Classification of three-qubit genuine entangled states using concurrence fill
arXiv:2506.16935 · doi:10.1007/s10773-025-06152-w
Abstract
Despite the successful experimental generation and verification of genuine multipartite entanglement, several existing entanglement measures remain insufficient to reliably capture its presence. In this study, we overcome this challenge by utilizing a geometric measure known as concurrence fill, which quantifies genuine multipartite entanglement of pure states using the area associated with the underlying concurrence triangle. Firstly, the concurrence fill for three-qubit pure states is reformulated using three tangle and partial tangles. This yields a representation that is more tractable and operational. Using this formulation, we derive a criterion to classify GHZ and W class of states. Next, we analyse the rank-2 mixture of generalized GHZ and W class of states for which three-tangle is known to vanish over a zero polytope. Furthermore, we derive the concurrence fill for the eigenstates of the corresponding mixture and obtain its upper bound for mixed states with zero tangle.
5 figures, 8 pages
References in corpus (39)
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- A computable measure of entanglement
- Three qubits can be entangled in two inequivalent ways
- Quantum secret sharing
- Entanglement of a Pair of Quantum Bits
- Distributed Entanglement
- Quantifying Entanglement
- General Monogamy Inequality for Bipartite Qubit Entanglement
- Robustness of entanglement
- Teleportation and Dense Coding with Genuine Multipartite Entanglement
- Decoherence and multipartite entanglement
- Taming multiparticle entanglement
- Measure of genuine multipartite entanglement with computable lower bounds
- Monogamy Inequality in terms of Negativity for Three-Qubit States
- Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity
- Entangled three-qubit states without concurrence and three-tangle
- Three-qubit pure-state canonical forms
- Tsallis entropy and entanglement constraints in multi-qubit systems
- A Triangle Governs Genuine Tripartite Entanglement
- Evaluation of convex roof entanglement measures
- Monogamy and polygamy for multi-qubit entanglement using Rényi entropy
- Monogamy of entanglement of formation
- Three-tangle for mixtures of generalized GHZ and generalized W states
- General Monogamy of Tsallis -Entropy Entanglement in Multiqubit Systems
- Tangles of superpositions and the convex-roof extension
- Generalized Monogamy Relations of Concurrence for N-qubit Systems
- Entanglement swapping and swapped entanglement
- Entanglement Polygon Inequality in Qubit Systems
- Entanglement of three-qubit pure states in terms of teleportation capability
- Multipartite monogamy of the concurrence
- Tripartite entanglement measure under local operations and classical communication
- Geuine tripartite entanglement in three-flavor neutrino oscillations
- Parameterized multipartite entanglement measures
- Entanglement Classification of Four-partite States under the SLOCC
- Distinguishing different classes of entanglement of three-qubit pure states
- Quantum State Concentration and Classification of Multipartite Entanglement
- Geometric genuine multipartite entanglement for four-qubit systems
- Projection based lower bounds of concurrence for multipartite quantum systems