Quantum de Finetti theorem in phase-space representation
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Leverrier-2009-Quantum de Finetti t.pdf
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Checksum (MD5)
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Author(s)
Leverrier, Anthony
Cerf, Nicolas J.
Date Issued
July 2009
Journal
Physical review A
Publisher
American Physical Society
Citation
Leverrier, Anthony, and Nicolas Cerf. “Quantum De Finetti Theorem in Phase-space Representation.” Physical Review A 80.1 (2009) : n. pag. © 2009 The American Physical Society
Version
Author's final manuscript
Abstract
The quantum versions of de Finetti’s theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ⊗n [delta superscript x n]. Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).
MIT Department
Massachusetts Institute of Technology. Research Laboratory of Electronics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.80.010102
