Entanglement witnesses from mutually unbiased bases

Chruściński, Dariusz; Sarbicki, Gniewomir; Wudarski, Filip

doi:10.1103/physreva.97.032318

Cited by 28 publications

(37 citation statements)

References 62 publications

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“…This means adding the results from different MUB setups gives in general lower and upper bounds, which may be violated for an entangled state. Generally, witnesses based on MUBs have turned out to be powerful in detecting entanglement 22,23,41 and quite same considerations hold true if one uses symmetric informationally complete positive operator-valued measures (SICs), see ref. 42 , because in the case of complete sets MUBs or SICs are related by a quantum 2-design 43 .…”

Section: Resultsmentioning

confidence: 98%

Witnessing Entanglement In Compton Scattering Processes Via Mutually Unbiased Bases

Hiesmayr

Moskal

2019

Sci Rep

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We present a quantum information theoretic version of the Klein-Nishina formula. This formulation singles out the quantity, the a priori visibility, that quantifies the ability to deduce the polarisation property of single photons. The Kraus-type structure allows a straightforward generalisation to the multiphoton cases, relevant in the decay of positronium which is utilized e.g. for metabolic PET-imaging (Positron- Emission- Tomograph). Predicted by theory but never experimentally proven, the two- or three-photon states should be entangled. We provide an experimentally feasible method to witness entanglement for these processes via MUBs (Mutually Unbiased Bases), exploiting Bohr’s complementarity. Last but not least we present explicit cases exemplifying the interrelation of geometry and entanglement including relations to its potentiality for teleportation schemes or Bell inequality violations or in future for detecting cancer in human beings.

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Section: Resultsmentioning

confidence: 98%

Witnessing Entanglement In Compton Scattering Processes Via Mutually Unbiased Bases

Hiesmayr

Moskal

2019

Sci Rep

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“…The slice is one where also is successfully detecting bound entangled states 54 . Generally, the construction of entanglement witnesses from MUBs cover several well-known entanglement witnesses 55 such as the Choi map.…”

Section: Appendixmentioning

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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“…A natural following research direction is to connect the recently developed concept of coherence [55] to the Dicke basis, and to explore further its connection to PPT-entangled symmetric states. Furthremore, it seems plausible that one can find further connections between the properties of M (ρ) and those of MUBs since it has been shown that one can construct EWs based on MUBs that are capable of detecting bound entangled states (See [56] for a recent construction or [57] for an application to magic simplex states in an experimentally feasible way). Whether there is a clear connection between EWs from MUBs and EWs for bound entangled DS states in terms of the properties of M (ρ) remains an open research direction.…”

Section: Discussionmentioning

confidence: 99%

“…(56) Let us inspect the possible values for the sums in parenthesis in Eq. (56). The expression involving k will be zero whenever l 1 , l 2 , l 3 , l 4 are all different (half of the sum will come with a plus sign and the other half with a minus sign).…”

Section: Discussionmentioning

confidence: 99%

Separability of diagonal symmetric states: a quadratic conic optimization problem

Tura

Aloy

Quesada

et al. 2018

Quantum

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We study the separability problem in mixtures of Dicke states i.e., the separability of the so-called Diagonal Symmetric (DS) states. First, we show that separability in the case of DS in C d ⊗ C d (symmetric qudits) can be reformulated as a quadratic conic optimization problem. This connection allows us to exchange concepts and ideas between quantum information and this field of mathematics. For instance, copositive matrices can be understood as indecomposable entanglement witnesses for DS states. As a consequence, we show that positivity of the partial transposition (PPT) is sufficient and necessary for separability of DS states for d ≤ 4. Furthermore, for d ≥ 5, we provide analytic examples of PPT-entangled states. Second, we develop new sufficient separability conditions beyond the PPT criterion for bipartite DS states. Finally, we focus on N -partite DS qubits, where PPT is known to be necessary and sufficient for separability. In this case, we present a family of almost DS states that are PPT with respect to each partition but nevertheless entangled.

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Entanglement witnesses from mutually unbiased bases

Cited by 28 publications

References 62 publications

Witnessing Entanglement In Compton Scattering Processes Via Mutually Unbiased Bases

Witnessing Entanglement In Compton Scattering Processes Via Mutually Unbiased Bases

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

Separability of diagonal symmetric states: a quadratic conic optimization problem

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