Quantifying nonorthogonality

An exploratory approach to the possibility of analyzing nonorthogonality as a quantifiable property is presented. Three different measures for the nonorthogonality of pure states are introduced, and one of these measures is extended to single-particle density matrices using methods that are similar to recently introduced techniques for quantifying entanglement. Several interesting special cases are considered. It is pointed out that a measure of nonorthogonality can meaningfully be associated with a single mixed quantum state. It is then shown how nonorthogonality can be unlocked with classical information; this analysis reveals interesting inequalities and points to a number of connections between nonorthogonality and entanglement.Comment: Accepted for publication in Phys. Rev.

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 The previous Section 6 is now in quant-ph/0105104 and the previous Section 8 is superseded by quant-ph/010501

A very brief introduction to quantum computing and quantum information theory for mathematicians

This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic representation theory. Proofs of most statements can be found in standard references

Quantum dense coding by spatial state entanglement

We have presented a theoretical extended version of dense coding protocol using entangled position state of two particles shared between two parties. A representation of Bell states and the required unitary operators are shown utilizing symmetric normalized Hadamard matrices. In addition, some explicit and conceivable forms for the unitary operators are presented by using some introduced basic operators. It is shown that, the proposed version is logarithmically efficient than some other multi-qubit dense coding protocols.Comment: 4 pages, 1 figure, Revte

Relations between Entropies Produced in Nondeterministic Thermodynamic Processes

Landauer's erasure principle is generalized to nondeterministic processes on systems having an arbitrary number of non-symmetrical logical states. The condition that the process is applied in the same way, irrespective of the initial logical state, imposes some restrictions on the individual heat exchanges associated with each possible transition. The complete set of such restrictions are derived by a statistical analysis of the phase-space flow induced by the process. Landauer's erasure principle can be derived from and is a special case of these.Comment: 12 pages with one figure; a final major revision in presentation; physical assumptions are clarified no

Mathematical Modeling of the Nikon Lampas Reflection Measuring Microscope

A mathematical model of the Nikon Lampas Reflection Measuring Microscope for the fine-line lithography in integrated circuit manufacture has been developed. Optical intensity profiles of a perfect line were computed using computer software supplied by the National Bureau of Standards. The programs were modified for the Lampas microscope. From line profiles, the accuracy of the microscope was calculated. The microscope is accurate down to 6/10 of a micron. All lines below 6/10 of a micron were unresolved

Mapping the Foot of the Continental Slope with Spline-Smoothed Data Using the Second Derivative in the Gradient Direction

The United States National Oceanic and Atmospheric Administration’s (NOAA) ET0P05 worldwide digital bathymetric dataset has been in the public domain for some years. Because it is noisy, it has not found much use in oceanography. A bi-cubic spline approach is used to smooth out the noise and represent the data as an explicit mathematical function, thus making it useful in many areas of oceanography. This method requires the data to have a rectangular grid. This report2 gives an effective approach for ET0P05 data’s bi-cubic spline representation and smoothing. It presents a new procedure designed to determine the Foot of the Continental Slope (FCS). This procedure is in accord with The United Nations Law of the Sea (LOS) article 76, section 4.b legal definition of the FCS, which is "the rate of maximum change of the gradient at its base". This explicit mathematical function can also be used to refine the grid. This function can also be differentiated exactly. One may compute from this function, at any point, the second derivative in the normalized gradient direction. The resulting surface is called for brevity "Surface of Directed Gradient" (SDG). The location of the crest of its highest ridge is a good approximation of the FCS. This approach gives an accurate mathematical representation of the LOS Convention’s legal description of the FCS as stated above. The'SDG technique is used to compute the FCS for the U.S. Atlantic coast. The FCS computed by the SDG method is compared to the FCS' computed by the surface of maximum curvature approach that is in general use

Annotation of Heterogenous Media Using OntoMedia

While ontologies exist for the annotation of monomedia, interoperability between these schemes is an important issue. The OntoMedia ontology consists of a generic core, capable of representing a diverse range of media, as well as extension ontologies to focus on specific formats. This paper provides an overview of the OntoMedia ontologies, together with a detailed case study when applied to video, a scripted form, and an associated short story

Classification by means of B-spline potential functions with applications to remote sensing

A method is presented for using B-splines as potential functions in the estimation of likelihood functions (probability density functions conditioned on pattern classes), or the resulting discriminant functions. The consistency of this technique is discussed. Experimental results of using the likelihood functions in the classification of remotely sensed data are given