Complexity of quantum processes

该提案旨在研究各种量子信息过程中产生的复杂性理论问题。特别是，研究涉及：***（1）具有共享纠缠的本地通道，其中量子纠缠（可能是大量纠缠）的存在可以增加可以以有趣的方式执行的操作类型； ***(2) 马尔可夫（又名 Lindbladian 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性。***这两个项目都涉及极端环境下的量子信息模型。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。马尔可夫演化项目还关注极端情况，因为通过较大系统上的哈密顿演化来模拟有界大小系统上的这种演化需要较大系统的大小和基础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.