Random qubit-states and how best to measure them

We consider the problem of measuring a single qubit, known to have been prepared in either a randomly selected pure state or a randomly selected real pure state. We seek the measurements that provide either the best estimate of the state prepared or maximise the accessible information. Surprisingly, any sensible measurement turns out to be optimal. We discuss the application of these ideas to multiple qubits and higher-dimensional systems

High-fidelity quantum driving

The ability to accurately control a quantum system is a fundamental requirement in many areas of modern science such as quantum information processing and the coherent manipulation of molecular systems. It is usually necessary to realize these quantum manipulations in the shortest possible time in order to minimize decoherence, and with a large stability against fluctuations of the control parameters. While optimizing a protocol for speed leads to a natural lower bound in the form of the quantum speed limit rooted in the Heisenberg uncertainty principle, stability against parameter variations typically requires adiabatic following of the system. The ultimate goal in quantum control is to prepare a desired state with 100% fidelity. Here we experimentally implement optimal control schemes that achieve nearly perfect fidelity for a two-level quantum system realized with Bose-Einstein condensates in optical lattices. By suitably tailoring the time-dependence of the system's parameters, we transform an initial quantum state into a desired final state through a short-cut protocol reaching the maximum speed compatible with the laws of quantum mechanics. In the opposite limit we implement the recently proposed transitionless superadiabatic protocols, in which the system perfectly follows the instantaneous adiabatic ground state. We demonstrate that superadiabatic protocols are extremely robust against parameter variations, making them useful for practical applications.Comment: 17 pages, 4 figure

Dynamic Emotional and Neural Responses to Music Depend on Performance Expression and Listener Experience

Apart from its natural relevance to cognition, music provides a window into the intimate relationships between production, perception, experience, and emotion. Here, emotional responses and neural activity were observed as they evolved together with stimulus parameters over several minutes. Participants listened to a skilled music performance that included the natural fluctuations in timing and sound intensity that musicians use to evoke emotional responses. A mechanical performance of the same piece served as a control. Before and after fMRI scanning, participants reported real-time emotional responses on a 2-dimensional rating scale (arousal and valence) as they listened to each performance. During fMRI scanning, participants listened without reporting emotional responses. Limbic and paralimbic brain areas responded to the expressive dynamics of human music performance, and both emotion and reward related activations during music listening were dependent upon musical training. Moreover, dynamic changes in timing predicted ratings of emotional arousal, as well as real-time changes in neural activity. BOLD signal changes correlated with expressive timing fluctuations in cortical and subcortical motor areas consistent with pulse perception, and in a network consistent with the human mirror neuron system. These findings show that expressive music performance evokes emotion and reward related neural activations, and that music's affective impact on the brains of listeners is altered by musical training. Our observations are consistent with the idea that music performance evokes an emotional response through a form of empathy that is based, at least in part, on the perception of movement and on violations of pulse-based temporal expectancies