Entanglement Theory & Quantum Information Theory

Our group is located at the Institute for Theoretical Physics at the University of Innsbruck, Austria. We are working on several different topics within Quantum Information Theory.

Our main research interests are fundamental problems in Quantum Information Theory. We focus on the development of new theoretical tools for the investigation of quantum many-body systems. One of the aims is the characterization of the entanglement and complexity properties of multipartite systems. We are investigating new applications of multipartite entanglement and novel tools for the generation and manipulation of multipartite entangled states in specific experimental set-ups, like trapped ions or atoms in optical lattices.


February 2020 (left to right: Antoine Neven, Eda Harmanci, Jose Carrasco, Martin Hebenstreit, Matthias Englbrecht, David Gunn, Albert Rico Andres, Barbara Kraus, Marc Langer)



February 2019 (left to right: David Gunn, David Sauerwein, Martin Hebenstreit, Matthias Englbrecht, Barbara Kraus)



May 2018 (left to right: Farid Shahandeh, Barbara Kraus, Martin Hebenstreit, Raphael Brieger, David Sauerwein, Leonhard Czarnetzki, Katharina Schwaiger)


December 2017 (left to right: Raphael Brieger, Yaiza Aragones Soria, Martin Hebenstreit, Katharina Schwaiger, David Sauerwein, Leonhard Czarnetzki, Barbara Kraus)

FG Kraus

November 2016 (left to right: Barbara Kraus, David Sauerwein, Martin Hebenstreit, Raphael Brieger, Yaiza Aragones Soria, Katharina Schwaiger)


March 2013

March 2015 (left to right and top to bottom: Barbara Kraus, Cornelia Spee, David Sauerwein, Martin Hebenstreit, Elke Wölflmaier, Walter Boyajian, Katharina Schwaiger, Michalis Skotiniotis)


March 2013

March 2013 (left to right: Katharina Schwaiger, Barbara Kraus, Walter Boyajian, Cornelia Spee, Tatjana Carle, Michalis Skotiniotis, Elke Wölflmaier, Christoph Spengler, Marti Cuquet)


December 2012December 2012

Group members:

Former members:

  • Eda Harmanci, BSc
  • Albert Rico Andres, MSc
  • Leonhard Czarnetzki, MSc 
  • David Sauerwein, PhD
  • Farid Shahandeh, PhD
  • Katharina Schwaiger, PhD
  • Raphael Brieger, MSc
  • Yaiza Aragones Soria, MSc
  • Walter Boyajian, PhD
  • Dr. Tatjana Carle
  • Dr. Marti Cuquet
  • Dr. Julio de Vicente
  • Dr. Michalis Skotiniotis
  • Dr. Christoph Spengler
  • Clemens Streitberger



Publications (peer-review):

  1. B. Kraus, J. I. Cirac, S. Karnas, and M. Lewenstein, Separability in 2xN Composite Quantum Systems, Phys. Rev. A 61, p. 062302 (2000).

  2. M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, Optimization of Entanglement Witnesses, Phys. Rev. A 62, p. 052310 (2000). 

  3. M. Lewenstein, D. Bruss, J. I. Cirac, B. Kraus, M. Küs, J. Samsonowicz, A. Sanpera, and R. Tarrach, Separability and Distillability in Composite Quantum Systems -a Primer-, J. Mod. Opt. 47, p. 2481 (2000).

  4. M. Lewenstein, B. Kraus, P. Horodecki, and J. I. Cirac, Characterization of Separable States and Entanglement Witnesses, Phys. Rev. A 63, p. 044304 (2001).

  5. J. I. Cirac, W. Dür, B. Kraus, and M. Lewenstein, Entangling Operations and Their Implementation Using a Small Amount of Entanglement, Phys. Rev. Lett. 86, p. 544 (2001).

  6. B. Kraus and J. I. Cirac, Optimal Creation of Entanglement Using a Two-qubit Gate, Phys. Rev. A 63, p.062309 (2001).

  7. G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, Separability Properties of Three-mode Gaussian States, Phys. Rev. A 64, p. 052303 (2001).

  8. G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, Entanglement Criteria for All Bipartite Gaussian States, Phys. Rev. Lett. 87, p. 167904 (2001).

  9. B. Kraus, M. Lewenstein, and J. I. Cirac, Characterization of Distillable and Activatable States using Entanglement Witnesses, Phys. Rev. A 65, p. 042327 (2002).

  10. B. Kraus, K. Hammerer, G. Giedke, and J. I. Cirac, Entanglement generation and Hamiltonian simulation in continuous-variable systems, Phys. Rev. A 67, p. 042314 (2003).

  11. B. Kraus and J. I. Cirac, Discrete Entanglement Distribution with Squeezed Light, Phys. Rev. Lett. 92, p. 13602 (2004).

  12. R. Renner, N. Gisin, and B. Kraus, Information-theoretic security proof for quantum-key-distribution protocols, Phys. Rev. A 72, p. 012332 (2005).

  13. C. Branciard, N. Gisin, B. Kraus, and V. Scarani, Security of two quantum cryptography protocols using the same four qubit states, Phys. Rev. A 72, p. 032301 (2005).

  14. B. Kraus, N. Gisin, and R. Renner, Lower and Upper Bounds on the Secret-Key Rate for Quantum Key Distribution Protocols Using One-Way Classical Communication, Phys. Rev. Lett. 95, p. 080501 (2005).

  15. B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kröll, J. I. Cirac, Quantum memory for non-stationary light fields based on controlled reversible inhomogeneous broadening, Phys. Rev. A 73, 020302 (2006).

  16. N. Gisin, S. Fasel, B. Kraus, H. Zbinden, and G. Ribordy, Trojan Horse Attacks on Quantum Key Distribution Systems, Phys. Rev. A 73, 022320 (2006).

  17. L. Hartmann, B. Kraus, H.-J. Briegel, W. Dür, Role of memory errors in quantum repeaters, Phys. Rev. A 75, 032310 (2007).

  18. B. Kraus, C. Branciard, R. Renner Security of quantum key distribution protocols using two-way classical communication or weak coherent pulses, Phys. Rev. A 75, 012316 (2007).

  19. C. Mora, H. Briegel, B. Kraus, Quantum Kolmogorov complexity and its applications, Int. J. Quant. Inf. 5, 729 (2007).

  20. B. Kraus, H. P. Büchler, S. Diehl, A. Kantian, A. Micheli, P. Zoller, Preparation of Entangled States by Quantum Markov Processes, Phys. Rev. A 78, 042307 (2008).

  21. S. Diehl, A. Micheli, A. Kantian, B. Kraus, H.P. Büchler, P. Zoller, Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms, Nature Physics 4, 878 (2008).

  22. C. Kruszynska and B. Kraus, Local entanglability and multipartite entanglement, Phys. Rev. A, 79, 052304 (2009).

  23. R. Jozsa, B. Kraus, A. Miyake, J. Watrous, Matchgate and space-bounded quantum computations are equivalent, Proc. R. Soc. A 466, 809 (2010).

  24. B. Kraus, Local unitary equivalence of multipartite pure states, Phys. Rev. Lett. 104, 020504 (2010).

  25. B. Kraus, Local unitary equivalence and entanglement of multipartite pure states, Phys. Rev. A 82, 032121 (2010).

  26. T. Carle, H. J. Briegel, B. Kraus, Decoherence of many-body systems due to many-body interactions, Phys. Rev. A 84, 012105 (2011).

  27. B. Kraus, Compressed quantum simulation of the Ising model, Phys. Rev. Lett. 107, 250503 (2011).

  28. J. I. de Vicente, T. Carle, C. Streitberger, B. Kraus, Complete set of operational measures for the characterization of 3-qubit entanglement, Phys. Rev. Lett. 108, 041805 (2012).

  29. T. Carle, B. Kraus, W. Dür, J. I. de Vicente, Purification to Locally Maximally Entangleable States, Phys. Rev. A 87, 012328 (2013).

  30. M. Skotiniotis, W. Dür, B. Kraus, Efficient quantum communication under collective noise, Quantum Information and Computation, 13, 3, 0290-0323 (2013).

  31. C. Spee, J. de Vicente, B. Kraus, Remote entanglement preparation, Phys. Rev. A 88, 010305(R) (2013).

  32. J. de Vicente, C. Spee, B. Kraus, Maximally entangled sets of multipartite states, Phys. Rev. Lett. 111, 110502 (2013).

  33. Ch. Spengler, B. Kraus, A graph state formalism for mutually unbiased bases, Phys. Rev. A 88, 052323 (2013).

  34. W. Boyajian, V. Murg, B. Kraus, Compressed Simulation of evolutions of the XY-model, Phys. Rev. A 88, 052329 (2013).

  35. G. Giedke, B. Kraus, Gaussian local unitary equivalence of n-mode Gaussian states and Gaussian transformations by local operations with classical communication, Phys. Rev. A.89.012335 (2014).

  36. W. Dür, M. Skotiniotis, F. Fröwis, B. Kraus, Improved quantum metrology using quantum error-correction, Phys. Rev. Lett. 112, 080801 (2014).

  37. O. Gühne, M. Cuquet, F.E.S. Steinhoff, T. Moroder, M. Rossi, D. Bruß, B. Kraus, C. Macchiavello, Entanglement and nonclassical properties of hypergraph states, J. Phys. A: Math. Theor. 47. 335303 (2014).

  38. F. Fröwis, M. Skotiniotis, B. Kraus, W. Dür, Optimal quantum states for frequency estimation, New J. Phys. 16, 083010 (2014).

  39. Michalis Skotiniotis, Florian Fröwis, Wolfgang Dür, Barbara Kraus, Algebraic metrology: Pretty good states and bounds, Phys. Rev. A 92, 022323 (2015).

  40. W. L. Boyajian, B. Kraus, Compressed simulation of thermal and excited states of the 1-D XY-model, Phys. Rev. A 92, 032323 (2015).

  41. K. Schwaiger, D. Sauerwein, M. Cuquet, J.I. de Vicente, B. Kraus, Operational multipartite entanglement measures, Phys. Rev. Lett. 115, 150502 (2015).

  42. D. Sauerwein, K. Schwaiger, M. Cuquet, J.I. de Vicente, B. Kraus, The source and accessible entanglement of few-body systems, Phys. Rev. A 92, 062340 (2015).

  43. C. Spee, J. I. de Vicente, B. Kraus, The maximally entangled set for 4-qubit states, J. Math. Phys. 57, 052201 (2016).

  44. M. Hebenstreit, C. Spee, B. Kraus, The MES of tripartite qutrit states and pure state separable transformations which are not possible via LOCC, Phys. Rev. A 93, 012339 (2016), Editor's Suggestion.

  45. W. L. Boyajian, M. Skotiniotis, W. Dür, B. Kraus, Compressed quantum metrology for the Ising Hamiltonian, Phys. Rev. A. 94,.062326 (2016).

  46. J.I. de Vicente, C. Spee, D. Sauerwein, B. Kraus, Entanglement manipulation of multipartite pure states with finite rounds of classical communication, Phys. Rev. A 95, 012323 (2017).

  47. C. Spee, J.I. de Vicente, D. Sauerwein, B. Kraus, Entangled Pure State Transformations via Local Operations Assisted by Finitely Many Rounds of Classical Communication, Phys. Rev. Lett. 118, 040503 (2017).

  48. M. Hebenstreit, B. Kraus, L. Ostermann, H. Ritsch, Subradiance via Entanglement in Atoms with Several Independent Decay Channels, Phys. Rev. Lett. 118, 143602 (2017).

  49. D. Sauerwein, C. Macchiavello, L. Maccone, B. Kraus, Multipartite correlations in mutually unbiased bases, Phys. Rev. A 95, 042315 (2017).

  50. M. Hebenstreit, D. Alsina, J. I. Latorre, B. Kraus, Compressed quantum computation using a remote five-qubit quantum computer, Phys. Rev. A 95, 052339 (2017).

  51. G. Gour, B. Kraus, N. R. Wallach, Almost all multipartite qubit quantum states have trivial stabilizer, J. Math. Phys. 58, 092204 (2017).

  52. K. Schwaiger, B. Kraus, Relations between bipartite entanglement measures, Quant. Inf. Comput. 18, 0085 (2018).

  53. M. Hebenstreit, M. Gachechiladze, O. Gühne, B. Kraus, Coarse graining of entanglement classes in 2xmxn systems, Phys. Rev. A 97, 032330 (2018).

  54. C. Spee, K. Schwaiger, G. Giedke, B. Kraus, Mode entanglement of Gaussian fermionic states, Phys. Rev. A 97, 042325 (2018), Editor's Suggestion.

  55. D. Sauerwein, N. R. Wallach, G. Gour, B. Kraus, Transformations among Pure Multipartite Entangled States via Local Operations are Almost Never Possible, Phys. Rev. X 8, 031020 (2018).

  56. H. Yamasaki, A. Pirker, M. Murao, W. Dür, B. Kraus, Multipartite entanglement outperforming bipartite entanglement under limited quantum system sizes, Phys. Rev. A 98, 052313 (2018), Editor's Suggestion.

  57. M. Hebenstreit, R. Jozsa, B. Kraus, S. Strelchuk, M. Yoganathan, All Pure Fermionic Non-Gaussian States Are Magic States for Matchgate Computations, Phys. Rev. Lett. 123, 080503 (2019).

  58. D. Sauerwein, A. Molnar, J. I. Cirac, B. Kraus, Matrix Product States: Entanglement, Symmetries, and State Transformations, Phys. Rev. Lett. 123, 170504 (2019).

  59. M. Englbrecht, B. Kraus, Symmetries and entanglement of stabilizer states,  Phys. Rev. A 101, 062302 (2020).

  60. O. Słowik, M. Hebenstreit, B. Kraus, A. Sawicki, A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems, Quantum 4, 300 (2020).

  61. M. Hebenstreit, R. Jozsa, B. Kraus, S. Strelchuk, Computational power of matchgates with supplementary resources, Phys. Rev. A 102, 052604 (2020), Editor's Suggestion.

  62. A. Elben, R. Kueng, H.-Y. Huang, R. van Bijnen, C. Kokail, M. Dalmonte, P. Calabrese, B. Kraus, J. Preskill, P. Zoller, B. Vermersch, Mixed-State Entanglement from Local Randomized Measurements, Phys. Rev. Lett. 125, 200501 (2020).

  63. M. Hebenstreit, M. Englbrecht, C. Spee, J. I. de Vicente, B. Kraus, Measurement outcomes that do not occure and their role in entanglement transformations, New J. Phys. 23, 033046 (2021).

  64. J. Carrasco, A. Elben, C. Kokail, B. Kraus, and P. Zoller, Theoretical and Experimental Perspectives of Quantum Verification, PRX Quantum 2, 010102 (2021).


  1. B. Kraus, P. Törmä, Transition phenomena in networks of quantum systems, Quantum Communication, Computing, and Measurement 2, p. 347 (2000);

  2. G. Giedke, B. Kraus, L.-M. Duan, P. Zoller, M. Lewenstein, and J. I. Cirac, Separability and Distillability of Gaussian states - the Complete Story, Fort. Phys. 49, p. 973 (2001);

  3. B. Kraus, W. Dür, G. Vidal, J. I. Cirac, M. Lewenstein, N. Linden, and S. Popescu, Entanglement Capability of Two-qubit Operations, Z. Naturforsch. 56 a, p. 91 (2001);

  4. D. Bruss, J. I. Cirac, P. Horodecki, F. Hulpke, B. Kraus, M. Lewenstein, and A. Sanpera, Reflections upon Separability and Distillability, J. Mod. Opt. 49, p. 1399-1418 (2002);

  5. B. Kraus, G. Giedke, M. Lewenstein, and J. I. Cirac, Entanglement Properties of Gaussian States, Fort. Phys. 51 (4-5), p. 305 (2003);

  6. B. Kraus, Compressed quantum simulations, AIP proceedings 1633, 131, Eleventh International Conference on Quantum Communication , Measurement and Computation, (QCMC 2012), edited by H. J. Schmiedmayer, Ph. Walther

  7. C. Spee, J. I. de Vicente, B. Kraus, Few-body entanglement manipulation. Quantum [Un]Speakables II, edited by R. Bertlmann and A. Zeilinger (Springer, 2017), pp. 365-380; arXiv:quant-ph/1504.02643 (2015).


  1. D. Sauerwein, K. Schwaiger, B. Kraus, Discrete And Differentiable Entanglement Transformations, arXiv:1808.02819 [quant-ph] (2018).

  2.  A. Neven, D. Gunn, M. Hebenstreit, B. Kraus, Local Transformations of Multiple Multipartite States, arXiv:2007.06256 [quant-ph] (2020).

  3. V. Vitale, A. Elben, R. Kueng, A. Neven, J. Carrasco, B. Kraus, P. Zoller, P. Calabrese, B. Vermersch, M. Dalmonte, Symmetry-resolved dynamical purification in synthetic quantum matter, arXiv:2103.07443 [quant-ph] (2021).
  4.  A. Neven, J. Carrasco, V. Vitale, C. Kokail, A. Elben, M. Dalmonte, P. Calabrese, P. Zoller, B. Vermersch, R. Kueng, B. Kraus, Symmetry-resolved entanglement detection using partial transpose moments, arXiv:2103.07443 [quant-ph] (2021).


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