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Rigorous treatment of distillable entanglement
Open accessAbstract
The notion of distillable entanglement is one of the fundamental concepts of quantum information theory. Unfortunately, there is an apparent mismatch between the intuitive and rigorous definitions of distillable entanglement. To be precise, the existing rigorous definitions impose the constraint that the distillation protocol produce an output of constant dimension. It is therefore conceivable that this unnecessary constraint might have led to underestimation of the true distillable entanglement. We give a definition of distillable entanglement which removes this constraint, but could conceivably overestimate the true value. Since the definitions turn out to be equivalent, neither underestimation nor overestimation is possible, and both definitions are arguably correct.
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Cites
Entanglement measures and purification procedures
Vedral, V., & Plenio, M. B. (1998) · Physical Review A · doi:10.1103/physreva.57.1619 · Cited by 1,419
Quantum-channel capacity of very noisy channels
DiVincenzo, D. P., Shor, P. W., & Smolin, J. A. (1998) · Physical Review A · doi:10.1103/physreva.57.830 · Cited by 297
Cited by
Coffman, V., Kundu, J., & Wootters, W. K. (2000) · Physical Review A · doi:10.1103/physreva.61.052306 · Cited by 2,619
Intrinsic randomness as a measure of quantum coherence
Yuan, X., Zhou, H., Cao, Z., & Ma, X. (2015) · Physical Review A · doi:10.1103/physreva.92.022124 · Cited by 403
Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
DiVincenzo, D. P., Mor, T., Shor, P. W., Smolin, J. A., & Terhal, B. M. (2003) · Communications in Mathematical Physics · doi:10.1007/s00220-003-0877-6 · Cited by 349
The asymptotic entanglement cost of preparing a quantum state
Hayden, P. M., Horodecki, M., & Terhal, B. M. (2001) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/34/35/314 · Cited by 342
Quantum channels and memory effects
Caruso, F., Giovannetti, V., Lupo, C., & Mancini, S. (2012) · arXiv · doi:10.48550/arxiv.1207.5435 · Cited by 331
Metadata
- Authors
- Rains, E. M.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1999-07-01
- Volume
- 60
- Issue
- 1
- Pages
- 173-178
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2107152752
- Cited by
- 216
- References
- 2
- FWCI
- 13.83
- Type
- journal article
- Language
- en
- Open access
- green
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- Rains, E. M. (1999). Rigorous treatment of distillable entanglement. Physical Review A. https://doi.org/10.1103/physreva.60.173
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