The rebit three-tangle and its relation to two-qubit entanglement

Abstract

The three-tangle is a measure of three-way entanglement in a system of three qubits. For a pure state, it can be understood as the residual entanglement not accounted for by pairwise entanglements between individual qubits. Here we define and evaluate the analogous quantity for three rebits (that is, binary systems in the real-amplitude variant of quantum theory). We find that the resulting formula is the same as in the complex case, except that an overall absolute value sign is missing. As a result, the rebit three-tangle can be negative, expressing the possibility of non-monogamous entanglement in real-amplitude quantum theory (for entanglement based on the convex-roof construction). We then relate the entanglement among three rebits to the entanglement of two qubits, by re-expressing the two-qubit state as a three-rebit state in the ubit model.

9 pages; minor correction in v3

References in corpus (8)

• Entanglement detection
• Measure of genuine multipartite entanglement with computable lower bounds
• The structure of multidimensional entanglement in multipartite systems
• Entangled three-qubit states without concurrence and three-tangle
• All Maximally Entangled Four Qubits States
• Simulating quantum systems using real Hilbert spaces
• Practical method to obtain a lower bound to the three-tangle
• A type of localized quadripartite entanglement

Cited by in corpus (14)

• Operational Resource Theory of Imaginarity
• Toolbox for reconstructing quantum theory from rules on information acquisition
• Quaternionic quantum mechanics in real Hilbert space
• Resource Theory of Imaginarity: New Distributed Scenarios
• Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like state and 9 families of 4-qubit entangled states
• Virial theorem and generalized momentum in quaternic quantum mechanics
• Positive maps and entanglement in real Hilbert spaces
• Nonlocal Advantages of Quantum Imaginarity
• Process tomography in general physical theories
• Spread and asymmetry of typical quantum coherence and their inhibition in response to glassy disorder
• Non-locality of conjugation symmetry: characterization and examples in quantum network sensing
• Exploring Non-Multiplicativity in the Geometric Measure of Entanglement
• Measure of tripartite quantum correlation in multiqubit symmetric pure state
• Markovian dynamics of single-rebit open quantum systems with applications to colour perception