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Over the last twenty years, quantum information and quantum computing have profoundly shaped our thinking about the basic concepts of quantum physics. But can these insights also shape the way we /teach/ quantum mechanics to undergraduate physics students? A recent adventure in textbook-writing suggests some strategies and dilemmas.

A Majorana fermion is a particle that is its own antiparticle. It has been studied in high energy physics for decades, but has not been definitely observed. In condensed matter physics, Majorana fermions appear as low energy fractionalized quasi-particles with non-Abelian statistics and inherent nonlocality. In this talk I will first discuss recent theoretical proposals of realizing Majorana fermions in solid-state systems, including topological insulators and nanowires. I will next propose experimental setups to detect the existence of Majorana fermions and their striking properties.

The uncertainty principle bounds the uncertainties about the outcomes of two incompatible measurements, such as position and momentum, on a particle. It implies that one cannot predict the outcomes for both possible choices of measurement to arbitrary precision, even if information about the preparation of the particle is available in a classical memory. However, if the particle is prepared entangled with a quantum memory, it is possible to predict the outcomes for both measurement choices precisely. I will explain a recent extension of the uncertainty principle to incorporate this case. The new relation gives a lower bound on the uncertainties, which depends on the amount of entanglement between the particle and the quantum memory. If time permits, I will also outline a couple of applications.

The quantum spin Hall effect relates seemingly unrelated degrees of freedom, i.e., charge and spin degrees of freedom. We will discuss such "duality" can be extended to much wider class of quantum numbers, and the corresponding order parameters. In particular, two valleys in graphene can be viewed as an SU(2) pseudo spin degree of freedom, which turns out to be "dual" to the charge degree of freedom, pretty much in the same way as spin in the quantum spin Hall effect is closely tied with charge. I.e., graphene can host "the quantum valley Hall effect" (QVHE). We will show that one of the best venues to observe the QVHE in graphene is actually superconductivity that can be induced in graphene by proximity effect, say, where passing supercurrent in one direction induces accumulation of pseudo spin ("valley spin") at the boundary of graphene sample. We will also discuss the "inverse QVHE" as a possible scenario to explain the highly resistive state found in N=0 Landau level in graphene in a high magnetic field.

We give a detailed derivation of a supersymmetric configuration of wrapped D5-branes on a two-cycle of a warped resolved conifold. Our analysis reveals that the resolved conifold should support a non-Kahler metric with an SU(3) structure. We use this as a starting point of the geometric transition in type IIB theory. A mirror, and a subsequent flop transition using an intermediate M-theory configuration with a G2 structure, gives rise to the complete IR geometric transition in type IIA theory. A further mirror transformation gives the type IIB gravity dual of the IR gauge theory on the wrapped D5-branes. Expectedly non-Kahler deformations of the resolved and the deformed conifolds appear as the gravity duals of the confining gauge theories in type IIA and type IIB theories respectively, although in more generic cases these manifolds could also be non-geometric. In the local limit we reproduce precisely the scenarios presented in our earlier works. Our present work should therefore be viewed as providing a supergravity proof of geometric transitions in the full global scenarios in type II theories.