Thermoacoustic tomography arising in brain imaging

We study the mathematical model of thermoacoustic and photoacoustic tomography when the sound speed has a jump across a smooth surface. This models the change of the sound speed in the skull when trying to image the human brain. We derive an explicit inversion formula in the form of a convergent Neumann series under the assumptions that all singularities from the support of the source reach the boundary

Qualification of CuCr1Zr for the SLM Process

Working coils for electromagnetic forming processes need to comply with a wide list of requirements such as durability, efficiency and a tailored pressure distribution. Due to its unique combination of high strength and high electrical conductivity CuCr1Zr meets these requirements and is a common material for coil turns. In combination with conventional coil production processes like winding or waterjet cutting the use of this material is state of the art. A promising approach for coil production is the use of additive manufacturing (AM) processes. In comparison to conventional manufacturing processes, AM offers tremendous advantages such as feature-integration e.g. undercuts or lattice structures. However, this increased design freedom only leads to improved working coils if copper alloys with high strength and high electrical conductivity such as CuCr1Zr can be processed. Due to the high thermal conductivity and reflectivity the use of suchlike materials in additive manufacturing processes is challenging. Considering the effects of the required pre- and post-processing treatments for additive manufactured parts the need for research is further increased. The objective of this paper is to develop a method for the qualification of CuCr1Zr for the selective laser melting (SLM) process. This comprises the powder characterization, the process parameter identification and the microstructure investigation of the generated test geometries

Global-fidelity limits of state-dependent cloning of mixed states

By relevant modifications, the known global-fidelity limits of state-dependent cloning are extended to mixed quantum states. We assume that the ancilla contains some a priori information about the input state. As it is shown, the obtained results contribute to the stronger no-cloning theorem. An attainability of presented limits is discussed.Comment: 8 pages, ReVTeX, 1 figure. In revised form an attainability of presented limits is discussed. Detected errors are corrected. Elucidative figure is added. Minor grammatical changes are made. More explanation

Entropy as a function of Geometric Phase

We give a closed-form solution of von Neumann entropy as a function of geometric phase modulated by visibility and average distinguishability in Hilbert spaces of two and three dimensions. We show that the same type of dependence also exists in higher dimensions. We also outline a method for measuring both the entropy and the phase experimentally using a simple Mach-Zehnder type interferometer which explains physically why the two concepts are related.Comment: 19 pages, 7 figure

A General Setting for Geometric Phase of Mixed States Under an Arbitrary Nonunitary Evolution

The problem of geometric phase for an open quantum system is reinvestigated in a unifying approach. Two of existing methods to define geometric phase, one by Uhlmann's approach and the other by kinematic approach, which have been considered to be distinct, are shown to be related in this framework. The method is based upon purification of a density matrix by its uniform decomposition and a generalization of the parallel transport condition obtained from this decomposition. It is shown that the generalized parallel transport condition can be satisfied when Uhlmann's condition holds. However, it does not mean that all solutions of the generalized parallel transport condition are compatible with those of Uhlmann's one. It is also shown how to recover the earlier known definitions of geometric phase as well as how to generalize them when degeneracy exists and varies in time.Comment: 4 pages, extended result

Geometric observation for the Bures fidelity between two states of a qubit

In this Brief Report, we present a geometric observation for the Bures fidelity between two states of a qubit.Comment: 4 pages, 1 figure, RevTex, Accepted by Phys. Rev.

An entanglement monotone derived from Grover's algorithm

This paper demonstrates that how well a state performs as an input to Grover's search algorithm depends critically upon the entanglement present in that state; the more entanglement, the less well the algorithm performs. More precisely, suppose we take a pure state input, and prior to running the algorithm apply local unitary operations to each qubit in order to maximize the probability P_max that the search algorithm succeeds. We prove that, for pure states, P_max is an entanglement monotone, in the sense that P_max can never be decreased by local operations and classical communication.Comment: 7 page

Geometric phase in open systems

We calculate the geometric phase associated to the evolution of a system subjected to decoherence through a quantum-jump approach. The method is general and can be applied to many different physical systems. As examples, two main source of decoherence are considered: dephasing and spontaneous decay. We show that the geometric phase is completely insensitive to the former, i.e. it is independent of the number of jumps determined by the dephasing operator.Comment: 4 pages, 2 figures, RevTe

Geometric Phases for Mixed States during Cyclic Evolutions

The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the Aharonov and Anandan phase in the pure state case. Our definition is consistent with the phase shift in the proposed experiment [Phys. Rev. Lett. \textbf{85}, 2845 (2000)] for a cyclic evolution if the unitary transformation satisfies the parallel transport condition. A comprehensive geometric interpretation is also given. It shows that the geometric phases for mixed states share the same geometric sense with the pure states.Comment: 9 pages, 1 figur

A Geometric Picture of Entanglement and Bell Inequalities

We work in the real Hilbert space H_s of hermitian Hilbert-Schmid operators and show that the entanglement witness which shows the maximal violation of a generalized Bell inequality (GBI) is a tangent functional to the convex set S subset H_s of separable states. This violation equals the euclidean distance in H_s of the entangled state to S and thus entanglement, GBI and tangent functional are only different aspects of the same geometric picture. This is explicitly illustrated in the example of two spins, where also a comparison with familiar Bell inequalities is presented.Comment: 17 pages, 5 figures, 4 references adde