Mirrored entanglement witnesses

Bae, Joonwoo; Chruściński, Dariusz; Hiesmayr, Beatrix C.

doi:10.1038/s41534-020-0242-z

Cited by 20 publications

(10 citation statements)

References 36 publications

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“…Therefore, we exploited the recently discovered fact that an entanglement witness has an upper bound (the very definition of a witness) and in general often also a non-trivial lower bound 44 . Furthermore, we exploited the structure of the magic simplex by noting that an effective witness in the magic simplex can have the form .…”

Section: Resultsmentioning

confidence: 99%

Free versus bound entanglement, a NP-hard problem tackled by machine learning

Hiesmayr

2021

Sci Rep

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Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently by the PPT-criterion (Peres-Horodecki criterion), in contrast to detecting bound entanglement, i.e. a curious form of entanglement that can also not be distilled into maximally (free) entangled states. Only a few bound entangled states have been found, typically by constructing dedicated entanglement witnesses, so naturally the question arises how large is the volume of those states. We define a large family of magically symmetric states of bipartite qutrits for which we find $$82\%$$ 82 % to be free entangled, $$2\%$$ 2 % to be certainly separable and as much as $$10\%$$ 10 % to be bound entangled, which shows that this kind of entanglement is not rare. Via various machine learning algorithms we can confirm that the remaining $$6\%$$ 6 % of states are more likely to belonging to the set of separable states than bound entangled states. Most important we find via dimension reduction algorithms that there is a strong two-dimensional (linear) sub-structure in the set of bound entangled states. This revealed structure opens a novel path to find and characterize bound entanglement towards solving the long-standing problem of what the existence of bound entanglement is implying.

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Section: Resultsmentioning

confidence: 99%

Free versus bound entanglement, a NP-hard problem tackled by machine learning

Hiesmayr

2021

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“…E5: Numerically generated entanglement witnesses Leveraging the fact that separable states form a convex set, entanglement witnesses [38] ("EWs") are an important tool to detect entangled states. An EW W is an observable which implies an upper bound U and, as recently shown [39], also a lower, mostly nontrivial, bound L (U, L ∈ R), for separable states ρ s :…”

Section: E3: Quasi-pure Concurrence Criterionmentioning

confidence: 98%

Almost complete solution for the NP-hard separability problem of Bell diagonal qutrits

Popp,

Hiesmayr

2022

Preprint

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With a probability of success of 95% we solve the separability problem for Bell diagonal qutrit states with positive partial transposition (PPT). The separability problem, i.e. distinguishing separable and entangled states, generally lacks an efficient solution due to the existence of bound entangled states. In contrast to free entangled states that can be used for entanglement distillation via local operations and classical communication, these states cannot be detected by the Peres-Horodecki criterion or PPT criterion. We analyze a large family of bipartite qutrit states that can be separable, free entangled or bound entangled. Leveraging a geometrical representation of these states in Euclidean space, novel methods are presented that allow the classification of separable and bound entangled Bell diagonal states in an efficient way. Moreover, the classification allows the precise determination of relative volumes of the classes of separable, free and bound entangled states. In detail, out of all Bell diagonal PPT states 81.0% ± 0.1% are determined to be separable while 13.9 ± 0.1% are bound entangled and only 5.1 ± 0.1% remain unclassified. Moreover, our applied criteria are compared for their effectiveness and relation as detectors of bound entanglement, which reveals that not a single criterion is capable to detect all bound entangled states.

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“…These are Hermitian operators being non-negative for all separable states and negative for some entangled ones [33][34][35][36]. Recently, the framework of EW 2.0 has been presented [37], where all standard EWs can be upgraded to detect a twice larger set of entangled states. The framework of EW 2.0 considers a non-negative and unit trace operator W constructed by an EW such that two EWs can be realized simultaneously,…”

Section: Quantum Detector Tomographymentioning

confidence: 99%