RECORD
On the equivalence of separability and extendability of quantum states
Quantum Physics · Submitted 11 Jan 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It turns out that the complete extendability property is equivalent to the separability property of a bipartite Gaussian state.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
Motivated by the notions of $k$-extendability and complete extendability of the state of a finite level quantum system as described by Doherty et al (Phys. Rev. A, 69:022308), we introduce parallel definitions in the context of Gaussian states and using only properties of their covariance matrices derive necessary and sufficient conditions for their complete extendability. It turns out that the complete extendability property is equivalent to the separability property of a bipartite Gaussian state. Following the proof of quantum de Finetti theorem as outlined in Hudson and Moody (Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 33(4):343--351), we show that separability is equivalent to complete extendability for a state in a bipartite Hilbert space where at least one of which is of dimension greater than 2. This, in particular, extends the result of Fannes, Lewis, and Verbeure (Lett. Math. Phys. 15(3): 255--260) to the case of an infinite dimensional Hilbert space whose C* algebra of all bounded operators is not separable.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Motivated by the notions of $k$-extendability and complete extendability of the state of a finite level quantum system as described by Doherty et al (Phys. Rev. A, 69:022308), we introduce parallel definitions in the context of Gaussian states and using only properties of their covariance matrices derive necessary and sufficient conditions for their complete extendability. | contribution 0.98 | 0.92 | 0.10 | asserted 0.98 |
| s1 | It turns out that the complete extendability property is equivalent to the separability property of a bipartite Gaussian state. | result 1.00 | 0.87 | 0.72 | asserted 1.00 |
| s2 | Following the proof of quantum de Finetti theorem as outlined in Hudson and Moody (Z. | method 0.88 | 0.36 | 0.02 | unclear 0.85 |
| s3 | Wahrscheinlichkeitstheorie und Verw. | background 0.73 | 0.04 | 0.02 | unclear 0.99 |
| s4 | Gebiete, 33(4):343--351), we show that separability is equivalent to complete extendability for a state in a bipartite Hilbert space where at least one of which is of dimension greater than 2. | result 0.91 | 0.90 | 0.60 | asserted 1.00 |
| s5 | This, in particular, extends the result of Fannes, Lewis, and Verbeure (Lett. Math. | interpretation 0.54 | 0.65 | 0.05 | asserted 0.92 |
| s6 | Phys. 15(3): 255--260) to the case of an infinite dimensional Hilbert space whose C* algebra of all bounded operators is not separable. | interpretation 0.53 | 0.78 | 0.10 | asserted 0.99 |
What was examined, and what was not
- arXiv listing abstract v5
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Motivated by the notions of $k$-extendability and complete extendability of the state of a finite level quantum system as described by Doherty et al (Phys. Rev. A, 69:022308), we introduce parallel definitions in the context of Gaussian states and using only properties of their covariance matrices derive necessary and sufficient conditions for their complete extendability. It turns out that the complete extendability property is equivalent to the separability property of a bipartite Gaussian state. Following the proof of quantum de Finetti theorem as outlined in Hudson and Moody (Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 33(4):343--351), we show that separability is equivalent to complete extendability for a state in a bipartite Hilbert space where at least one of which is of dimension greater than 2. This, in particular, extends the result of Fannes, Lewis, and Verbeure (Lett. Math. Phys. 15(3): 255--260) to the case of an infinite dimensional Hilbert space whose C* algebra of all bounded operators is not separable.
Human review
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.