Non-full rank bound entangled states satisfying the range criterion

Abstract

A systematic method for generating bound entangled states in any bipartite system, with ranks ranging from five to full rank, is presented. These states are constructed by mixing separable states with UPB (Unextendible Product Basis) - generated PPT bound entangled states. A subset of this class of PPT bound entangled states, having less than full rank, is shown to satisfy the range criterion [Phys. Lett. A, vol. 232 (1997) 333].

6 pages, Latex. Minor corrections and additions. More references added. Accepted for publication in Phys. Rev. A

References in corpus (14)

• Separability criterion and inseparable mixed states with positive partial transposition
• Unextendible Product Bases and Bound Entanglement
• Optimization of entanglement witnesses
• A complete family of separability criteria
• Bound entanglement can be activated
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Evidence for Bound Entangled States with Negative Partial Transpose
• Distillability and partial transposition in bipartite systems
• Reflections upon separability and distillability
• Construction of quantum states with bound entanglement
• A separability criterion for density operators
• Activating NPPT distillation with an infinitesimal amount of bound entanglement
• New classes of n-copy undistillable quantum states with negative partial transposition
• Deciding separability with a fixed error

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• Construction of noisy bound entangled states and the range criterion
• Distance between Bound Entangled States from Unextendible Product Bases and Separable States
• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory
• Robustness of entangled states that are positive under partial transposition
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• Bound entanglement in symmetric random induced states
• Enhanced separability criteria based on symmetric measurements