Special entangled quantum systems and the Freudenthal construction

Abstract

We consider special quantum systems containing both distinguishable and identical constituents. It is shown that for these systems the Freudenthal construction based on cubic Jordan algebras naturally defines entanglement measures invariant under the group of stochastic local operations and classical communication (SLOCC). For this type of multipartite entanglement the SLOCC classes can be explicitly given. These results enable further explicit constructions of multiqubit entanglement measures for distinguishable constituents by embedding them into identical fermionic ones. We also prove that the Plucker relations for the embedding system provide a sufficient and necessary condition for the separability of the embedded one. We argue that this embedding procedure can be regarded as a convenient representation for quantum systems of particles which are really indistinguishable but for some reason they are not in the same state of some inner degree of freedom.

16 pages LATEX, Table 2 was corrected, a new paragraph was added

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Cited by in corpus (27)

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• Black holes admitting a Freudenthal dual
• The black-hole/qubit correspondence: an up-to-date review
• STU Black Holes as Four Qubit Systems
• Partial separability revisited: Necessary and sufficient criteria
• Entanglement in fermionic Fock space
• Freudenthal Dual Lagrangians
• Qubits from extra dimensions
• Entanglement classification of three fermions with up to nine single-particle states
• Embedding qubits into fermionic Fock space, peculiarities of the four-qubit case
• Four-qubit pure states as fermionic states
• Hitchin functionals are related to measures of entanglement
• Mermin pentagrams arising from Veldkamp lines for three qubits
• The attractor mechanism as a distillation procedure
• Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems
• Coffman-Kundu-Wootters inequality for fermions
• A Kind of Magic
• STU attractors from vanishing concurrence
• Black hole qubit correspondence from quantum circuits
• Local unitary invariants for multipartite quantum systems
• Classification of multipartite systems featuring only $|W⟩$ and $|GHZ⟩$ genuine entangled states
• Quantum entanglement in finite-dimensional Hilbert spaces
• Multipartite entanglement in fermionic systems via a geometric measure
• Freudenthal ranks: GHZ vs. W
• Attractor Flows in st^2 Black Holes
• Qubit entanglement: A Jordan algebraic perspective
• Entanglement distillation using Schur-Weyl decomposition for three qubits