QIP 2021 | Leaking information to gain entanglement via log-singularities (Vikesh Siddhu)

Speaker: Vikesh Siddhu, Carnegie Mellon University

Abstract:
Entanglement lies at the root of quantum theory. It is a remarkable resource that is generally believed to diminish when entangled systems interact with their environment. On the contrary, we find that engaging a system with its environment increases its ability to retain entanglement. The maximum rate of retaining entanglement is given by the quantum capacity. We counter-intuitively boost the quantum capacity of a channel by leaking almost all quantum information to the channel's environment. This result also has surprising implication for quantum key distribution: maximum rates for key distribution are boosted by allowing leakage of information to the eavesdropping environment. These boosts exploit two-letter level non-additivity in the channel's coherent information. The resulting non-additivity has a far larger magnitude and a qualitatively wider extent than previously known. This wide extent is proven using a new insight into the von-Neumann entropy which shows that logarithmic singularities in the entropy are a source of quantum capacity and non-additivity. These singularities can be used further to show a new type of non-additivity displayed by a zero quantum capacity qubit amplitude damping channel used in parallel with a simple qutrit channel.