Semantic categories underlying the meaning of ‘place’

This paper analyses the semantics of natural language expressions that are associated with the intuitive notion of ‘place’. We note that the nature of such terms is highly contested, and suggest that this arises from two main considerations: 1) there are a number of logically distinct categories of place expression, which are not always clearly distinguished in discourse about ‘place’; 2) the many non-substantive place count nouns (such as ‘place’, ‘region’, ‘area’, etc.) employed in natural language are highly ambiguous. With respect to consideration 1), we propose that place-related expressions should be classified into the following distinct logical types: a) ‘place-like’ count nouns (further subdivided into abstract, spatial and substantive varieties), b) proper names of ‘place-like’ objects, c) locative property phrases, and d) definite descriptions of ‘place-like’ objects. We outline possible formal representations for each of these. To address consideration 2), we examine meanings, connotations and ambiguities of the English vocabulary of abstract and generic place count nouns, and identify underlying elements of meaning, which explain both similarities and differences in the sense and usage of the various terms

Recovery of entanglement lost in entanglement manipulation

When an entangled state is transformed into another one with probability one by local operations and classical communication, the quantity of entanglement decreases. This letter shows that entanglement lost in the manipulation can be partially recovered by an auxiliary entangled pair. As an application, a maximally entangled pair can be obtained from two partially entangled pairs with probability one. Finally, this recovery scheme reveals a fundamental property of entanglement relevant to the existence of incomparable states.Comment: 4 pages, 2 figures, REVTeX; minor correction

Unifying principles in terrestrial locomotion: Do hopping Australian marsupials fit in?

Mammalian terrestrial locomotion has many unifying principles. However, the Macropodoidea are a particularly interesting group that exhibit a number of significant deviations from the principles that seem to apply to other mammals. While the properties of materials that comprise the musculoskeletal system of mammals are similar, evidence suggests that tendon properties in macropodoid marsupials may be size or function dependent, in contrast to the situation in placental mammals. Postural differences related to hopping versus running have a dramatic effect on the scaling of the pelvic limb musculoskeletal system. Ratios of muscle fibre to tendon cross-sectional areas for ankle extensors and digital flexors scale with positive allometry in all mammals, but exponents are significantly higher in macropods. Tendon safety factors decline with increasing body mass in mammals, with eutherians at risk of ankle extensor tendon rupture at a body mass of about 150 kg, whereas kangaroos encounter similar problems at a body mass of approximately 35 kg. Tendon strength appears to limit locomotor performance in these animals. Elastic strain energy storage in tendons is mass dependent in all mammals, but exponents are significantly larger in macropodid. Tibial stresses may scale with positive allometry in kangaroos, which result in lower bone safety factors in macropods compared to eutherian mammals

On the origin of noisy states whose teleportation fidelity can be enhanced through dissipation

Recently Badziag \emph{et al.} \cite{badziag} obtained a class of noisy states whose teleportation fidelity can be enhanced by subjecting one of the qubits to dissipative interaction with the environment via amplitude damping channel (ADC). We show that such noisy states result while sharing the states (| \Phi ^{\pm}> =\frac{1}{\sqrt{2}}(| 00> \pm | 11>)) across ADC. We also show that under similar dissipative interactions different Bell states give rise to noisy entangled states that are qualitatively very different from each other in the sense, only the noisy entangled states constructed from the Bell states (| \Phi ^{\pm}>) can \emph{}be made better sometimes by subjecting the unaffected qubit to a dissipative interaction with the environment. Importantly if the noisy state is non teleporting then it can always be made teleporting with this prescription. We derive the most general restrictions on improvement of such noisy states assuming that the damping parameters being different for both the qubits. However this curious prescription does not work for the noisy entangled states generated from (| \Psi ^{\pm}> =\frac{1}{\sqrt{2}}(| 01> \pm | 10>)). This shows that an apriori knowledge of the noisy channel might be helpful to decide which Bell state needs to be shared between Alice and Bob. \emph{}Comment: Latex, 18 pages: Revised version with a new result. Submitted to PR

The Initial Value Problem For Maximally Non-Local Actions

We study the initial value problem for actions which contain non-trivial functions of integrals of local functions of the dynamical variable. In contrast to many other non-local actions, the classical solution set of these systems is at most discretely enlarged, and may even be restricted, with respect to that of a local theory. We show that the solutions are those of a local theory whose (spacetime constant) parameters vary with the initial value data according to algebraic equations. The various roots of these algebraic equations can be plausibly interpreted in quantum mechanics as different components of a multi-component wave function. It is also possible that the consistency of these algebraic equations imposes constraints upon the initial value data which appear miraculous from the context of a local theory.Comment: 8 pages, LaTeX 2 epsilo

A new class of entanglement measures

We introduce new entanglement measures on the set of density operators on tensor product Hilbert spaces. These measures are based on the greatest cross norm on the tensor product of the sets of trace class operators on Hilbert space. We show that they satisfy the basic requirements on entanglement measures discussed in the literature, including convexity, invariance under local unitary operations and non-increase under local quantum operations and classical communication.Comment: Revised version accepted by J Math Phys, 12 pages, LaTeX, contains Sections 1-5 & 7 of the previous version. The previous Section 6 is now in quant-ph/0105104 and the previous Section 8 is superseded by quant-ph/010501

Purification and correlated measurements of bipartite mixed states

We prove that all purifications of a non-factorable state (i.e., the state which cannot be expressed in a form $\rho_{AB}=\rho_A\otimes\rho_B$) are entangled. We also show that for any bipartite state there exists a pair of measurements which are correlated on this state if and only if the state is non-factorable.Comment: 4 revtex pages, to appear in Phys. Rev.

The Nature and Location of Quantum Information

Quantum information is defined by applying the concepts of ordinary (Shannon) information theory to a quantum sample space consisting of a single framework or consistent family. A classical analogy for a spin-half particle and other arguments show that the infinite amount of information needed to specify a precise vector in its Hilbert space is not a measure of the information carried by a quantum entity with a $d$-dimensional Hilbert space; the latter is, instead, bounded by log d bits (1 bit per qubit). The two bits of information transmitted in dense coding are located not in one but in the correlation between two qubits, consistent with this bound. A quantum channel can be thought of as a "structure" or collection of frameworks, and the physical location of the information in the individual frameworks can be used to identify the location of the channel. Analysis of a quantum circuit used as a model of teleportation shows that the location of the channel depends upon which structure is employed; for ordinary teleportation it is not (contrary to Deutsch and Hayden) present in the two bits resulting from the Bell-basis measurement, but in correlations of these with a distant qubit. In neither teleportation nor dense coding does information travel backwards in time, nor is it transmitted by nonlocal (superluminal) influences. It is (tentatively) proposed that all aspects of quantum information can in principle be understood in terms of the (basically classical) behavior of information in a particular framework, along with the framework dependence of this information.Comment: Latex 29 pages, uses PSTricks for figure

The Parity Bit in Quantum Cryptography

An $n$-bit string is encoded as a sequence of non-orthogonal quantum states. The parity bit of that $n$-bit string is described by one of two density matrices, $\rho_0^{(n)}$ and $\rho_1^{(n)}$, both in a Hilbert space of dimension $2^n$. In order to derive the parity bit the receiver must distinguish between the two density matrices, e.g., in terms of optimal mutual information. In this paper we find the measurement which provides the optimal mutual information about the parity bit and calculate that information. We prove that this information decreases exponentially with the length of the string in the case where the single bit states are almost fully overlapping. We believe this result will be useful in proving the ultimate security of quantum crytography in the presence of noise.Comment: 19 pages, RevTe

The Magnetic Ordering of the 3d Wigner Crystal

Using Path Integral Monte Carlo, we have calculated exchange frequencies as electrons undergo ring exchanges of 2, 3 and 4 electrons in a ``clean'' 3d Wigner crystal (bcc lattice) as a function of density. We find pair exchange dominates and estimate the critical temperature for the transition to antiferromagnetic ordering to be roughly $1 \times 10^{-8}$Ry at melting. In contrast to the situation in 2d, the 3d Wigner crystal is different from the solid bcc 3He in that the pair exchange dominates because of the softer interparticle potential. We discuss implications for the magnetic phase diagram of the electron gas