Quantum Information

It is widely known in the
quantum information community that the states that satisfy strong subadditivity
of entropy with equality have the form of quantum Markov chain. Based on a
recent strengthening of strong subadditivity of entropy, I will describe how
such structure can be exploited in the studies of gapped quantum many-body
system. In particular, I will describe a diagrammatic trick to i) give a
quantitative statement about the locality of entanglement spectrum ii)

We study the robustness of quantum information stored in
the degenerate ground space of a local, frustration-free Hamiltonian with
commuting terms on a 2D spin lattice. On one hand, a macroscopic energy barrier
separating the distinct ground states under local transformations would protect
the information from thermal fluctuations. On the other hand, local topological
order would shield the ground space from static perturbations.

Self-testing a multipartite quantum state means verifying
the existence of the state based on the outcomes of unknown or untrusted
measurements.

This concept is important in device-independent quantum
cryptography.

Winter's measurement compression theorem stands as one of the most important, yet perhaps less well-known coding theorems in quantum information theory. Not only does it make an illuminative statement about measurement in quantum theory, but it also underlies several other general protocols used for entanglement distillation or local purity distillation.