Quantum Distillation Literature Review

introduction

Quick Introduction

• high level intro video

目标

• 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。

各类distillation protocols的基础论文

• 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.
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• • explanation of QECC

Literature Review

综述 Survey

• • 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

Recursive Protocols

• • 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.

Hashing and breeding

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

Continuous Variable Distillation of Entanglement with Linear Optics

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
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• • • 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
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Non-Gaussian Resource States

• • • 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
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• • • • 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
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• • • • A. Ourjoumtsev, R. Tualle-Brouri, and P. Grangier. Quantum homodyne tomography of a two-photon fock state. Physical Review Letters, 96:213601, 2006. link
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The $({\rho }^{(i)},{\rho }^{(0)})$ Protocol

Homodyne Distillation Pumping

• • • 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
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• • • 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
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2011 - 2021 论文整理

• 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