Probing the geometry of two-qubit state space by evolution
arXiv:1809.00731 · doi:10.1007/s11128-019-2199-4
Abstract
We derive an explicit expressions for geometric description of state manifold obtained from evolution governed by a three parameter family of Hamiltonians covering most cases related to real interacting two-qubit systems. We discuss types of evolution in terms of the defining parameters and obtain relevant explicit description of the pure state spaces and their Remannian geometry with the Fubini-Study metric . In particular, there is given an analysis of the modification of known geometry of quantum state manifold by the linear noncommuting perturbation of the Hamiltonian. For families of states resulting from the unitary evolution, we characterize a degree of entanglement using the squared concurrence as its measure.
arXiv comment19 p
References in corpus (25)
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Elementary gates for quantum computation
- Entanglement of a Pair of Quantum Bits
- Universal Quantum Computation with the Exchange Interaction
- Quantum Computation as Geometry
- A geometric theory of non-local two-qubit operations
- Optimal control theory for unitary transformations
- Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer
- Classifying and measuring the geometry of the quantum ground state manifold
- Optimal control, geometry, and quantum computing
- On optimum Hamiltonians for state transformations
- Solution to the quantum Zermelo navigation problem
- Time-optimal navigation through quantum wind
- Zermelo Navigation in the Quantum Brachistochrone
- Quantum brachistochrone problem for spin-1 in a magnetic field
- Entanglement and the geometry of two qubits
- The quantum brachistochrone problem for an arbitrary spin in a magnetic field
- Geometric characteristics of quantum evolution: curvature and torsion
- Coherent states and rational surfaces
- Quantum brachistochrone problem for two spins-1/2 with anisotropic Heisenberg interaction
- Geometry of Discrete Quantum Computing
- Geometry of a two-spin quantum state in evolution
- Quantum state geometry and entanglement of two spins with anisotropic interaction in evolution
- The Volume of Two-Qubit States by Information Geometry
- Geometry of quantum state manifolds generated by the Lie algebra operators