ASSESSMENT OF CURRENT RESULTS AND OUTLOOK ON FUTURE EFFORTS

QUANTUM INFORMATION SCIENCE THEORY

MULTI-PARTY ENTANGLEMENT & APPLICATIONS

Research on multi-particle entanglement is on the one hand expected to be focused on novel protocols for quantum information processing in the multi-partite setting. Entanglement in quantum systems embodying more than two constituents is fundamentally different from two-party entanglement, allowing for novel applications. This work on novel protocols includes work on instances of secret sharing or multi-partite fingerprinting. Notably, such multi-partite fingerprinting schemes would allow for the determination whether a number of databases are identical with little resources.

For quantum computation purposes it seems a major milestone to develop computation schemes that require minimal local control over interactions, such as in novel measurement-based computation schemes using multi-particle entangled resources as in cluster-state based approaches or in linear optics quantum computation. Alternatively, quantum cellular-automata based approaches may offer the potential of implementing quantum computation with little requirements of local control. Research work towards a complete understanding of the classification and quantification of multi-particle entanglement is expected to support such work, notably using methods from convex and global optimization, which give rise to novel methods for classification and quantification of entanglement. Laboratory quantum states such as random states or graph states as generalizations of cluster states may facilitate such studies.

On the other hand, there are good reasons to believe that a refined picture of criticality and phase transitions can be reached with the help of tools coming from the theory of entanglement. These ideas help in devising new simulation methods of ground states of many-body Hamiltonians in solid state physics (and many-body quantum systems in general). Finally, studies seem to indicate that questions in quantum field theory may become significantly more accessible using methods from entanglement theory (see also section 4.3.10).

Key references

[1] N. Linden, S. Popescu, B. Schumacher, and M. Westmoreland, ‘‘Reversibility of local transformations of multiparticle entanglement’’, quant-ph/9912039, http://xxx.arxiv.org.

[2] W. Dür, J. I. Cirac, and R. Tarrach, ‘‘Separability and distillability of multiparticle quantum systems’’, Phys. Rev. Lett. 83, 3562 (1999).

[3] V. Coffman, J. Kundu, and W. K. Wootters, “Distributed entanglement”, Phys. Rev. A 61, 052306 (2000).

[4] C. H. Bennett, S. Popescu, D. Rohrlich, J. A. Smolin, and A. V. Thapliyal, ‘‘Exact and Asymptotic Measures of Multipartite Pure State Entanglement’’, Phys. Rev. A 63, 012307 (2001).

[5] M. Hein, J. Eisert, and H. J. Briegel, ‘‘Multi-party entanglement in graph states’’, Phys. Rev. A 69, 062311 (2004).