introduction

在只使用local operations and classical communication (LOCC)的前提下，将N个entangled state为 $\rho$ 的entangled pair的copies转化为少量近似纯净的Bell pairs。这样做的好处是能够减少channel noise引起的退相干。

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters. Purification of noisy entanglement and faithful teleportation via noisy channels. Physical Review Letters, 76:722–725, 1996, link 1.
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters. Mixed-state entanglement and quantum error correction. Physical Review A, 54:3824–3851, 1996, link 2.
explanation of QECC

Literature Review

Entanglement Distillation: A Discourse on Bound Entanglement in Quantum Information Theory, Lieven Clarisse. survey_1
Generation and Manipulation of Entanglement in Quantum Optical Systems, Daniel Edward Browne, p89 - p143. survey_2
Tools and Methods for the Distillation of Entanglement in Continuous Variable Quantum Optics, Alvaro Felipe Feito Boirac. survey_3

The recurrence protocol (IBM protocol)：开头处的基础论文
The QPA protocol (Oxford protocol)
- D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera. Quantum privacy amplification and the security of quantum cryptography over noisy channels. Physical Review Letters, 77:2818–2821, 1996, link.
- C. Macchiavello. On the analytical convergence of the qpa procedure. Physics Letters A, 246:385–388, 1998, link.
Local Permutation优化
- J. Dehaene, M. Van den Nest, B. De Moor, and F. Verstraete. Local permutations of products of Bell states and entanglement distillation. Physical Review A, 67: 022310, 2003, link.
- E. Hostens, J. Dehaene, and B. De Moor. The equivalence of two approaches to the design of entanglement distillation protocols. 2004, link.

P.W. Shor and J. A. Smolin. Quantum error-correcting codes need not completely reveal the error syndrome. 1996, link.

The $(\rho^{(i)}, \rho^{(i)})$ Protocol / Gaussian Operation:

D.E. Browne, J. Eisert, S. Scheel, and M.B. Plenio. Driving non-gaussian to gaussian states with linear optics. Physical Review A, 67:062320, 2003. link
Takahashi, H., Neergaard-Nielsen, J. S., Takeuchi, M., Takeoka, M., Hayasaka, K., Furusawa, A., & Sasaki, M. (2010). Entanglement distillation from Gaussian input states. Nature photonics, 4(3), 178-181. link

Photon Subtraction and Heralding

S. Olivares and M. G. A. Paris. Squeezed fock state by inconclusive photon subtraction. SEMICLASS.OPT., 7:S616, 2005. link
J. S. Neergaard-Nielsen, B. Melholt Nielsen, C. Hettich, K. Moelmer, and E. S. Polzik. Generation of a superposition of odd photon number states for quantum information networks. Physical Review Letters, 97:083604, 2006. link
H. Jeong A. Ourjoumtsev, R. Tualle Brouri, and P. Grangier. Generation of optical Schr¨odinger cats from photon number states. Nature, 448:784, 2007. link
A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier. Quantum homodyne tomography of a two-photon fock state. Physical Review Letters, 96:213601, 2006. link

J. Eisert, D. E. Browne, S. Scheel, and M. B. Plenio. Distillation of continuous-variable entanglement with optical means. Annals of Physics, 311:431, 2004. link
J. Eisert, M. B. Plenio, D. E. Browne, S. Scheel, and A. Feito. On the experimental feasibility of continuous-variable optical entanglement distillation. Optics and Spectroscopy, 103:181, 2007. link

Kalb, N., Reiserer, A. A., Humphreys, P. C., Bakermans, J. J., Kamerling, S. J., Nickerson, N. H., ... & Hanson, R. (2017). Entanglement distillation between solid-state quantum network nodes. Science, 356(6341), 928-932. link
Seshadreesan, K. P., Krovi, H., & Guha, S. (2019). Continuous-variable entanglement distillation over a pure loss channel with multiple quantum scissors. Physical Review A, 100(2), 022315. link