Simple test for quantum channel capacity

Abstract

Basing on states and channels isomorphism we point out that semidefinite programming can be used as a quick test for nonzero one-way quantum channel capacity. This can be achieved by search of symmetric extensions of states isomorphic to a given quantum channel. With this method we provide examples of quantum channels that can lead to high entanglement transmission but still have zero one-way capacity, in particular, regions of symmetric extendibility for isotropic states in arbitrary dimensions are presented. Further we derive {\it a new entanglement parameter} based on (normalised) relative entropy distance to the set of states that have symmetric extensions and show explicitly the symmetric extension of isotropic states being the nearest to singlets in the set of symmetrically extendible states. The suitable regularisation of the parameter provides a new upper bound on one-way distillable entanglement.

6 pages, no figures, RevTeX4. Signifficantly corrected version. Claim on continuity of channel capacities removed due to flaw in the corresponding proof. Changes and corrections performed in the part proposing a new upper bound on one-way distillable etanglement which happens to be not one-way entanglement monotone

References in corpus (4)

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• Non-additivity of quantum capacity for multiparty communication channels

Cited by in corpus (13)

• On quantum advantage in dense coding
• Symmetric Extension of Two-Qubit States
• Extendibility limits the performance of quantum processors
• Quantum correlations of two-qubit states with one maximally mixed marginal
• Symmetric extension in two-way quantum key distribution
• Spectrum conditions for symmetric extendible states
• Extendibility of bosonic Gaussian states
• Hierarchy of efficiently computable and faithful lower bounds to quantum discord
• Symmetric extension of bipartite quantum states and its use in quantum key distribution with two-way postprocessing
• Reducible Correlations in Dicke States
• Quantifying the unextendibility of entanglement
• Conditions for degradability of tripartite quantum states
• Efficient bounds on quantum communication rates via their reduced variants