Some Properties of the Computable Cross Norm Criterion for Separability

The computable cross norm (CCN) criterion is a new powerful analytical and computable separability criterion for bipartite quantum states, that is also known to systematically detect bound entanglement. In certain aspects this criterion complements the well-known Peres positive partial transpose (PPT) criterion. In the present paper we study important analytical properties of the CCN criterion. We show that in contrast to the PPT criterion it is not sufficient in dimension 2 x 2. In higher dimensions we prove theorems connecting the fidelity of a quantum state with the CCN criterion. We also analyze the behaviour of the CCN criterion under local operations and identify the operations that leave it invariant. It turns out that the CCN criterion is in general not invariant under local operations.Comment: 7 pages; accepted by Physical Review A; error in Appendix B correcte

Method of convex rigid frames and applications in studies of multipartite quNit pure-states

In this Letter we suggest a method of convex rigid frames in the studies of the multipartite quNit pure-states. We illustrate what are the convex rigid frames and what is the method of convex rigid frames. As the applications we use this method to solve some basic problems and give some new results (three theorems): The problem of the partial separability of the multipartite quNit pure-states and its geometric explanation; The problem of the classification of the multipartite quNit pure-states, and give a perfect explanation of the local unitary transformations; Thirdly, we discuss the invariants of classes and give a possible physical explanation.Comment: 6 pages, no figur

Alternatively spliced exons of the beta tropomyosin gene exhibit different affinities for F-actin and effects with nonmuscle caldesmon

The rat beta-tropomyosin (TM) gene expresses two isoforms via alternative RNA splicing, namely skeletal muscle beta-TM and fibroblast TM-1. The latter is also expressed in smooth muscle where it corresponds to smooth muscle beta-TM. Skeletal muscle beta-TM contains exons 7 and 10, whereas exons 6 and 11 are used in fibroblasts and smooth muscle. In order to study the properties of the alternatively spliced proteins, recombinant TMs derived from bacterial and insect cell expression systems were produced, including the normal beta gene products, fibroblast TM-1 and beta skeletal muscle TM, two carboxy-terminal chimeric TMs, TM-6/10 and TM-7/11, as well as a carboxyl-truncated version of each, TM-6Cla and TM-7Cla. The purified TM isoforms were used in actin filament association studies. The apparent TM association constants (Ka) were taken as the free concentration at half saturation and were found to be 6 microM for beta Sk TM, 8.5 for TM-6/10, 25 microM for TM-1, and 30 microM for TM-7/11 at an F-actin concentration of 42 microM. For the truncated TMs, the values determined were higher still but the binding was not carried out to full saturation. Isoforms were also produced using the baculovirus-insect cell system which produces proteins with an acetylated amino terminus as is normally found in vivo. This modification significantly enhanced the F-actin association of TM-1 but not the beta skeletal TM or the other isoforms. Fibroblast TM-2 or TM-3, both products of the alpha gene, enhanced the affinity of TM-1 for F-actin, demonstrating different isoforms can act cooperatively on binding to actin. This effect was not detected with the other expressed beta gene products. The presence of 83 kDa nonmuscle caldesmon was found to enhance the binding of TM-1 for F-actin. This effect was dependent on the presence of both exons 6 and 11, as caldesmon had little effect on the other beta gene products. Collectively these results demonstrate TMs differ in their affinity for F-actin, which can be altered by other TMs or actin-binding proteins. The beta tropomyosin isoforms were fluorescently-tagged and microinjected into cultured cells to study their in vivo localization where it was found that each of the full-length TMs bound to microfilaments but, at the light microscopy level, the isoforms were not differentially localized in these fibroblasts

Robust control of decoherence in realistic one-qubit quantum gates

We present an open loop (bang-bang) scheme to control decoherence in a generic one-qubit quantum gate and implement it in a realistic simulation. The system is consistently described within the spin-boson model, with interactions accounting for both adiabatic and thermal decoherence. The external control is included from the beginning in the Hamiltonian as an independent interaction term. After tracing out the environment modes, reduced equations are obtained for the two-level system in which the effects of both decoherence and external control appear explicitly. The controls are determined exactly from the condition to eliminate decoherence, i.e. to restore unitarity. Numerical simulations show excellent performance and robustness of the proposed control scheme.Comment: 21 pages, 8 figures, VIth International Conference on Quantum Communication, Measurement and Computing (Boston, 2002

Probabilistic Quantum Memories

Typical address-oriented computer memories cannot recognize incomplete or noisy information. Associative (content-addressable) memories solve this problem but suffer from severe capacity shortages. I propose a model of a quantum memory that solves both problems. The storage capacity is exponential in the number of qbits and thus optimal. The retrieval mechanism for incomplete or noisy inputs is probabilistic, with postselection of the measurement result. The output is determined by a probability distribution on the memory which is peaked around the stored patterns closest in Hamming distance to the input.Comment: Revised version to appear in Phys. Rev. Let

Geometrical approach to mutually unbiased bases

We propose a unifying phase-space approach to the construction of mutually unbiased bases for a two-qubit system. It is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We also consider the feasible transformations between different kinds of curves and show that they correspond to local rotations around the Bloch-sphere principal axes. We suggest how to generalize the method to systems in dimensions that are powers of a prime.Comment: 10 pages. Some typos in the journal version have been correcte

Valence bond solid formalism for d-level one-way quantum computation

The d-level or qudit one-way quantum computer (d1WQC) is described using the valence bond solid formalism and the generalised Pauli group. This formalism provides a transparent means of deriving measurement patterns for the implementation of quantum gates in the computational model. We introduce a new universal set of qudit gates and use it to give a constructive proof of the universality of d1WQC. We characterise the set of gates that can be performed in one parallel time step in this model.Comment: 26 pages, 9 figures. Published in Journal of Physics A: Mathematical and Genera

Quantum information distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit

We show that for any Hilbert-space dimension, the optimal universal quantum cloner can be constructed from essentially the same quantum circuit, i.e., we find a universal design for universal cloners. In the case of infinite dimensions (which includes continuous variable quantum systems) the universal cloner reduces to an essentially classical device. More generally, we construct a universal quantum circuit for distributing qudits in any dimension which acts covariantly under generalized displacements and momentum kicks. The behavior of this covariant distributor is controlled by its initial state. We show that suitable choices for this initial state yield both universal cloners and optimized cloners for limited alphabets of states whose states are related by generalized phase-space displacements.Comment: 10 revtex pages, no figure

Detection of multipartite entanglement with two-body correlations

We show how to detect entanglement with criteria built from simple two-body correlation terms. Since many natural Hamiltonians are sums of such correlation terms, our ideas can be used to detect entanglement by energy measurement. Our criteria can straightforwardly be applied for detecting different forms of multipartite entanglement in familiar spin models in thermal equilibrium.Comment: 5 pages including 2 figures, LaTeX; for the proceedings of the DPG spring meeting, Berlin, March 200

Constant-time solution to the Global Optimization Problem using Bruschweiler's ensemble search algorithm

A constant-time solution of the continuous Global Optimization Problem (GOP) is obtained by using an ensemble algorithm. We show that under certain assumptions, the solution can be guaranteed by mapping the GOP onto a discrete unsorted search problem, whereupon Bruschweiler's ensemble search algorithm is applied. For adequate sensitivities of the measurement technique, the query complexity of the ensemble search algorithm depends linearly on the size of the function's domain. Advantages and limitations of an eventual NMR implementation are discussed.Comment: 14 pages, 0 figure