A semidefinite program for distillable entanglement
By Eric M. Rains. IEEE Transactions on Information Theory, 2000
325 citations recorded by the source corpus.
We show that the maximum fidelity obtained by a positive partial transpose (p.p.t.) distillation protocol is given by the solution to a certain semidefinite program. This gives a number of new lower and upper bounds on p.p.t. distillable entanglement (and thus new upper bounds on 2-locally distillable entanglement). In the presence of symmetry, the semidefinite program simplifies considerably, becoming a linear program in the case of isotropic and Werner states. Using these techniques, we determine the p.p.t. distillable entanglement of asymmetric Werner states and "maximally correlated" states. We conclude with a discussion of possible applications of semidefinite programming to quantum codes and 1-local distillation.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/023d8ea210bf19211d8adf49a50899d8d995ecd9
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In Artificial Intelligence
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- Vittorio Giovannetti
- Cosmo Lupo
- Stefano Mancini
- Karol Zyczkowski
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In Atomic and Molecular Physics, and Optics
- Andreas J. Winter
- Igor Devetak
- Filippo Caruso
- Vittorio Giovannetti
- Cosmo Lupo
- Stefano Mancini
- Karol Zyczkowski
- Ingemar Bengtsson
Citations in the corpus
- Optimal sequence of quantum measurements in the sense of Stein's lemma in quantum hypothesis testing (2002, background): “As was discussed in several papers, this problem also can be applied to other related topics in quantum information, for example, quantum channel coding [1, 2, 3, 4], distillable entanglement [5], quantum estimation [6], quantum universal variable-length source coding [7], and quantum coin tossing [”
- Distillation of secret key and entanglement from quantum states (2003, background): “1997), the Rains bound R(ρ) (Rains 2001) (which may well equal the regularized relative entropy of entanglement with respect to the states with positive partial transpose, see Audenaert et al.”
- Quantum channels and memory effects (2012, background): “The latter are defined as those channels which produce output states (Φ⊗ id )(ρQA) with positive partial transpose (PPT) (Horodecki et al., 1996; Peres, 1996; Rains, 2001).”
- Geometry of Quantum States: Index (2007, methodology): “Log-negativity was used by Rains [762] to obtain bounds on distillable entanglement.”