Open Problems

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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 "", 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 That site was getting badly outdated, and we are currently overhauling it, both updating the content (several problems were solved, and new ones ready to be added) and the format.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 -