Extrapolated States, Void States, and a Huge Novel Class of Distillable Entangled States
A nice and interesting property of any pure tensor-product state is that each such state has distillable entangled states at an arbitrarily small distance ε in its neighbourhood. We say that such nearby states are ε-entangled, and we call the tensor product state in that case, a “boundary separable state”, as there is entanglement at any distance from this “boundary”. Here we find a huge class of separable states that also share that property mentioned above – they all have ε-entangled states at any small distance in their neighbourhood. Furthermore, the entanglement they have is proven to be distillable.
Keywordsquantum computing and quantum information entanglement distillability
Unable to display preview. Download preview PDF.
- 1.Bennett, C.H., DiVincenzo, D.P., Mor, T., Shor, P.W., Smolin, J.A., Terhal, B.M.: Unextendible Product Bases and Bound Entanglement. Phys. Rev. Lett. 82, 5385–5388 (1999), http://link.aps.org/doi/10.1103/PhysRevLett.82.5385 CrossRefMathSciNetGoogle Scholar
- 2.Dur, W., Vidal, G., Cirac, J.I.: Three Qubits Can Be Entangled in Two Inequivalent Ways. Phys. Rev. A 62, 062314 (2000), http://link.aps.org/doi/10.1103/PhysRevA.62.062314
- 3.Horodecki, M., Horodecki, P., Horodecki, R.: Separability of Mixed States: Necessary and Sucient Conditions. Physics Letters A 223(12), 1–8 (1996), http://www.sciencedirect.com/science/article/pii/S0375960196007062 CrossRefzbMATHMathSciNetGoogle Scholar
- 4.Horodecki, M., Horodecki, P., Horodecki, R.: Inseparable Two Spin- 1 2 Density Matrices Can Be Distilled to a Singlet Form. Phys. Rev. Lett. 78, 574–577 (1997), http://link.aps.org/doi/10.1103/PhysRevLett.78.574 CrossRefGoogle Scholar
- 5.Horodecki, M., Horodecki, P., Horodecki, R.: Mixed-State Entanglement and Distillation: Is There a Entanglement in Nature? Phys. Rev. Lett. 80, 5239–5242 (1998), http://link.aps.org/doi/10.1103/PhysRevLett.80.5239 CrossRefzbMATHMathSciNetGoogle Scholar
- 6.Horodecki, P.: Separability Criterion and Inseparable Mixed States with Positive Partial Transposition. Physics Letters A 232(5), 333–339 (1997), http://www.sciencedirect.com/science/article/pii/S0375960197004167 CrossRefzbMATHMathSciNetGoogle Scholar
- 7.Peres, A.: Separability Criterion for Density Matrices. Phys. Rev. Lett. 77(8), 1413–1415 (1996), http://link.aps.org/doi/10.1103/PhysRevLett.77.1413 CrossRefzbMATHMathSciNetGoogle Scholar