A de Finetti representation for finite symmetric quantum states

By Robert Koenig, Renato Renner. 2004

138 citations recorded by the source corpus.

Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number of subsystems, the state in the remaining subsystems is close to having product form. This immediately generalizes the so-called de Finetti representation to the case of finite symmetric quantum states.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/79ffcfd72343d54e64f5c94454c8b65fb5cbf3c4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

The Theory of Quantum Information (2018, result): “A finite quantum formulation of de Finetti’s theorem, closer in spirit to classical results due to Diaconis and Freedman [59], was proved by König and Renner [133].”
Less is Different: Emergence and Reduction Reconciled (2011, background): “…on N systems, by tracing out (partial tracing over) N −M systems, can be approximated by a mixture of product states on the M systems (i.e. states ω⊗M), with an error that goes to zero with the ratio M/N , e.g. an error like O(M/N); (Koenig and Renner 2005, Renner 2007, Koenig and Mitchison 2007).”
Tight informationally complete quantum measurements (2006, methodology): “Besides this practical purpose, IC-POVMs with special properties are used for quantum cryptography [15], quantum fingerprinting [16], and are relevant to foundational studies of quantum mechanics [17, 18, 19].”
Symmetry of large physical systems implies independence of subsystems (2007, background): “In particular, it has been shown that the statement above holds for any quantum system with ﬁnite-dimensional subsystems [KR05, CKMR07] as well as for certain systems with inﬁnite-dimensional sub-systems [DOS06].”
Faithful Squashed Entanglement (2010, background): “Indeed, quantum versions of the de Finetti theorem [ 44 ,45] show that any k-extendible state ρA:B is such that”
A Generalization of Quantum Stein’s Lemma (2009, methodology): “The next lemma, due to Konig and Renner, appeared in [ 59 ]a s Theorem A.1 and is used in the proof of Corollary II.2.”