Complexity of quantum processes

这项提议是为了研究各种量子信息过程中出现的复杂性理论问题。这项研究特别关注：*(1)共享纠缠的局域信道，其中量子纠缠的存在(可能是巨大的纠缠)可以增加可以以有趣的方式执行的操作的种类；以及*(2)马尔可夫(又名林布拉德或耗散)演化，其中量子态的连续时间轨迹可以以有趣的方式演化，超出了哈密顿演化的可能。*这两个项目都与极端情况下的量子信息模型有关。对于本地通道上的项目，纠缠被发挥到了极致，同时限制了输入和输出寄存器的大小。马尔可夫演化的项目还涉及到极端情况，即通过较大系统上的哈密顿演化在有限大小的系统上模拟此类演化需要较大系统的大小和潜在哈密顿量的范数接近无穷大。

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.