A fermionic de Finetti theorem

Krumnow C, Zimboras Z, Eisert J (2017)

Publication Type: Journal article

Publication year: 2017


Book Volume: 58

Article Number: 122204

Journal Issue: 12

DOI: 10.1063/1.4998944


Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing one to bound the error made by mean-field approaches. Such theorems link the symmetry of a quantum state under the exchange of subsystems to negligible quantum correlations and are well understood and established in the context of distinguishable particles. In this work, we derive a de Finetti theorem for finite sized Majorana fermionic systems. It is shown, much reflecting the spirit of other quantum de Finetti theorems, that a state which is invariant under certain permutations of modes loses most of its anti-symmetric character and is locally well described by a mode separable state. We discuss the structure of the resulting mode separable states and establish in specific instances a quantitative link to the quality of the Hartree-Fock approximation of quantum systems. We hint at a link to generalized Pauli principles for one-body reduced density operators. Finally, building upon the obtained de Finetti theorem, we generalize and extend the applicability of Hudson's fermionic central limit theorem.

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How to cite


Krumnow, C., Zimboras, Z., & Eisert, J. (2017). A fermionic de Finetti theorem. Journal of Mathematical Physics, 58(12). https://doi.org/10.1063/1.4998944


Krumnow, Christian, Zoltan Zimboras, and Jens Eisert. "A fermionic de Finetti theorem." Journal of Mathematical Physics 58.12 (2017).

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