2016/01/31 by B. V. Rajarama Bhat, K. R. Parthasarathy, Ritabrata Sengupta · 8 citations
Computer Science · Mathematics · Physics and Astronomy · #Bipartite graph #Bounded function #Context (archaeology) #Dimension (graph theory) #Equivalence (formal languages) #Hilbert space #POVM #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum state #Spectral Theory in Mathematical Physics #msc:81P40 #msc:81P99 #msc:94A15 #quant-ph
paper · pdf · doi:10.1142/s0129055x1750012x
published in Reviews in Mathematical Physics 29(04), 1750012 (World Scientific) · Proved a conjecture proposed in earlier version. Added Theorem 2.3. Added Section 3 based on quantum de Finetty theorem. Background materials taken from 1506.06526 and 1504.07054. Comments welcome
arxiv created 2016/05/27 · openalex created_date 2016/06/24 · openalex publication_date 2017/03/20 · arxiv updated 2017/09/13 · openalex updated_date 2026/08/05
Motivated by the notions of [Formula: see text]-extendability and complete extendability of the state of a finite level quantum system as described by Doherty et al. [Complete family of separability criteria, Phys. Rev. A 69 (2004) 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 [Locally normal symmetric states and an analogue of de Finetti’s theorem, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 33(4) (1975/76) 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 [Symmetric states of composite systems, Lett. Math. Phys. 15(3) (1988) 255–260] to the case of an infinite dimensional Hilbert space whose C* algebra of all bounded operators is not separable.