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

Probability distributions consistent with a mixed state

A density matrix $\rho$ may be represented in many different ways as a mixture of pure states, \rho = \sum_i p_i |\psi_i\ra \la \psi_i|. This paper characterizes the class of probability distributions $(p_i)$ that may appear in such a decomposition, for a fixed density matrix $\rho$. Several illustrative applications of this result to quantum mechanics and quantum information theory are given.Comment: 6 pages, submitted to Physical Review

Concurrence of mixed bipartite quantum states in arbitrary dimensions

We derive a lower bound for the concurrence of mixed bipartite quantum states, valid in arbitrary dimensions. As a corollary, a weaker, purely algebraic estimate is found, which detects mixed entangled states with positive partial transpose.Comment: accepted py PR

Investigation into Energy Efficiency of Outdated Cutting Machine Tools and Identification of Improvement Potentials to Promote Sustainability

AbstractCutting machine tools have a significant impact on manufacturing and sustainability. There exist a large number of outdated cutting machine tools especially in developing and emerging countries which are still taking a considerable share in global value creation. Furthermore, an increasing trend in field of reuse, retrofitting and upgrading can be observed. For Life-Cycle-Assessment and analyses of end-of-life behavior of such machine tools in context of sustainability, reliable values for energy consumption and machining efficiency under realistic machining conditions are indispensable. In the present paper the energy consumption and machining efficiency of an exemplary outdated milling machine have been measured and analyzed under consideration of different influences such as process parameter, machining material and ratio of prim time to secondary time. Additionally a comparison between a newer and the outdated milling machine has been carried out in order to identify and quantify possible improvement potentials of outdated machine tool concerning energy consumption and machining efficiency. Based on obtained results more accurate and realistic decision can be made by enterprises who aim to promote sustainable manufacturing

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

Fidelity and Concurrence of conjugated states

We prove some new properties of fidelity (transition probability) and concurrence, the latter defined by straightforward extension of Wootters notation. Choose a conjugation and consider the dependence of fidelity or of concurrence on conjugated pairs of density operators. These functions turn out to be concave or convex roofs. Optimal decompositions are constructed. Some applications to two- and tripartite systems illustrate the general theorem.Comment: 10 pages, RevTex, Correction: Enlarged, reorganized version. More explanation

Improvement of Surface Accuracy and Shop Floor Feed Rate Smoothing Through Open CNC Monitoring System and Cutting Simulation

AbstractIn the milling process of complex workpiece shapes the feed rate normally becomes instable due to the high degree of surface curvature that requires high acceleration and deceleration of the interpolated axes. This condition impacts on process time and on the surface accuracy regarding the manufactured part form and texture. The challenge to simulate the real machine and control behavior requires accurate models with a set of experiments to tune and dimension the model to the respective machine tool. The aim is to improve the HSC milling process of complex surfaces before removing any material. In this paper experiments show that the surface form accuracy and texture can be optimized through an automatic feed rate smoothing of the finishing operation directly on the machine tool. The axis positions and spindle speeds monitored through the open CNC are used as input for a geometric cutting simulation, thus enabling to predict and optimize the surface quality