On the Geometric Measures of Entanglement

The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three qubit case is discussed and argued that the distance to the W states is a new monotone.Comment: 7 pages, 1 figures, minor content change, references added, 1 figure adde

Deterministic Transformations of Multipartite Entangled States with Tensor Rank 2

Transformations involving only local operations assisted with classical communication are investigated for multipartite entangled pure states having tensor rank 2. All necessary and sufficient conditions for the possibility of deterministically converting truly multipartite, rank-2 states into each other are given. Furthermore, a chain of local operations that successfully achieves the transformation has been identified for all allowed transformations. The identified chains have two nice features: (1) each party needs to carry out at most one local operation and (2) all of these local operations are also deterministic transformations by themselves. Finally, it is found that there are disjoint classes of states, all of which can be identified by a single real parameter, which remain invariant under deterministic transformations.Comment: 27 pages, 1 figure; added new references and improved the presentatio

Axial magnetic field sensing for pulsed magnetic flux leakage hairline crack detection and quantification

The Magnetic Flux Leakage (MFL) testing method is a well-established branch of electromagnetic non-destructive testing technology extensively used to observe, analyze and estimate the level of imperfections (cracks, corrosions, pits, dents, etc.) affecting the quality of ferromagnetic steel structures. However the conventional MFL (DCMFL) method are not capable of estimating the defect sizes and orientation, hence an additional transducer is required to provide the extra information needed. This paper takes the detection and quantification of tangentially oriented rectangular surface and far-surface hairline cracks as the research objective. It uses an optimized pulsed magnetic flux leakage probe system to establish the location and geometries of such cracks. The results gathered from the approach show that data using the axial (Bx) field component can provide detailed locational information about hairline cracks especially the shape, size and orientation when positioned perpendicular to the applied field

Yang-Mills Theory on a Cylinder Coupled to Point Particles

We study a model of quantum Yang-Mills theory with a finite number of gauge invariant degrees of freedom. The gauge field has only a finite number of degrees of freedom since we assume that space-time is a two dimensional cylinder. We couple the gauge field to matter, modeled by either one or two nonrelativistic point particles. These problems can be solved {\it without any gauge fixing}, by generalizing the canonical quantization methods of Ref.\[rajeev] to the case including matter. For this, we make use of the geometry of the space of connections, which has the structure of a Principal Fiber Bundle with an infinite dimensional fiber. We are able to reduce both problems to finite dimensional, exactly solvable, quantum mechanics problems. In the case of one particle, we find that the ground state energy will diverge in the limit of infinite radius of space, consistent with confinement. In the case of two particles, this does not happen if they can form a color singlet bound state (`meson').Comment: 37 pages, UR-1327 ER-40685-77

Heat Transfer Operators Associated with Quantum Operations

Any quantum operation applied on a physical system is performed as a unitary transformation on a larger extended system. If the extension used is a heat bath in thermal equilibrium, the concomitant change in the state of the bath necessarily implies a heat exchange with it. The dependence of the average heat transferred to the bath on the initial state of the system can then be found from the expectation value of a hermitian operator, which is named as the heat transfer operator (HTO). The purpose of this article is the investigation of the relation between the HTOs and the associated quantum operations. Since, any given quantum operation on a system can be realized by different baths and unitaries, many different HTOs are possible for each quantum operation. On the other hand, there are also strong restrictions on the HTOs which arise from the unitarity of the transformations. The most important of these is the Landauer erasure principle. This article is concerned with the question of finding a complete set of restrictions on the HTOs that are associated with a given quantum operation. An answer to this question has been found only for a subset of quantum operations. For erasure operations, these characterizations are equivalent to the generalized Landauer erasure principle. For the case of generic quantum operations however, it appears that the HTOs obey further restrictions which cannot be obtained from the entropic restrictions of the generalized Landauer erasure principle.Comment: A significant revision is made; 33 pages with 2 figure

Large N limit of SO(N) scalar gauge theory

In this paper we study the large $N_c$ limit of SO(N_c) gauge theory coupled to a real scalar field following ideas of Rajeev. We see that the phase space of this resulting classical theory is Sp_1(H)/U(H_+) which is the analog of the Siegel disc in infinite dimensions. The linearized equations of motion give us a version of the well-known 't Hooft equation of two dimensional QCD.Comment: 16 pages, no figure