Quantum fidelity measures for mixed states.

Applications of quantum technology often require fidelities to quantify performance. These provide a fundamental yardstick for the comparison of two quantum states. While this is straightforward in the case of pure states, it is much more subtle for the more general case of mixed quantum states often found in practice. A large number of different proposals exist. In this review, we summarize the required properties of a quantum fidelity measure, and compare them, to determine which properties each of the different measures has. We show that there are large classes of measures that satisfy all the required properties of a fidelity measure, just as there are many norms of Hilbert space operators, and many measures of entropy. We compare these fidelities, with detailed proofs of their properties. We also summarize briefly the applications of these measures in teleportation, quantum memories and quantum computers, quantum communications, and quantum phase-space simulations.

Observation of the rose petal effect over single- and dual-scale roughness surfaces.

Rose petals exhibit superhydrophobicity with strong adhesion to pin water drops, known as the 'petal effect.' It is generally believed that the petal effect is attributed to dual-scale roughness, that is, the surface possesses both a nanostructure and a microstructure (Feng et al 2008 Langmuir 24 4114). In this study, we demonstrate that the dual-scale roughness is not a necessary condition for a surface of the petal effect. A surface of single-scale roughness, either at the nanoscale or the microscale alone, within a certain roughness region may also exhibit the petal effect. The surface roughness plays the essential role on the wetting behavior and governs the contact angle in the Wenzel or Cassie state, as well as the contact angle hysteresis. A water drop on the surface of the petal effect under the condition of the advancing and receding contact angle would fall into, respectively, the Cassie and Wenzel state, which leads to a contact angle hysteresis large enough to pin the water drop. On both single and dual textured hydrophobic surfaces, a sequence of wetting transitions: Wenzel state → petal state (sticky superhydrophobic state) → lotus state (slippery superhydrophobic state) is consistently observed by simply increasing the surface roughness.