nLab quantum embezzlement

Idea

In the theory of quantum entanglement, embezzlement [van Dam & Hayden 2003] refers to the approximation of entangled quantum states by images of (local) unitary transformations on unentangled (tensor product-)states upon tensoring with an ancillary state that is approximately left invariant under the transformation (the “catalyst” of the embezzlement).

Related concepts

• quantum entanglement

• quantum information theory

References

The original article:

• Wim van Dam, Patrick Hayden, Embezzling Entangled Quantum States, Physical Review A, Rapid Communications 67 6 (2003) 060302(R) [arXiv:quant-ph/0201041, doi:10.1103/PhysRevA.67.060302]

Review:

• Debbie Leung, Embezzlement of entanglement, talk at PIRSA (2019) [doi:10.48660/19050012, pdf]

Further developments:

• Richard Cleve, Li Liu, Vern I. Paulsen, Perfect Embezzlement of Entanglement, J. Math Phys (2017) [arXiv:1606.05061, doi:10.1063/1.4974818]

In relation to quantum observables forming von Neumann algebras:

• Lauritz van Luijk, Alexander Stottmeister, Reinhard F. Werner, Henrik Wilming, Embezzlement of entanglement, quantum fields, and the classification of von Neumann algebras [arXiv:2401.07299]