Bounds on the entanglability of thermal states in liquid-state nuclear magnetic resonance

The role of mixed state entanglement in liquid-state nuclear magnetic resonance (NMR) quantum computation is not yet well-understood. In particular, despite the success of quantum information processing with NMR, recent work has shown that quantum states used in most of those experiments were not entangled. This is because these states, derived by unitary transforms from the thermal equilibrium state, were too close to the maximally mixed state. We are thus motivated to determine whether a given NMR state is entanglable - that is, does there exist a unitary transform that entangles the state? The boundary between entanglable and nonentanglable thermal states is a function of the spin system size $N$ and its temperature $T$. We provide new bounds on the location of this boundary using analytical and numerical methods; our tightest bound scales as $N \sim T$, giving a lower bound requiring at least $N \sim 22,000$ proton spins to realize an entanglable thermal state at typical laboratory NMR magnetic fields. These bounds are tighter than known bounds on the entanglability of effective pure states.Comment: REVTeX4, 15 pages, 4 figures (one large figure: 414 K

Mixed state geometric phases, entangled systems, and local unitary transformations

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution not only depends on the geometry of the path of the system alone but also on a constrained bi-local unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires uni-local transformations and is therefore essentially a property of the system alone.Comment: minor changes, journal reference adde

The boundary rigidity problem in the presence of a magnetic field

For a compact Riemannian manifold with boundary, endowed with a magnetic potential $\alpha$, we consider the problem of restoring the metric $g$ and the magnetic potential $\alpha$ from the values of the Ma\~n\'e action potential between boundary points and the associated linearized problem. We study simple magnetic systems. In this case, knowledge of the Ma\~n\'e action potential is equivalent to knowledge of the scattering relation on the boundary which maps a starting point and a direction of a magnetic geodesic into its end point and direction. This problem can only be solved up to an isometry and a gauge transformation of $\alpha$. For the linearized problem, we show injectivity, up to the natural obstruction, under explicit bounds on the curvature and on $\alpha$. We also show injectivity and stability for $g$ and $\alpha$ in a generic class $\mathcal{G}$ including real analytic ones. For the nonlinear problem, we show rigidity for real analytic simple $g$, $\alpha$. Also, rigidity holds for metrics in a given conformal class, and locally, near any $(g,\alpha)\in \mathcal{G}$.Comment: This revised version contains a proof that 2D simple magnetic systems are boundary rigid. Some references have been adde

Implementation of quantum maps by programmable quantum processors

A quantum processor is a device with a data register and a program register. The input to the program register determines the operation, which is a completely positive linear map, that will be performed on the state in the data register. We develop a mathematical description for these devices, and apply it to several different examples of processors. The problem of finding a processor that will be able to implement a given set of mappings is also examined, and it is shown that while it is possible to design a finite processor to realize the phase-damping channel, it is not possible to do so for the amplitude-damping channel.Comment: 10 revtex pages, no figure

Studies on conventional cutting of intermetallic nickel and titanium aluminides

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Owing to the high percentage of covalent bonds, intermetallic nickel and titanium aluminides have specific physical and chemical characteristics that predestine them for components under high thermal and mechanical load. However, the relatively low ductility and thermal conductivity at room temperature, linked to high tensile strength, impede the machining with geometrically defined cutting edges in series production. The conventional machining process is characterized by microcrack formation at the component surface. One possible way is to warm up the intermetallic alloys locally above the quasi-brittle-ductile transition temperature by the interaction of the workpiece material and the tool. The subjects of investigation were the influences of feed rate and cutting speed on the tool-face temperature and cutting force as well as on the chip formation and fringe-area formation during longitudinal cylindrical turning. The experiments were carried out with intermetallic nickel and titanium aluminides in an as-cast and extruded state. The goal was to elaborate the technological basic knowledge for a damage-minimized and productive machining of intermetallic aluminides with geometrically defined cutting edges

Modified sorting technique to mitigate the collateral mortality of trawled school prawns (Metapenaeus macleayi)

The potential for changes to onboard handling practices in order to improve the fate of juvenile school prawns (Metapenaeus macleayi) discarded during trawling were investigated in two Australian rivers (Clarence and Hunter) by comparing a purpose-built, water-filled sorting tray against a conventional dry tray across various conditions, including the range of typical delays before the start of sorting the catch (2 min vs. 15 min). Juvenile school prawns (n= 5760), caught during 32 and 16 deployments in each river, were caged and sacrificed at four times: immediately (T0), and at 24 (T24), 72 (T72), and 120 (T12 0) hours after having been discarded. In both rivers, most mortalities occurred between T0 and T24 and, after adjusting for control deaths (<12%), were greatest for the 15-min conventional treatment (up to 41% at T120). Mixed-effects logistic models revealed that in addition to the sampling time, method of sorting, and delay in sorting, the weight of the catch, salinity, and percentage cloud cover were significant predictors of mortality. Although trawling caused some mortalities and comparable stress (measured as L -lactate) in all school prawns, use of the water tray lessened the negative impacts of some of the above factors across both the 2-min and 15-min delays in sorting so that the overall discard mortality was reduced by more than a third. When used in conjunction with selective trawls, widespread application of the water tray should help to improve the sustainability of trawling for school prawns

Uhlmann's geometric phase in presence of isotropic decoherence

Uhlmann's mixed state geometric phase [Rep. Math. Phys. {\bf 24}, 229 (1986)] is analyzed in the case of a qubit affected by isotropic decoherence treated in the Markovian approximation. It is demonstrated that this phase decreases rapidly with increasing decoherence rate and that it is most fragile to weak decoherence for pure or nearly pure initial states. In the unitary case, we compare Uhlmann's geometric phase for mixed states with that occurring in standard Mach-Zehnder interferometry [Phys. Rev. Lett. {\bf 85}, 2845 (2000)] and show that the latter is more robust to reduction in the length of the Bloch vector. We also describe how Uhlmann's geometric phase in the present case could in principle be realized experimentally.Comment: New ref added, refs updated, journal ref adde

Connections and Metrics Respecting Standard Purification

Standard purification interlaces Hermitian and Riemannian metrics on the space of density operators with metrics and connections on the purifying Hilbert-Schmidt space. We discuss connections and metrics which are well adopted to purification, and present a selected set of relations between them. A connection, as well as a metric on state space, can be obtained from a metric on the purification space. We include a condition, with which this correspondence becomes one-to-one. Our methods are borrowed from elementary *-representation and fibre space theory. We lift, as an example, solutions of a von Neumann equation, write down holonomy invariants for cyclic ones, and ``add noise'' to a curve of pure states.Comment: Latex, 27 page