Complexity of quantum processes

点击翻译按钮获取中文摘要

The proposal is to investigate complexity-theoretic questions that arise from various quantum information processes. In particular, the investigation concerns: (1) Local channels with shared entanglement, where the presence of quantum entanglement (possibly enormous quantities of entanglement) can increase the kinds of operations that can be performed in interesting ways; and(2) Markovian (a.k.a., Lindbladian or dissipative) evolution, where continuous-time trajectories of quantum states can evolve in interesting ways, beyond what is possible with Hamiltonian evolution.Both projects are concerned with the model of quantum information in extreme settings. For the project on local channels, the entanglement is taken to extremes, while bounding the sizes of the input and output registers. The project on Markovian evolution is also concerned with extremes in the sense that simulating such evolution on a system of bounded size via Hamiltonian evolution on a larger system requires the size of the larger system and the norm of underlying Hamiltonian to approach infinity.