Classification of bi-qutrit positive partial transpose entangled edge states by their ranks

Abstract

We construct $3\otimes 3$ PPT entangled edge states with maximal ranks, to complete the classification of $3\otimes 3$ PPT entangled edge states by their types. The ranks of the states and their partial transposes are 8 and 6, respectively. These examples also disprove claims in the literature.

correct the title to avoid an acronym, correct few texts

References in corpus (19)

• Separability Criterion for Density Matrices
• Separability criterion and inseparable mixed states with positive partial transposition
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Unextendible Product Bases and Bound Entanglement
• General Entanglement Breaking Channels
• Schmidt number witnesses and bound entanglement
• Characterization of separable states and entanglement witnesses
• Separability in 2xN composite quantum systems
• Operational criterion and constructive checks for the separability of low rank density matrices
• Entangled states with positive partial transpose arising from indecomposable positive linear maps
• Three-by-three bound entanglement with general unextendible product bases
• Construction of entangled states with positive partial transposes based on indecomposable positive linear maps
• A (5,5) and (6,6) PPT edge state
• Unique decompositions, faces, and automorphisms of separable states
• Construction of $3\otimes 3$ entangled edge states with positive partial transposes
• Unextendible product bases and extremal density matrices with positive partial transpose
• Description of rank four PPT entangled states of two qutrits
• Low rank positive partial transpose states and their relation to product vectors
• Existence of product vectors and their partial conjugates in a pair of spaces

Cited by in corpus (21)

• Four-qubit entangled symmetric states with positive partial transpositions
• The Structure of Qubit Unextendible Product Bases
• Entangled symmetric states of N qubits with all positive partial transpositions
• Facial structures for various notions of positivity and applications to the theory of entanglement
• Non-positive-partial-transpose quantum states of rank four are distillable
• Separable states with unique decompositions
• Diagonal unitary and orthogonal symmetries in quantum theory
• The structural physical approximations and optimal entanglement witnesses
• Properties and construction of extreme bipartite states having positive partial transpose
• Entanglement witnesses arising from Choi type positive linear maps
• Entangled symmetric states and copositive matrices
• Exposedness of Choi type entanglement witnesses and applications to lengths of separable states
• Unextendible product bases, bound entangled states, and the range criterion
• Characterization of equivariant maps and application to entanglement detection
• Multi-partite separable states with unique decompositions and construction of three qubit entanglement with positive partial transpose
• Equivalence classes and canonical forms for two-qutrit entangled states of rank four having positive partial transpose
• Product vectors in the ranges of multi-partite states with positive partial transposes and permanents of matrices
• Random covariant quantum channels
• Entangled edge states of corank one with positive partial transposes
• Global geometric difference between separable and Positive partial transpose states
• Rank-based entanglement detection for bound entangled states