报告题目：Quantum Maps Between CPTP and HPTP

报告时间：2023年10月31日 16:00

报告地点：成龙校区办公楼125会议室

报告摘要：

  For an open quantum system to evolve under CPTP maps, assumptions are made on the initial correlations between the system and the environment. Hermitian-preserving trace-preserving (HPTP) maps are considered as the local dynamic maps beyond CPTP. In this work, we provide a succinct answer to the question of what physical maps are in the HPTP realm by two approaches. The first is by taking one step out of the CPTP set, which provides us with Semi-Positivity (SP) TP maps. The second way is by examining the physicality of HPTP maps, which leads to Semi-Nonnegative (SN) TP maps. Physical interpretations and geometrical structures are studied for these maps. The non- CP SPTP maps Ψ correspond to the quantum non-Markovian process under the CP-divisibility definition (Ψ = Ξ ◦ Φ−1, where Ξ and Φ are CPTP). When removing the invertibility assumption on Φ, we land in the set of SNTP maps. A by-product of set relations is an answer to the following question – what kind of dynamics the system will go through when the previous dynamic Φ is non-invertible. In this case, the only locally well-defined maps are in SNSP, they live on the boundary of SN. Otherwise, the non-local information will be irreplaceable in the system’s dynamic. With the understanding of physical maps beyond CPTP, we prove that the current quantum error correction scheme is still sufficient to correct quantum non-Markovian errors. In some special cases, lack of complete positivity could provide us with more error correction methods with less overhead.

报告人简介：

  曹凝萍目前是加拿大安大略省圆周理论研究所（Perimeter Institute）和量子计算研究所（Institute for Quantum Computing）的联合博士后研究员。她于2021年在加拿大安大略省的圭尔夫大学获得博士学位。她对量子信息和量子计算的各种主题都很感兴趣。她的研究主要集中在量子信息的基础、开放量子系统和量子机器学习领域。