A Melanic Pieris Rapae from Michigan (Lepidoptera: Pierdae)

The Arthur J. Yates collection of Michigan Lepidoptera, recently donated to Michigan State University (see Fischer, 1967), contained a striking melanic male cabbage butterfly [Pieris rapae (Linnaeus)] (Figs. 1, 2) now incorporated into the MSU series. Yates collected the specimen on 29 May 1934 in Roseville, Macomb County, near the western shore of Lake St. Clair in southeastern Michigan. An examination of the androconia and genitalia, using the characters described by Chang (1963), assured proper identification of the specimen. Although we have found no record of a similar rapae taken in North America, there are some named European forms of various species of Pieris that resemble our specimen

A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles

The development of accurate constitutive models of fibrous soft-tissues is a challenging problem. Many consider the tissue to be a collection of fibres with a continuous distribution function representing their orientations. A novel discrete fibre model is presented consisting of six weighted fibre bundles. Each bundle is oriented such that they pass through opposing vertices of a regular icosahedron. A novel aspect of the model is the use of simple analytical distribution functions to simulate the undulated collagen fibres. This approach yields a closed form analytical expression for the strain energy function for the collagen fibre bundle that avoids the sometimes costly numerical integration of some statistical distribution functions. The elastin fibres are characterized by a neo-Hookean strain energy function. The model accurately simulates the biaxial stretching of rabbit-skin (error-of-fit 8.7%), the uniaxial stretching of pig-skin (error-of-fit 7.6%), equibiaxial loading of aortic valve cusp (error-of-fit 0.8%), and the simple shear of rat septal myocardium (error-of-fit 9.1%). The proposed model compares favourably with previously published soft-tissue models and alternative methods of representing undulated collagen fibres. The stiffness of collagen fibres predicted by the model ranges from 8.0 MPa to 0.93 GPa. The stiffness of elastin fibres ranges from 2.5 kPa to 154.4 kPa. The anisotropy of model resulting from the representation of the fibre field with a discrete number of fibres is also explored

Entanglement of a Laguerre-Gaussian cavity mode with a rotating mirror

It has previously been shown theoretically that the exchange of linear momentum between the light field in an optical cavity and a vibrating end mirror can entangle the electromagnetic field with the vibrational motion of that mirror. In this paper we consider the rotational analog of this situation and show that radiation torque can similarly entangle a Laguerre-Gaussian cavity mode with a rotating end mirror. We examine the mirror-field entanglement as a function of ambient temperature, radiation detuning and orbital angular momentum carried by the cavity mode.Comment: 5 figures, 1 table, submitted to Phys.Rev.

Generation and detection of bound entanglement

We propose a method for the experimental generation of two different families of bound entangled states of three qubits. Our method is based on the explicit construction of a quantum network that produces a purification of the desired state. We also suggest a route for the experimental detection of bound entanglement, by employing a witness operator plus a test of the positivity of the partial transposes

Optimal Quantum Circuits for General Two-Qubit Gates

In order to demonstrate non-trivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence of one-qubit and two-qubit gates. We contribute to this effort by providing a method to construct an optimal quantum circuit for a general two-qubit gate that requires at most 3 CNOT gates and 15 elementary one-qubit gates. Moreover, if the desired two-qubit gate corresponds to a purely real unitary transformation, we provide a construction that requires at most 2 CNOTs and 12 one-qubit gates. We then prove that these constructions are optimal with respect to the family of CNOT, y-rotation, z-rotation, and phase gates.Comment: 6 pages, 8 figures, new title, final journal versio

Mixed state Pauli channel parameter estimation

The accuracy of any physical scheme used to estimate the parameter describing the strength of a single qubit Pauli channel can be quantified using standard techniques from quantum estimation theory. It is known that the optimal estimation scheme, with m channel invocations, uses initial states for the systems which are pure and unentangled and provides an uncertainty of O[1/m^(1/2)]. This protocol is analogous to a classical repetition and averaging scheme. We consider estimation schemes where the initial states available are not pure and compare a protocol involving quantum correlated states to independent state protocols analogous to classical repetition schemes. We show, that unlike the pure state case, the quantum correlated state protocol can yield greater estimation accuracy than any independent state protocol. We show that these gains persist even when the system states are separable and, in some cases, when quantum discord is absent after channel invocation. We describe the relevance of these protocols to nuclear magnetic resonance measurements

Measures of entanglement in multipartite bound entangled states

Bound entangled states are states that are entangled but from which no entanglement can be distilled if all parties are allowed only local operations and classical communication. However, in creating these states one needs nonzero entanglement resources to start with. Here, the entanglement of two distinct multipartite bound entangled states is determined analytically in terms of a geometric measure of entanglement and a related quantity. The results are compared with those for the negativity and the relative entropy of entanglement.Comment: 5 pages, no figure; title change

Entanglement Patterns in Mutually Unbiased Basis Sets for N Prime-state Particles

A few simply-stated rules govern the entanglement patterns that can occur in mutually unbiased basis sets (MUBs), and constrain the combinations of such patterns that can coexist (ie, the stoichiometry) in full complements of p^N+1 MUBs. We consider Hilbert spaces of prime power dimension (as realized by systems of N prime-state particles, or qupits), where full complements are known to exist, and we assume only that MUBs are eigenbases of generalized Pauli operators, without using a particular construction. The general rules include the following: 1) In any MUB, a particular qupit appears either in a pure state, or totally entangled, and 2) in any full MUB complement, each qupit is pure in p+1 bases (not necessarily the same ones), and totally entangled in the remaining p^N-p. It follows that the maximum number of product bases is p+1, and when this number is realized, all remaining p^N-p bases in the complement are characterized by the total entanglement of every qupit. This "standard distribution" is inescapable for two qupits (of any p), where only product and generalized Bell bases are admissible MUB types. This and the following results generalize previous results for qubits and qutrits. With three qupits there are three MUB types, and a number of combinations (p+2) are possible in full complements. With N=4, there are 6 MUB types for p=2, but new MUB types become possible with larger p, and these are essential to the realization of full complements. With this example, we argue that new MUB types, showing new entanglement characteristics, should enter with every step in N, and when N is a prime plus 1, also at critical p values, p=N-1. Such MUBs should play critical roles in filling complements.Comment: 27 pages, one figure, to be submitted to Physical Revie

Entanglement generation resonances in XY chains

We examine the maximum entanglement reached by an initially fully aligned state evolving in an XY Heisenberg spin chain placed in a uniform transverse magnetic field. Both the global entanglement between one qubit and the rest of the chain and the pairwise entanglement between adjacent qubits is analyzed. It is shown that in both cases the maximum is not a monotonous decreasing function of the aligning field, exhibiting instead a resonant behavior for low anisotropies, with pronounced peaks (a total of [n/2] peaks in the global entanglement for an $n$-spin chain), whose width is proportional to the anisotropy and whose height remains finite in the limit of small anisotropy. It is also seen that the maximum pairwise entanglement is not a smooth function of the field even in small finite chains, where it may exhibit narrow peaks above strict plateaus. Explicit analytical results for small chains, as well as general exact results for finite n-spin chains obtained through the Jordan-Wigner mapping, are discussed