Extremal extensions of entanglement witnesses and their connection with UPB

Abstract

In this paper we describe a new connection between UPB (unextendable product bases) and P (positive) maps which are not CP (completely positive). We show that inner automorphisms of the set of P maps which are not CP, produce extremal extensions of these maps that help in entanglement detection. By constructing such an extension of the well-known Choi map, we strengthen its power to unearth PPT (positive under partial transpose) entangled states. We further show that the class of maps generated from the Choi map via an inner automorphism naturally detects the entanglement of states in the orthogonal complement of certain UPB. This brings out a hitherto undiscovered connection between the Choi map and UPB. We also show that certain other recently considered extremal extensions are obtainable by such extensions of the Choi map.

6 pages 2 figures

References in corpus (8)

• Entanglement detection
• Optimal entanglement criterion for mixed quantum states
• Separability criteria and bounds for entanglement measures
• Entanglement witnesses arising from exposed positive linear maps
• Positive finite rank elementary operators and characterizing entanglement of states
• Optimality for indecomposable entanglement witnesses
• Entanglement witnesses arising from Choi type positive linear maps
• Optimal indecomposable witnesses without extremality as well as spanning property

Cited by in corpus (8)

• Entanglement witnesses: construction, analysis and classification
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• Construction of noisy bound entangled states and the range criterion
• Exposedness of Choi type entanglement witnesses and applications to lengths of separable states
• Nonlocality of tripartite orthogonal product states
• Measurement-based local quantum filters and their ability to transform quantum entanglement
• Increasing distillable key rate from bound entangled states by using local filtration
• Criteria and new classes of k-positive maps