Rank three bipartite entangled states are distillable
arXiv:0803.1011 · doi:10.1103/PhysRevA.78.022318
Abstract
We prove that the bipartite entangled state of rank three is distillable. So there is no rank three bipartite bound entangled state. By using this fact, We present some families of rank four states that are distillable. We also analyze the relation between the low rank state and the Werner state.
5 pages; no figure
References in corpus (28)
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Mixed State Entanglement and Quantum Error Correction
- Separability Criterion for Density Matrices
- Separability of Mixed States: Necessary and Sufficient Conditions
- Three qubits can be entangled in two inequivalent ways
- Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
- Entanglement Measures and Purification Procedures
- Separability criterion and inseparable mixed states with positive partial transposition
- Quantum privacy amplification and the security of quantum cryptography over noisy channels
- Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
- Distillation of secret key and entanglement from quantum states
- Unextendible Product Bases and Bound Entanglement
- An improved bound on distillable entanglement
- Evidence for Bound Entangled States with Negative Partial Transpose
- Distillability and partial transposition in bipartite systems
- A rigorous treatment of distillable entanglement
- Separability in 2xN composite quantum systems
- Operational criterion and constructive checks for the separability of low rank density matrices
- Remote information concentration using a bound entangled state
- Construction of quantum states with bound entanglement
- Distillability via protocols respecting the positivity of partial transpose
- Activating NPPT distillation with an infinitesimal amount of bound entanglement
- Characterization of Distillable and Activable States using Entanglement Witnesses
- Study of the Distillability of Werner States Using Entanglement Witnesses and Robust Semidefinite Programs
- Characterization of distillability of entanglement in terms of positive maps
- New classes of n-copy undistillable quantum states with negative partial transposition
- Some Features of the Conditional -Entropies of Composite Quantum Systems
- Inclusion relations among separability criteria
Cited by in corpus (18)
- Gaussian entanglement revisited
- Sudden death of distillability in qutrit-qutrit systems
- Family of bound entangled states on the boundary of Peres set
- Distillability and PPT entanglement of low-rank quantum states
- Non-positive-partial-transpose quantum states of rank four are distillable
- Geometry of entanglement in the Bloch sphere
- Non-classical correlations in quantum mechanics and beyond
- Limits for entanglement distribution with separable states
- Unextendible product bases, bound entangled states, and the range criterion
- Construction of genuine multipartite entangled states
- Equivalence classes and canonical forms for two-qutrit entangled states of rank four having positive partial transpose
- A complete picture of the four-party linear inequalities in terms of the 0-entropy
- On a matrix inequality related to the distillability problem
- A Note on Quantum Entanglement and PPT
- Bipartite Bound Entanglement
- A matrix inequality related to the entanglement distillation problem
- New Partial Trace Inequalities and Distillability of Werner States
- Entanglement distillation in terms of a conjectured matrix inequality