Control of quantum noise: on the role of dilations

Abstract

We show that every finite-dimensional quantum system with Markovian (i.e., GKLS-generated) time evolution has an autonomous unitary dilation which can be dynamically decoupled. Since there is also always an autonomous unitary dilation which cannot be dynamically decoupled, this highlights the role of dilations in the control of quantum noise. We construct our dilation via a time-dependent version of Stinespring in combination with Howland's clock Hamiltonian and certain point-localised states, which may be regarded as a C*-algebraic analogue of improper bra-ket position eigenstates and which are hence of independent mathematical and physical interest.

18p, to appear in Ann. H. Poincaré

References in corpus (4)

• Noisy intermediate-scale quantum (NISQ) algorithms
• Optimal control, geometry, and quantum computing
• Nonexponential quantum decay under environmental decoherence
• Clock-Driven Quantum Thermal Engines

Cited by in corpus (5)

• Quantum simulation for time-dependent Hamiltonians -- with applications to non-autonomous ordinary and partial differential equations
• Finite-Dimensional Stinespring Curves Can Approximate Any Dynamics
• Unifying framework for quantum simulation algorithms for time-dependent Hamiltonian dynamics
• Quantum Zeno-like Paradox for Position Measurements: A Particle Precisely Found in Space is Nowhere to be Found in Hilbert Space
• Stability and convergence of dynamical decoupling with finite amplitude control