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

DOI10.1080/03081087.2013.801963zbMath1295.81047arXiv1407.1350OpenAlexW1993930882MaRDI QIDQ5495747

David W. Kribs, Sarah Plosker

Publication date: 7 August 2014

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.1350

zbMATH Keywords

density operatorquantum cryptographycompletely positive maphigher rank numerical rangeprivate quantum code

Mathematics Subject Classification ID

Quantum computation (81P68) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12) Quantum cryptography (quantum-theoretic aspects) (81P94)

Cites Work

• Efficient quantum error correction for fully correlated noise
• Higher-rank numerical ranges and compression problems
• Higher rank numerical ranges and low rank perturbations of quantum channels
• Quantum error correcting codes from the compression formalism
• Higher Rank Numerical Ranges of Normal Matrices
• Condition for the higher rank numerical range to be non-empty
• Minimal entropy of states emerging from noisy quantum channels
• Geometry of higher-rank numerical ranges
• The higher rank numerical range is convex