Symmetric extendibility for a class of qudit states

Abstract

The concept of symmetric extendibility has recently drawn attention in the context of tolerable error rates in quantum cryptography, where it can be used to decide whether quantum states shared between two parties can be purified by means of entanglement purification with one-way classical communication only. Unfortunately, at present there exists no simple general criterion to decide whether a state possesses a symmetric extension or not. In this article we derive criteria for symmetric extendibility within subclasses of all two-qudit states. Using these criteria, we can completely solve the problem for a two-parameter family of two-qudit states, which includes the isotropic states as a subclass.

12 pages, no figures

References in corpus (6)

• Local Hidden Variable Theories for Quantum States
• Unconditionally Secure Key Distribution In Higher Dimensions By Depolarization
• Symmetric extension in two-way quantum key distribution
• Spectrum conditions for symmetric extendible states
• Symmetric extendibility for qudits and tolerable error rates in quantum cryptography
• Asymptotic correctability of Bell-diagonal qudit states and lower bounds on tolerable error probabilities in quantum cryptography

Cited by in corpus (7)

• Symmetric Extension of Two-Qubit States
• Compatible quantum correlations: on extension problems for Werner and isotropic states
• Extendibility of bosonic Gaussian states
• Numerical evidence for bound secrecy from two-way post-processing in quantum key distribution
• Detecting Consistency of Overlapping Quantum Marginals by Separability
• Sufficient condition for nonexistence of symmetric extension of qudits using Bell inequalities
• Distributing bipartite quantum systems under timing constraints