Purity-Based Continuity Bounds for von Neumann Entropy

Abstract

We propose continuity bounds for the von Neumann entropy of qubits whose difference in purity is bounded. Considering the purity difference of two qubits to capture the notion of distance between them results into bounds which are demonstrably tighter than the trace distance-based existing continuity bounds of quantum states. Continuity bounds can be utilized in bounding the information-theoretic quantities which are generally difficult to compute.