Bounding quantum capacities via partial orders and complementarity

IQC-QuICS Math-CS Seminar

Christoph Hirche (Technische Universität München and National University of Singapore)
Thursday, October 7, 2021 - 10:00am
Virtual Via Zoom

Calculating quantities such as the quantum or private capacity of a quantum channel is a fundamental, but unfortunately a generally very hard, problem. A well known class of channels for which the task simplifies is that of degradable channels, and it was later shown that the same also holds for a potentially bigger class of channels, the so called less noisy channels. Based on the former, the concept of approximately degradable channels was introduced to find bounds on capacities for general channels. We discuss how the idea can be transferred to other partial orders, such as less noisy and more capable channels, to find potentially better capacity bounds. Unfortunately these are not necessarily easy to compute, but we show how they can be used to find operationally meaningful bounds on capacities that are based on the complement of the quantum channel and might give a deeper understanding of phenomena such as superadditivity. Finally, we discuss how the framework can be transferred to quantum states to bound the one-way distillable entanglement and secret key of a bipartite state.