Quantum entanglement, supersymmetry, and the generalized Yang-Baxter equation
arXiv:1911.02577 · doi:10.26421/QIC20.1-2
Abstract
Entangled states, such as the Bell and GHZ states, are generated from separable states using matrices known to satisfy the Yang-Baxter equation and its generalization. This remarkable fact hints at the possibility of using braiding operators as quantum entanglers, and is part of a larger speculated connection between topological and quantum entanglement. We push the analysis of this connection forward, by showing that supersymmetry algebras can be used to construct large families of solutions of the spectral parameter-dependent generalized Yang-Baxter equation. We present a number of explicit examples and outline a general algorithm for arbitrary numbers of qubits. The operators we obtain produce, in turn, all the entangled states in a multi-qubit system classified by the Stochastic Local Operations and Classical Communication protocol introduced in quantum information theory.
arXiv comment36 pages, 2 figures; v2: minor changes, added references
References in corpus (25)
- Fault-tolerant quantum computation by anyons
- Non-Abelian Anyons and Topological Quantum Computation
- Three qubits can be entangled in two inequivalent ways
- Supersymmetry and Quantum Mechanics
- Quantum Inverse Scattering Method and Correlation Functions
- Exact and Asymptotic Measures of Multipartite Pure State Entanglement
- Comparing Quantum Entanglement and Topological Entanglement
- Random matrix techniques in quantum information theory
- Entanglement Entropy and the Colored Jones Polynomial
- Towards topological quantum computer
- Entanglement from Topology in Chern-Simons Theory
- Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems
- Yang-Baxter operators need quantum entanglement to distinguish knots
- Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups
- The compositional structure of multipartite quantum entanglement
- Unitary Solutions to the Yang-Baxter Equation in Dimension Four
- Classifying Quantum Entanglement through Topological Links
- Solutions to generalized Yang-Baxter equations via ribbon fusion categories
- Multipartite level GHZ bases associated with generalized braid matrices
- Multi-qudit states generated by unitary braid quantum gates based on Temperley-Lieb algebra
- Borromean Entanglement Revisited
- GHZ States, Almost-Complex Structure and Yang--Baxter Equation (I)
- Generalized Yang-Baxter Equations and Braiding Quantum Gates
- Parameter-dependent Gaussian -generalized Yang-Baxter operators
- Braid group representations from twisted tensor products of algebras