Description of rank four PPT entangled states of two qutrits

Abstract

It is known that some two qutrit entangled states of rank 4 with positive partial transpose [PPT] can be built from the unextendible product bases [UPB]. We show that this fact is indeed universal, namely all such states can be constructed from UPB. We also classify the 5-dimensional subspaces of two qutrits which contain only finitely many product states (up to scalar multiple), and in particular those spanned by a UPB.

24 pages, 1 figure

References in corpus (7)

• A complete family of separability criteria
• Covariance matrices and the separability problem
• Entanglement and permutational symmetry
• Three-by-three bound entanglement with general unextendible product bases
• Extreme points of the set of density matrices with positive partial transpose
• Distillability and PPT entanglement of low-rank quantum states
• Numerical studies of entangled PPT states in composite quantum systems

Cited by in corpus (25)

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• Non-positive-partial-transpose quantum states of rank four are distillable
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• Unextendible Product Basis for Fermionic Systems
• Properties and construction of extreme bipartite states having positive partial transpose
• Separability of Completely Symmetric States in Multipartite System
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• Existence of product vectors and their partial conjugates in a pair of spaces
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• Nonexistence of $n$-qubit unextendible product bases of size $2^n-5$
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• Equivalence classes and canonical forms for two-qutrit entangled states of rank four having positive partial transpose
• Extremal states of positive partial transpose in a system of three qubits
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• Spectral characterizations of entanglement witnesses
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