Symmetric extendibility of quantum states

Abstract

Studies on symmetric extendibility of quantum states become especially important in a context of analysis of one-way quantum measures of entanglement, distilabillity and security of quantum protocols. In this paper we analyse composite systems containing a symmetric extendible part with a particular attention devoted to one-way security of such systems. Further, we introduce a new one-way monotone based on the best symmetric approximation of quantum state. We underpin those results with geometric observations on structures of multi-party settings which posses in sub-spaces substantial symmetric extendible components. Finally, we state a very important conjecture linking symmetric-extendibility with one-way distillability and security of all quantum states analyzing behavior of private key in neighborhood of symmetric extendible states.

Revised version with main changes in section II, 9 pages, 1 figure, RevTex

References in corpus (10)

• Distillation of secret key and entanglement from quantum states
• A complete family of separability criteria
• Relating quantum privacy and quantum coherence: an operational approach
• Uncertainty, Monogamy, and Locking of Quantum Correlations
• Quantum correlations of two-qubit states with one maximally mixed marginal
• One-way quantum key distribution: Simple upper bound on the secret key rate
• On quantum estimation, quantum cloning and finite quantum de Finetti theorems
• Symmetric extension in two-way quantum key distribution
• Spectrum conditions for symmetric extendible states
• Hierarchy of efficiently computable and faithful lower bounds to quantum discord

Cited by in corpus (5)

• Quantum Entanglement in Time
• Quantum communication on the bosonic loss-dephasing channel
• Hybrid quantum network design against unauthorized secret-key generation, and its memory cost
• Quantum Computational Complexity and Symmetry
• Upper bounds on the leakage of private data and operational approach to markovianity