2016
DOI: 10.1103/physreva.93.012339
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Maximally entangled set of tripartite qutrit states and pure state separable transformations which are not possible via local operations and classical communication

Abstract: Entanglement is the resource to overcome the restriction of operations to Local Operations assisted by Classical Communication (LOCC). The Maximally Entangled Set (MES) of states is the minimal set of n-partite pure states with the property that any truly n-partite entangled pure state can be obtained deterministically via LOCC from some state in this set. Hence, this set contains the most useful states for applications. In this work we characterize the MES for generic three qutrit states. Moreover, we analyze… Show more

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Cited by 27 publications
(61 citation statements)
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“…In Sec. IV we illustrate and discuss the picture of multipartite pure state transformations that emerges if we combine this work with previous findings on bipartite [8], 3-qutrit [18] and qubit systems [19,21]. In Sec.…”
Section: Introductionmentioning
confidence: 59%
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“…In Sec. IV we illustrate and discuss the picture of multipartite pure state transformations that emerges if we combine this work with previous findings on bipartite [8], 3-qutrit [18] and qubit systems [19,21]. In Sec.…”
Section: Introductionmentioning
confidence: 59%
“…1), can be generalized to arbitrary local dimension. [19,25]), green (generic states have finite, nontrivial stabilizer; regions C [18], F [19]), red (generic states have trivial stabilizer; D (see Th. 1), G [21]), grey (generic states have finite stabilizer [17,35]; unknown if it is trivial; region E).…”
Section: Multipartite Pure State Transformationsmentioning
confidence: 99%
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“…For this purpose we consider the class of Gaussian separable operations (GSEP). In general, SEP contains LOCC but is a strictly larger class [56][57][58][59]. We show, however, that for Gaussian operations on n-mode n-partite systems any transformation among pure fully entangled states via Gaussian SEP (GSEP) can be performed via GLU.…”
Section: Pure Gaussian Fermionic States and Local Transformationsmentioning
confidence: 95%
“…The multipartite case is much more complicated [19,[25][26][27][28]. Even for pure states, the nonexistence of a maximally entangled reference state [29,30] and the involved nature of state-transformations in general [31,32] seem to make the (S)LOCC-based classification practically unaccomplishable, and the standard (S)LOCC paradigm less enlightening so less expressive. Taking into account partial entanglement (partial separability) [33][34][35][36][37][38][39][40], or partial correlations [14,41,42] only, leads to a combinatoric [43][44][45], discrete classification (based on the lattice of set partitions [44]), endowed naturally with a well-behaving set of correlation and entanglement measures, characterizing the finite number of properties [14,40].…”
mentioning
confidence: 99%