Topic
Tangle
About: Tangle is a research topic. Over the lifetime, 591 publications have been published within this topic receiving 8932 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this article, it was shown that there is a trade-off between the entanglement between two qubits and the pair of qubits, and that for any values of the tangles satisfying the corresponding equality, one can find a quantum state consistent with those values.
Abstract: Consider three qubits A, B, and C which may be entangled with each other We show that there is a trade-off between A's entanglement with B and its entanglement with C This relation is expressed in terms of a measure of entanglement called the "tangle," which is related to the entanglement of formation Specifically, we show that the tangle between A and B, plus the tangle between A and C, cannot be greater than the tangle between A and the pair BC This inequality is as strong as it could be, in the sense that for any values of the tangles satisfying the corresponding equality, one can find a quantum state consistent with those values Further exploration of this result leads to a definition of the "three-way tangle" of the system, which is invariant under permutations of the qubits
2,702 citations
Book•
1 Jan 1996
TL;DR: This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory, and sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials.
Abstract: This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.
474 citations
TL;DR: In this paper, the authors construct a family of rings from a plane diagram of a tangle and associate a complex of bimodules over these rings, which is an invariant of the tangle.
Abstract: We construct a family of rings. To a plane diagram of a tangle we associate a complex of bimodules over these rings. Chain homotopy equivalence class of this complex is an invariant of the tangle. On the level of Grothendieck groups this invariant descends to the Kauffman bracket of the tangle. When the tangle is a link, the invariant specializes to the bigraded cohomology theory introduced in our earlier work.
381 citations
TL;DR: In this paper, the authors construct a family of rings from a plane diagram of a tangle and associate a complex of bimodules over these rings, which is an invariant of the tangle.
Abstract: We construct a family of rings. To a plane diagram of a tangle we associate a complex of bimodules over these rings. Chain homotopy equivalence class of this complex is an invariant of the tangle. On the level of Grothendieck groups this invariant descends to the Kauffman bracket of the tangle. When the tangle is a link, the invariant specializes to the bigraded cohomology theory introduced in our earlier work.
282 citations
TL;DR: The I-concurrence of a bipartite mixed state is the minimum average I-consistency (tangle) of ensemble decompositions of pure states of the joint density operator.
Abstract: We discuss properties of entanglement measures called I-concurrence and tangle. For a bipartite pure state, I-concurrence and tangle are simply related to the purity of the marginal density operators. The I-concurrence (tangle) of a bipartite mixed state is the minimum average I-concurrence (tangle) of ensemble decompositions of pure states of the joint density operator. Terhal and Vollbrecht [Phys. Rev. Lett. 85, 2625 (2000)] have given an explicit formula for the entanglement of formation of isotropic states in arbitrary dimensions. We use their formalism to derive comparable expressions for the I-concurrence and tangle of isotropic states.
256 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 33 |
| 2024 | 64 |
| 2023 | 65 |
| 2022 | 136 |
| 2021 | 25 |
| 2020 | 26 |