups of the group are given with equal a priori probability. The optimal measurement is seen to be a hybrid of the two previously discovered single copy optimal measurements for the hidden subgroup problem.Comment: 8 pages. Error in main proof fixe

Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms

The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient (size poly(n,d,log(1/\epsilon)) for accuracy \epsilon) quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. These circuits are based on efficient circuits for the Clebsch-Gordan transformation. We also present an efficient circuit for a limited version of the Schur transform in which one needs only to project onto different Schur subspaces. This second circuit is based on a generalization of phase estimation to any nonabelian finite group for which there exists a fast quantum Fourier transform.Comment: 4 pages, 3 figure

Electronic states and Landau levels in graphene stacks

We analyze, within a minimal model that allows analytical calculations, the electronic structure and Landau levels of graphene multi-layers with different stacking orders. We find, among other results, that electrostatic effects can induce a strongly divergent density of states in bi- and tri-layers, reminiscent of one-dimensional systems. The density of states at the surface of semi-infinite stacks, on the other hand, may vanish at low energies, or show a band of surface states, depending on the stacking order

Interactions of Bacillus Mojavensis and Fusarium Verticillioides With a Benzoxazolinone (Boa) and Its Transformation Product, Apo

En:Journal of Chemical Ecology (2007, vol. 33, n. 10, p. 1885-1897)The benzoxazolinones, specifically benzoxazolin-2(3H)-one (BOA), are important transformation products of the benzoxazinones that can serve as allelochemicals providing resistance to maize from pathogenic bacteria, fungi, and insects. However, maize pathogens such as Fusarium verticillioides are capable of detoxifying the benzoxazolinones to 2-aminophenol (AP), which is converted to the less toxic N-(2-hydroxyphenyl) malonamic acid (HPMA) and 2-acetamidophenol (HPAA). As biocontrol strategies that utilize a species of endophytic bacterium, Bacillus mojavensis, are considered efficacious as a control of this Fusarium species, the in vitro transformation and effects of BOA on growth of this bacterium was examined relative to its interaction with strains of F. verticillioides. The results showed that a red pigment was produced and accumulated only on BOA-amended media when wild type and the progeny of genetic crosses of F. verticillioides are cultured in the presence of the bacterium. The pigment was identified as 2-amino-3H-phenoxazin-3-one (APO), which is a stable product. The results indicate that the bacterium interacts with the fungus preventing the usual transformation of AP to the nontoxic HPMA, resulting in the accumulation of higher amounts of APO than when the fungus is cultured alone. APO is highly toxic to F. verticillioides and other organisms. Thus, an enhanced biocontrol is suggested by this in vitro study. =580 $aEn:Journal of Chemical Ecolog

The Stability of Quantum Concatenated Code Hamiltonians

Protecting quantum information from the detrimental effects of decoherence and lack of precise quantum control is a central challenge that must be overcome if a large robust quantum computer is to be constructed. The traditional approach to achieving this is via active quantum error correction using fault-tolerant techniques. An alternative to this approach is to engineer strongly interacting many-body quantum systems that enact the quantum error correction via the natural dynamics of these systems. Here we present a method for achieving this based on the concept of concatenated quantum error correcting codes. We define a class of Hamiltonians whose ground states are concatenated quantum codes and whose energy landscape naturally causes quantum error correction. We analyze these Hamiltonians for robustness and suggest methods for implementing these highly unnatural Hamiltonians.Comment: 18 pages, small corrections and clarification

The Voluntary Adjustment of Railroad Obligations

Automatic memory management techniques eliminate many programming errors that are both hard to find and to correct. However, these techniques are not yet used in embedded systems with hard realtime applications. The reason is that current methods for automatic memory management have a number of drawbacks. The two major ones are: (1) not being able to always guarantee short real-time deadlines and (2) using large amounts of extra memory. Memory is usually a scarce resource in embedded applications. In this paper we present a new technique, Real-Time Reference Counting (RTRC) that overcomes the current problems and makes automatic memory management attractive also for hard real-time applications. The main contribution of RTRC is that often all memory can be used to store live objects. This should be compared to a memory overhead of about 500% for garbage collectors based on copying techniques and about 50% for garbage collectors based on mark-and-sweep techniques

How to hide a secret direction

We present a procedure to share a secret spatial direction in the absence of a common reference frame using a multipartite quantum state. The procedure guarantees that the parties can determine the direction if they perform joint measurements on the state, but fail to do so if they restrict themselves to local operations and classical communication (LOCC). We calculate the fidelity for joint measurements, give bounds on the fidelity achievable by LOCC, and prove that there is a non-vanishing gap between the two of them, even in the limit of infinitely many copies. The robustness of the procedure under particle loss is also studied. As a by-product we find bounds on the probability of discriminating by LOCC between the invariant subspaces of total angular momentum N/2 and N/2-1 in a system of N elementary spins.Comment: 4 pages, 1 figur

SAURON Observations of Disks in Spheroids

The panoramic integral-field spectrograph SAURON is currently being used to map the stellar kinematics, gaseous kinematics, and stellar populations of a large number of early-type galaxies and bulges. Here, we describe SAURON observations of cold stellar disks embedded in spheroids (NGC3384, NGC4459, NGC4526), we illustrate the kinematics and ionization state of large-scale gaseous disks (NGC4278, NGC7742), and we show preliminary comparisons of SAURON data with barred galaxy N-body simulations (NGC3623).Comment: 8 pages including 5 figures. To appear in Galaxies: The Third Dimension, eds. M. Rosado, L. Binnette, & L. Arias (ASP: San Francisco

SAURON: An Innovative Look at Early-Type Galaxies

A summary of the SAURON project and its current status is presented. SAURON is a panoramic integral-field spectrograph designed to study the stellar kinematics, gaseous kinematics, and stellar populations of spheroids. Here, the sample of galaxies and its properties are described. The instrument is detailed and its capabilities illustrated through observational examples. These includes results on the structure of central stellar disks, the kinematics and ionization state of gaseous disks, and the stellar populations of galaxies with decoupled cores.Comment: 10 pages, 6 figures. To appear in "The Dynamics, Structure & History of Galaxies", eds. G. S. Da Costa & E. M. Sadler (San Francisco: ASP). Version with full resolution images available at http://www.strw.leidenuniv.nl/~dynamics/Instruments/Sauron/pub_list.htm

Exchange Interaction Between Three and Four Coupled Quantum Dots: Theory and Applications to Quantum Computing

Several prominent proposals have suggested that spins of localized electrons could serve as quantum computer qubits. The exchange interaction has been invoked as a means of implementing two qubit gates. In this paper, we analyze the strength and form of the exchange interaction under relevant conditions. We find that, when several spins are engaged in mutual interactions, the quantitative strengths or even qualitative forms of the interactions can change. It is shown that the changes can be dramatic within a Heitler-London model. Hund-Mulliken calculations are also presented, and support the qualititative conclusions from the Heitler-London model. The effects need to be considered in spin-based quantum computer designs, either as a source of gate error to be overcome or a new interaction to be exploited.Comment: 16 pages, 16 figures. v3: Added Hund-Mulliken calculations in 3-dots case. A few small corrections. This version submitted to PR