|Computational Mathematics Seminar Series|
|Semidefinite Optimization for Quantum Information Processing|
|Xin Wang, University of Maryland|
|Hartree Postdoctoral Fellow|
|Digital Media Center 1034
December 04, 2018 - 03:30 pm
In this talk, I will show how to apply semidefinite optimization to study two basic lines of quantum information processing: entanglement manipulation and communication over quantum channels. Novel mathematical tools improve our understanding of the structure of quantum entanglement and the limits of information processing with quantum systems. In the first part, I will discuss the fundamental features of quantum entanglement and develop quantitative approaches to better exploit the power of entanglement. I will introduce a computable and additive entanglement measure to quantify the amount of entanglement, which also plays an important role as the improved semidefinite programming (SDP) upper bound of distillable entanglement. Notably, I will demonstrate the irreversibility of asymptotic entanglement manipulation under positive-partial-transpose-preserving quantum operations, resolving a long-standing open problem in quantum information. In the second part, I will develop a framework of semidefinite programs to evaluate the classical and quantum communication capabilities of quantum channels in both the non-asymptotic and asymptotic regimes, which can be applied as benchmarks for near-term quantum codes. In particular, I will discuss the first general SDP strong converse bound on the classical capacity of an arbitrary quantum channel and give in particular the best known upper bound on the classical capacity of the amplitude damping channel. I will further establish a finite resource analysis of classical communication over basic channels such as the quantum erasure channel.