Fast rate estimation of an unitary operation in SU(d)

We give an explicit procedure based on entangled input states for estimating a $SU(d)$ operation $U$ with rate of convergence $1/N^2$ when sending $N$ particles through the device. We prove that this rate is optimal. We also evaluate the constant $C$ such that the asymptotic risk is $C/N^2$. However other strategies might yield a better const ant $C$.Comment: 8 pages, 1 figure Rewritten version, accepted for publication in Phys. Rev. A. The introduction is richer, the "tool section" on group representations has been suppressed, and a section proving that the 1/N^2 rate is optimum has been adde

All maximally entangling unitary gates

We characterize all maximally entangling bipartite unitary operators, acting on systems $A,B$ of arbitrary finite dimensions $d_A\le d_B$, when use of ancillary systems by both parties is allowed. Several useful and interesting consequences of this characterization are discussed, including an understanding of why the entangling and disentangling capacities of a given (maximally entangling) unitary can differ and a proof that these capacities must be equal when $d_A=d_B$.Comment: 7 pages, no figure

Optimizing local protocols implementing nonlocal quantum gates

We present a method of optimizing recently designed protocols for implementing an arbitrary nonlocal unitary gate acting on a bipartite system. These protocols use only local operations and classical communication with the assistance of entanglement, and are deterministic while also being "one-shot", in that they use only one copy of an entangled resource state. The optimization is in the sense of minimizing the amount of entanglement used, and it is often the case that less entanglement is needed than with an alternative protocol using two-way teleportation.Comment: 11 pages, 1 figure. This is a companion paper to arXiv:1001.546

Hermitian Young Operators

Starting from conventional Young operators we construct Hermitian operators which project orthogonally onto irreducible representations of the (special) unitary group.Comment: 15 page

Protecting Quantum Information Encoded in Decoherence Free States Against Exchange Errors

The exchange interaction between identical qubits in a quantum information processor gives rise to unitary two-qubit errors. It is shown here that decoherence free subspaces (DFSs) for collective decoherence undergo Pauli errors under exchange, which however do not take the decoherence free states outside of the DFS. In order to protect DFSs against these errors it is sufficient to employ a recently proposed concatenated DFS-quantum error correcting code scheme [D.A. Lidar, D. Bacon and K.B. Whaley, Phys. Rev. Lett. {\bf 82}, 4556 (1999)].Comment: 7 pages, no figures. Discussion in section V.A. significantly expanded. Several small changes. Two authors adde

Intermediate coupling fixed point study in the overscreened regime of generalized multichannel SU(N) Kondo models

We study a generalized multichannel single-impurity Kondo model, in which the impurity spin is described by a representation of the SU(N) group which combines bosonic and fermionic degrees of freedom. The impurity spin states are described by Abrikosov pseudofermions, and we make use of a method initiated by Popov and Fedotov which allows a proper handling of the fermionic constraint. The partition function is derived within a path integral approach. We use renormalization group techniques to calculate the $\beta$ scaling function perturbatively in powers of the Kondo coupling constant, which is justified in the weak coupling limit. The truncated expansion is valid in the overscreened (Nozieres-Blandin) regime, for an arbitrary SU(N) group and any value of the parameters characterizing the impurity spin representation. The intermediate coupling fixed point is identified. We derive the temperature dependence of various physical quantities at low T, controlled by a unique critical exponent, and show that the physics of the system in the overscreened regime governed by the intermediate coupling fixed point is characterized by a non-Fermi liquid behavior. Our results are in accordance with those obtained by other methods, as Bethe ansatz and boundary conformal field theory, in the case of various impurity spin symmetries. We establish in a unified way that the Kondo models in which the impurity spin is described successively by a fundamental, symmetric, antisymmetric and mixed symmetry representation yield all the same low-energy physics in the overscreened regime. Possible generalizations of the analysis we present to the case of arbitrary impurity spin representations of SU(N) are also discussed.Comment: 21 pages, 7 figures, REVTeX; final version accepted for publicatio

Decoherence-Free Subspaces for Multiple-Qubit Errors: (I) Characterization

Coherence in an open quantum system is degraded through its interaction with a bath. This decoherence can be avoided by restricting the dynamics of the system to special decoherence-free subspaces. These subspaces are usually constructed under the assumption of spatially symmetric system-bath coupling. Here we show that decoherence-free subspaces may appear without spatial symmetry. Instead, we consider a model of system-bath interactions in which to first order only multiple-qubit coupling to the bath is present, with single-qubit system-bath coupling absent. We derive necessary and sufficient conditions for the appearance of decoherence-free states in this model, and give a number of examples. In a sequel paper we show how to perform universal and fault tolerant quantum computation on the decoherence-free subspaces considered in this paper.Comment: 18 pages, no figures. Major changes. Section on universal fault tolerant computation removed. This section contained a crucial error. A new paper [quant-ph/0007013] presents the correct analysi

Genome amplification and gene expression in the ciliate macronucleus

The focus of this review is on the micronucleus and macronucleus in the ciliated protozoa and the organization and function of the DNA molecules within them. We present (1) some of the structural and functional differences which are known, (2) the genetic evidence for macronuclear units, (3) two hypotheses for the organization of the DNA molecules in the macronucleus to explain these units, and (4) experiments designed to discriminate between these hypotheses. We conclude that the size of the genome is not reduced in the macronucleus and that there are 45 copies of the haploid genome present in the macronucleus of normal strains of Tetrahymena pyriformis and 800 copies in the macronucleus of Paramecium aurelia . The ciliate genome is relatively simple in terms of repeated sequences. However, not all copies of the genes present in the macronucleus may be identical since fractions of differing thermal stability appear after renaturation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44178/1/10528_2004_Article_BF00486122.pd

Contributions to the theory of hydrodynamic stability : technical report

http://deepblue.lib.umich.edu/bitstream/2027.42/7439/5/bad1832.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/7439/4/bad1832.0001.001.tx

Studies in Radar Cross Sections VIII. Theoretical Cross Section as a Function of Separation Angle between Transmitter and Receiver at Small Wavelengths

http://deepblue.lib.umich.edu/bitstream/2027.42/21134/2/rl2009.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/21134/1/rl2009.0001.001.tx