Seminars

A number of noncontextual models exist which reproduce different subsets of quantum theory and admit a no-cloning theorem. Therefore, if one chooses noncontextuality as one’s notion of classicality, no-cloning cannot be regarded as a nonclassical phenomenon. In this work, however, we show that there are aspects of the phenomenology of quantum state cloning which are indeed nonclassical according to this principle. Specifically, we focus on the task of state-dependent cloning and prove that the optimal cloning fidelity predicted by quantum theory cannot be explained by any noncontextual model. We derive a noise-robust noncontextuality inequality whose violation by quantum theory not only implies a quantum advantage for the task of state-dependent cloning relative to noncontextual models, but also provides an experimental witness of noncontextuality.

The symmetries play important roles in physical systems. We study the symmetries of a Hamiltonian system by investigating the asymmetry of the Hamiltonian with respect to certain algebras.We define the asymmetry of an operator with respect to an algebraic basis in terms of their commutators. Detailed analysis is given to the Lie algebra SU(2) and its q-deformation. The asymmetry of the q-deformed integrable spin chain models is calculated. The corresponding geometrical pictures with respect to such asymmetry is presented.

The most general quantum object that can be shared between two distant parties is a bipartite quantum channel. While much effort over the last two decades has been devoted to the study of entanglement of bipartite states, very little is known about the entanglement of bipartite channels. In this work, for the first time we rigorously study the entanglement of bipartite channels. We follow a top-down approach, starting from general resource theories of processes, for which we present a new construction of a complete family of monotones, valid in all resource theories where the set of free superchannels is convex. In this setting, we define various general resource-theoretic protocols and resource monotones, which are then applied to the case of entanglement of bipartite channels. We focus in particular on the resource theory of NPT entanglement. Our definition of PPT superchannels allows us to express all resource protocols and monotones in terms of semi-definite programs. Along the way, we generalize the negativity measure to bipartite channels, and show that another monotone, the max-logarithmic negativity, has an operational interpretation as the exact asymptotic entanglement cost of a bipartite channel. Finally, we show that it is not possible to distill entanglement out of bipartite PPT channels under any set of free superchannels that can be used in entanglement theory, leading us in particular to the discovery of bound entangled POVMs.