Characterizing the geometrical edges of nonlocal two-qubit gates

Nonlocal two-qubit gates are geometrically represented by tetrahedron known as Weyl chamber within which perfect entanglers form a polyhedron. We identify that all edges of the Weyl chamber and polyhedron are formed by single parametric gates. Nonlocal attributes of these edges are characterized using entangling power and local invariants. In particular, SWAP (power)alpha family of gates constitutes one edge of the Weyl chamber with SWAP-1/2 being the only perfect entangler. Finally, optimal constructions of controlled-NOT using SWAP-1/2 gate and gates belong to three edges of the polyhedron are presented.Comment: 11 pages, 4 figures, Phys. Rev. A 79, 052339 (2009

P-T Constraints of Orthogneiss, Metapelites, and Ultra-Mafic Lenses Located in the Virgin Mountains of Northwestern Arizona

The Virgin Mountains, located in northwestern Arizona, host a variety of different geologic features. Many workers have focused on Tertiary extension within the mountain range, but little work has been done on the Paleo-Proterozoic basement rocks. Tertiary extension has exposed 1.73 – 1.80 Ga basement material that exhibits intense shear deformation and evidence of high temperature/high pressure and possibly ultra-high pressure metamorphism. These rocks are well exposed throughout Elbow and Lime Kiln Canyons, which are located east and south of Mesquite, Nevada. Some exposures enclose ultra-mafic lenses containing pyroxene/spinel pseudomorphs after garnet. These features suggest decompression through the garnet-spinel transition. These rocks occur in a broad shear zone exposed over 80-100 km in the Virgin Mountains and the Beaver Dam Mountains to the north. Most samples are mylonitic, but contain polygonal quartz grains consistent with shearing under high-temperature conditions. Other shear indicators include sigma and delta structures, mica-fish and S-C textures. Sillimanite and biotite within the S-C shear fabric suggest deformation and equilibration under upper amphibolite to lower granulite facies conditions (650o-800oC and 0.6-1.1 Kilobars). Also, sillimanite pseudomorphs after kyanite found within metapelites suggests decompression from high pressure conditions. Decompression of ultra-mafic lenses through the garnet-spinel transition documents pressures in excess of 2.0 GPa and depths of at least 70 Km. Structural considerations as well as the presence of high-pressure metamorphism are consistent with a collisional suture. The Virgin Mountains appear to host the Paleoproterozoic collisional boundary between Mojave and Yavapai crustal provinces

Entangling characterization of (SWAP)1/m and Controlled unitary gates

We study the entangling power and perfect entangler nature of (SWAP)1/m, for m>=1, and controlled unitary (CU) gates. It is shown that (SWAP)1/2 is the only perfect entangler in the family. On the other hand, a subset of CU which is locally equivalent to CNOT is identified. It is shown that the subset, which is a perfect entangler, must necessarily possess the maximum entangling power.Comment: 12 pages, 1 figure, One more paragraph added in Introductio

Scalability of Shor's algorithm with a limited set of rotation gates

Typical circuit implementations of Shor's algorithm involve controlled rotation gates of magnitude $\pi/2^{2L}$ where $L$ is the binary length of the integer N to be factored. Such gates cannot be implemented exactly using existing fault-tolerant techniques. Approximating a given controlled $\pi/2^{d}$ rotation gate to within $\delta=O(1/2^{d})$ currently requires both a number of qubits and number of fault-tolerant gates that grows polynomially with $d$. In this paper we show that this additional growth in space and time complexity would severely limit the applicability of Shor's algorithm to large integers. Consequently, we study in detail the effect of using only controlled rotation gates with $d$ less than or equal to some $d_{\rm max}$. It is found that integers up to length $L_{\rm max} = O(4^{d_{\rm max}})$ can be factored without significant performance penalty implying that the cumbersome techniques of fault-tolerant computation only need to be used to create controlled rotation gates of magnitude $\pi/64$ if integers thousands of bits long are desired factored. Explicit fault-tolerant constructions of such gates are also discussed.Comment: Substantially revised version, twice as long as original. Two tables converted into one 8-part figure, new section added on the construction of arbitrary single-qubit rotations using only the fault-tolerant gate set. Substantial additional discussion and explanatory figures added throughout. (8 pages, 6 figures

Detection of Asynchronous Message Passing Errors Using Static Analysis

Concurrent programming is hard and prone to subtle errors. In this paper we present a static analysis that is able to detect some commonly occurring kinds of message passing errors in languages with dynamic process creation and communication based on asynchronous message passing. Our analysis is completely automatic, fast, and strikes a proper balance between soundness and completeness: it is effective in detecting errors and avoids false alarms by computing a close approximation of the interprocess communication topology of programs. We have integrated our analysis in dialyzer, a widely used tool for detecting software defects in Erlang programs, and demonstrate its effectiveness on libraries and applications of considerable size. Despite the fact that these applications have been developed over a long period of time and are reasonably well-tested, our analysis has managed to detect a significant number of previously unknown message passing errors in their code

Role of Bell Singlet State in the Suppression of Disentanglement

The stability of entanglement of two atoms in a cavity is analyzed in this work. By studying the general Werner states we clarify the role of Bell-singlet state in the problem of suppression of disentanglement due to spontaneous emission. It is also shown explicitly that the final amount of entanglement depends on the initial ingredients of the Bell-singlet state.Comment: 5 pages, 2 figures, accepted by Phys. Rev.

Schmidt Analysis of Pure-State Entanglement

We examine the application of Schmidt-mode analysis to pure state entanglement. Several examples permitting exact analytic calculation of Schmidt eigenvalues and eigenfunctions are included, as well as evaluation of the associated degree of entanglement.Comment: 5 pages, 3 figures, for C.M. Bowden memoria

Generalized Limits for Parameter Sensitivity via Quantum Ziv-Zakai Bound

We study the generalized limit for parameter sensitivity in quantum estimation theory considering the effects of repeated and adaptive measurements. Based on the quantum Ziv-Zakai bound, we derive some lower bounds for parameter sensitivity when the Hamiltonian of system is unbounded and when the adaptive measurements are implemented on the system. We also prove that the parameter sensitivity is bounded by the limit of the minimum detectable parameter. In particular, we examine several known states in quantum phase estimation with non-interacting photons, and show that they can not perform better than Heisenberg limit in a much simpler way with our result.Comment: 8pages, 5 figure

Orbits of quantum states and geometry of Bloch vectors for NN-level systems

Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a stratification with strata given by unitary orbit manifolds, which can be identified with flag manifolds. The results are applied to study the geometry of the coherence vector for n-level quantum systems. It is shown that the unitary orbits can be naturally identified with spheres in R^{n^2-1} only for n=2. In higher dimensions the coherence vector only defines a non-surjective embedding into a closed ball. A detailed analysis of the three-level case is presented. Finally, a refined stratification in terms of symplectic orbits is considered.Comment: 15 pages LaTeX, 3 figures, reformatted, slightly modified version, corrected eq.(3), to appear in J. Physics

Alternative Mathematical Technique to Determine LS Spectral Terms

We presented an alternative computational method for determining the permitted LS spectral terms arising from $l^N$ electronic configurations. This method makes the direct calculation of LS terms possible. Using only basic algebra, we derived our theory from LS-coupling scheme and Pauli exclusion principle. As an application, we have performed the most complete set of calculations to date of the spectral terms arising from $l^N$ electronic configurations, and the representative results were shown. As another application on deducing LS-coupling rules, for two equivalent electrons, we deduced the famous Even Rule; for three equivalent electrons, we derived a new simple rule.Comment: Submitted to Phys. Rev.