Representing multiqubit unitary evolutions: spin coherences and infinitesimal coherences

Abstract

For the tensor of coherences parametrization of a multiqubit density operator, we provide an explicit formulation of the corresponding unitary dynamics at infinitesimal level. The main advantage of this formalism (clearly reminiscent of the idea of ``coherences'' and ``coupling Hamiltonians'' of spin systems) is that the pattern of correlation between qubits and the pattern of infinitesimal correlation are highlighted simultaneously and can be used constructively for qubit manipulation. For example, it allows to compute explicitly a Rodrigues' formula for the one-parameter orbits of nonlocal Hamiltonians. The result is easily generalizable to orbits of Cartan subalgebras and allows to write the Cartan decomposition of unitary propagators as a linear action.

significantly rewritten, 9 pages, 4 figures

References in corpus (5)

• Entanglement dynamics and quantum state transport in spin chains
• Separable states can be used to distribute entanglement
• Entanglement, Mixedness, and Spin-Flip Symmetry in Multiple-Qubit Systems
• A multi-photon Stokes-parameter invariant for entangled states
• Tensor of coherences parameterization of multiqubit density operators for entanglement characterization

Cited by in corpus (6)

• Feedback control of spin systems
• Reflection Symmetries for Multiqubit Density Operators
• Reaching Quantum Consensus with Directed Links: Missing Symmetry and Switching Interactions
• Commuting multiparty quantum observables and local compatibility
• Forgetting in the Synchronization of Quantum Networks
• Limitations imposed by complementarity