Candidate
Sukanya Ghosal | Applied Mathematics, University of Waterloo
Title
Novel Quantum Capacity Superadditivity with Platypus Channels and its Extensions
Abstract
Unlike in Classical Shannon theory, where classical correlations across joint input of two classical channels do not enhance their classical capacity, determining the capacities of quantum channels is fundamentally challenging due to superadditive effects arising from entanglement across channel inputs.
In the absence of additivity for dynamic information measures, it becomes difficult to interpret a given measure since we would need to assess the measure across an unlimited number of separate channel usage, rendering optimization impossible. Hence, the study of the non-additivity of channel capacities in Quantum Shannon Theory remains an active area of research.
Recently, in https://arxiv.org/abs/2202.08380, a hybrid (called the “platypus channel”) of a simple degradable channel and a completely useless channel has been shown to have additive quantum capacity subject to the “spin-alignment conjecture”. However, it does not belong to any class of channels for which additivity was previously known. In a following work by the same authors (https://arxiv.org/abs/2202.08377), it has been numerically demonstrated that the simplest member of the platypus family shows novel supperadditivity effects jointly with a large number of qubit channels, even though the quantum capacity of the platypus channel is significantly large.
We further explore the superadditivity of coherent information of the platypus channel and its higher-dimensional generalizations when used jointly with a generic qubit channel. We conjecture that for every single qubit channel, there exists a platypus channel of some dimension d, such that it exhibits strict superadditivity of quantum capacity when used jointly with the latter channel. Our objective is to study the mechanism of superadditivity of these channels and the generic structure of the input that attains the non-additivity of coherent information of the tensor product of the channels mentioned above.