Asymptotic correctability of Bell-diagonal qudit states and lower bounds on tolerable error probabilities in quantum cryptography

Abstract

The concept of asymptotic correctability of Bell-diagonal quantum states is generalised to elementary quantum systems of higher dimensions. Based on these results basic properties of quantum state purification protocols are investigated which are capable of purifying tensor products of Bell-diagonal states and which are based on $B$-steps of the Gottesman-Lo-type with the subsequent application of a Calderbank-Shor-Steane quantum code. Consequences for maximum tolerable error rates of quantum cryptographic protocols are discussed.

arXiv commentsubmitted to J. Phys. A

References in corpus (11)

• Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
• Good Quantum Error-Correcting Codes Exist
• Multiple Particle Interference and Quantum Error Correction
• Efficient bipartite quantum state purification in arbitrary dimensional Hilbert spaces
• Unconditionally Secure Key Distribution In Higher Dimensions By Depolarization
• Error tolerance of two-basis quantum key-distribution protocols using qudits and two-way classical communication
• Security bound of two-bases quantum key-distribution protocols using qudits
• Secrecy content of two-qubit states
• Reliability of Calderbank-Shor-Steane Codes and Security of Quantum Key Distribution
• Asymptotic correctability of Bell-diagonal quantum states and maximum tolerable bit error rates
• Distillation Protocols for Mixed States of Multilevel Qubits and the Quantum Renormalization Group

Cited by in corpus (3)

• Symmetric extendibility for qudits and tolerable error rates in quantum cryptography
• Symmetric extendibility for a class of qudit states
• Group-Theoretic Perspective on the PPT and Realignment Criteria in the Magic Simplex for Bipartite Qutrits