2018/03/23 by Gonçalo M. Quinta, Rui André · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Theoretical physics #Topology (electrical circuits) #quant-ph
paper · pdf · doi:10.1103/physreva.97.042307
published as Phys. Rev. A 97, 042307 (2018) · 13 pages, 12 figures
arxiv created 2018/03/23 · openalex publication_date 2018/04/05 · arxiv updated 2018/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose an alternative classification scheme for quantum entanglement based on topological links. This is done by identifying a nonrigid ring to a particle, attributing the act of cutting and removing a ring to the operation of tracing out the particle, and associating linked rings to entangled particles. This analogy naturally leads us to a classification of multipartite quantum entanglement based on all possible distinct links for a given number of rings. To determine all different possibilities, we develop a formalism that associates any link to a polynomial, with each polynomial thereby defining a distinct equivalence class. To demonstrate the use of this classification scheme, we choose qubit quantum states as our example of physical system. A possible procedure to obtain qubit states from the polynomials is also introduced, providing an example state for each link class. We apply the formalism for the quantum systems of three and four qubits and demonstrate the potential of these tools in a context of qubit networks.