Universal nonlinear entanglement witnesses

Kotowski, Marcin; Kotowski, Michał; Kuś, Marek

doi:10.1103/physreva.81.062318

Cited by 17 publications

(22 citation statements)

References 34 publications

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“…We were able to calculate the degeneracy in many relevant cases and give some estimates for the most general system of an arbitrary number of constituents with an arbitrary dimension of the single particle space. Let us remark that there exists a useful characterization of the highest weight vector orbits which allows to generalize and estimate effectively some other entanglement measures [19]. An obvious question is whether a method can be adapted to the case of mixed states.…”

Section: Discussionmentioning

confidence: 99%

Symplectic Geometry of Entanglement

Sawicki

Huckleberry

Kuś

2011

Commun. Math. Phys.

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Abstract:We present a description of entanglement in composite quantum systems in terms of symplectic geometry. We provide a symplectic characterization of sets of equally entangled states as orbits of group actions in the space of states. In particular, using the Kostant-Sternberg theorem, we show that separable states form a unique symplectic orbit, whereas orbits of entangled states are characterized by different degrees of degeneracy of the canonical symplectic form on the complex projective space. The degree of degeneracy may be thus used as a new geometric measure of entanglement. The above statements remain true for systems with an arbitrary number of components, moreover the presented method is general and can be applied also under different additional symmetry conditions stemming, e.g., from the indistinguishability of particles. We show how to calculate the degeneracy for various multiparticle systems providing also simple criteria of separability.

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Section: Discussionmentioning

confidence: 99%

Symplectic Geometry of Entanglement

Sawicki

Huckleberry

Kuś

2011

Commun. Math. Phys.

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“…Moreover, our results on quadratic symmetries distinguishing local properties from global ones can be generalized into an overarching framework that encapsulates concurrence (Example 1) and links naturally to entanglement detection via a quadratic invariant of the quantum system under local transformations in [75][76][77][78].…”

Section: Discussionmentioning

confidence: 99%

Symmetry criteria for quantum simulability of effective interactions

et al. 2015

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What can one do with a given tunable quantum device? We provide complete symmetry criteria deciding whether some effective target interaction(s) can be simulated by a set of given interactions. Symmetries lead to a better understanding of simulation and permit a reasoning beyond the limitations of the usual explicit Lie closure. Conserved quantities induced by symmetries pave the way to a resource theory for simulability. On a general level, one can now decide equality for any pair of compact Lie algebras just given by their generators without determining the algebras explicitly. Several physical examples are illustrated, including entanglement invariants, the relation to unitary gate membership problems, as well as the central-spin model.

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“…Let us briefly remember the construction of a nonlinear entanglement measure for the multiparty pure state space presented in [4]. It is based on an obvious observation that entanglement, or more general, quantum correlations do not change under local transformations.…”

Section: Nonlinear Entanglement Measuresmentioning

confidence: 99%

“…We refer the interested reader to the relevant literature on the subject [25,26]. For a more elaborate discussion of representation-theoretic methods in the context of entanglement theory see [4,5]. In this section we briefly describe basic facts from the representation theory of SU(N ).…”

Section: Representation Theory Of Su(n)mentioning

confidence: 99%

“…Entanglement is usually identified with correlations in the composite quantum system that are stronger then any correlations that can be exhibited by any classical system. In our article we elaborate on the method of entanglement detection based on identification of entangled states with particular orbits of an underlying group of local transformation [3][4][5]. For the another approach to entanglement which makes use of the formalism of commuting subalgebras of the algebra of all quantum observables see [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Universal framework for entanglement detection

Oszmaniec

Kuś

2013

Phys. Rev. A

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We construct nonlinear multiparty entanglement measures for distinguishable particles, bosons, and fermions. In each case properties of an entanglement measure are related to the decomposition of the suitably chosen representation of the relevant symmetry group onto irreducible components. In the case of distinguishable particles considered entanglement measure reduces to the well-known many-particle concurrence. We prove that our entanglement criterion is sufficient and necessary for pure states living in both finite and infinite dimensional spaces. We generalize our entanglement measures to mixed states by the convex roof extension and give a nontrivial lower bound of thus obtained generalized concurrence.

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Universal nonlinear entanglement witnesses

Cited by 17 publications

References 34 publications

Symplectic Geometry of Entanglement

Symplectic Geometry of Entanglement

Symmetry criteria for quantum simulability of effective interactions

Universal framework for entanglement detection

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