# Open Problems

On this page we collect problems in Quantum Information Theory we or our contributors find worthy of attention. The list is ordered by "last submission on top". Numbering is kept stable, so you can refer to the problems by number. Click on the title to find the statement of the problem and some information on known partial results. This information will be updated whenever significant progress is brought to our attention.

To make this page interesting we obviously need input from the community, so please contribute good problems. By this we mean problems in Quantum Information Theory, which are stated in a self-contained way in the current terminology of the field, are open to the best of your knowledge, and pose an interesting challenge to other researchers. We will make an effort to publish all good problems quickly, but may reject contributions we find less suitable.

This page is a new edition of the (now defunct) problem site "www.imaph.tu-bs.de/qi/problems", which our group hosted at the Technical University of Braunschweig. That site was getting badly outdated, and we are currently overhauling it, both updating the content (several problems were solved, and new ones ready to be added) and the format. We decided to go to wiki format. This will make it easier for anyone to add information and comments, and possibly new problems. The numbered list on this page, and the corresponding "problem front pages" are taken out of public editing in order to ensure some long term reliability: you can cite our problems by number, and be ensured that they will not be arbitrarily changed by just anyone. It will be the role of the contact person named for each problem to monitor the public comments, and add them in a possbly edited form to the front page of the problem. Similarly, our group will take the role of adding suggested problems to the numbered list. *Due to spam bot attacks we deactivated public comments indefinitely.*

The transition to wiki is not entirely done. We are still working on various technical aspects such as more citable URLs, and user-friendly interface for suggesting problems. For the time being, send contributions by email to Reinhard Werner. The format of contributions is free. Text written in simple LaTeX, and divided into sections such as Problem/ Background/ Partial Results/ Remarks/ Literature creates the smallest workload for us.

Number | Title | Contact | Date | Last progress | Solved by |
---|---|---|---|---|---|

1. | All the Bell Inequalities | R.F. Werner | 25 Oct 1999 | 2010 | |

2. | Undistillability implies ppt? | D. Bruß | 02 Mar 2000 | 16 Aug 2006 | - |

3. | Polynomial entanglement invariants | R.F. Werner | 13 Oct 2000 | 18 Dez 2001 | A. Sudbery |

4. | Catalytic majorization | M.B. Plenio | 18 Dec 2000 | 24 Sep 2007 | - |

5. | Maximally entangled mixed states | K. Audenaert | 08 Nov 2001 | - | - |

6. | Nice error bases | D. Schlingemann | 08 Nov 2001 | 28 May 2003 | A. Klappenecker, M. Roetteler |

7. | Additivity of Entanglement of Formation | K.G.H. Vollbrecht | 16 Nov 2001 | 11 Nov 2004 | (equivalent to 10) |

8. | Qubit formula for Relative Entropy of Entanglement | J. Eisert | 20 Jun 2003 | - | - |

9. | Reduction criterion implies majorization? | M.M. Wolf | 12 Feb 2002 | 20 May 2003 | T. Hiroshima |

10. | Additivity of classical capacity and related problems | A.S. Holevo | 31 Jan 2003 | 11 Nov 2004 | M. Hastings |

11. | Continuity of the Quantum channel capacity | M. Keyl | 2003 | - | - |

12. | Bell Inequalities for long range vacuum correlations | R. Verch | 22 Jan 2002 | - | - |

13. | Mutually unbiased bases | B.-G. Englert | 31 Jan 2003 | 07 Jan 2004 | - |

14. | Tough error models | E. Knill | 31 Jan 2003 | - | - |

15. | Separability from spectrum | E. Knill | 31 Jan 2003 | 13 Aug 2003 | - |

16. | Complexity of product preparations | E. Knill | 31 Jan 2003 | - | - |

17. | Reversibility of entanglement assisted coding | P. Shor | 31 Jan 2003 | - | - |

18. | Qubit bi-negativity | K.G.H. Vollbrecht | 10 Feb 2003 | 22 Apr 2005 | S. Ishizaka |

19. | Stronger Bell Inequalities for Werner states? | N. Gisin | 20 Jun 2003 | - | - |

20. | Reversible entanglement manipulation | M. Plenio | 08 Feb 2005 | - | - |

21. | Bell violation by tensoring | Y. C. Liang | 08 Feb 2005 | - | - |

22. | Asymptotic cloning is state estimation | M. Keyl | 08 Feb 2005 | 01 Nov 2006 | - G. Chiribella, M. D'Ariano |

23. | SIC POVMs and Zauner's Conjecture | D. Gross | 17 Feb 2005 | - | - |

24. | Secret key from all entangled states | P. Horodecki | 15 Mar 2005 | - | - |

25. | Lockable entanglement measures | P. Horodecki | 15 Mar 2005 | - | - |

26. | Bell inequalities holding for all quantum states | R. Gill | 11 Apr 2005 | 19 Apr 2010 | - |

27. | The power of CGLMP inequalities | R. Gill | 15 Apr 2005 | 28 Feb 2006 | - |

28. | Local equivalence of graph states | D. Schlingemann | 20 Apr 2005 | 09 Sep 2007 | Z. Ji, J. Chen, Z. Wei, M. Ying |

29. | Entanglement of formation for Gaussian states | O. Krüger | 20 Apr 2005 | - | - |

30. | Asymptotic Version of Birkhoff's Theorem | A. Winter | 06 Oct 2005 | - | M.Musat, H.Haagerup |

31. | Individual measurement strategies on geometrically uniform states | J. Bae | 06 Oct 2005 | - | - |

32. | Bell inequalities: many questions, a few answers | N. Gisin | 02 Feb 2007 | - | - |

33. | Bell inequalities and operator algebras | B. S. Tsirelson | 06 Juli 2006 | Jul 2010 | - |