Private quantum codes: introduction and connection with higher rank numerical ranges

2013/06/03 by David W. Kribs, D. W. Kribs, Sarah Plosker +1
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Connection (principal bundle) #Geometry #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum channel #Quantum cryptography #Quantum error correction #Quantum information #Quantum key distribution #Quantum mechanics #Quantum-Dot Cellular Automata #Rank (graph theory) #math.OA #msc:15A60 #msc:47A12 #msc:81P68 #msc:81P94 #quant-ph

paper · pdf · doi:10.1080/03081087.2013.801963

published as Linear and Multilinear Algebra, 62, pp. 639-647, 2014 · 9 pages

openalex publication_date 2013/06/03 · arxiv created 2014/07/05 · arxiv updated 2014/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We give a brief introduction to private quantum codes, a basic notion in quantum cryptography and key distribution. Private code states are characterized by indistinguishability of their output states under the action of a quantum channel, and we show that higher rank numerical ranges can be used to describe them. We also show how this description arises naturally via conjugate channels and the bridge between quantum error correction and cryptography.

Citations

• Condition for the higher rank numerical range to be non-empty
• Optimal encryption of quantum bits
• Complementarity of private and correctable subsystems in quantum cryptography and error correction
• Higher rank numerical ranges and low rank perturbations of quantum channels