Dynamical Decoupling and Homogenization of continuous variable systems

Abstract

For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for which the question if dynamical decoupling could be applied remained open. Here we first show that not every infinite-dimensional system can be protected from decoherence through dynamical decoupling. Then we develop dynamical decoupling for continuous variable systems which are described by quadratic Hamiltonians. We identify a condition and a set of operations that allow us to map a set of interacting harmonic oscillators onto a set of non-interacting oscillators rotating with an averaged frequency, a procedure we call homogenization. Furthermore we show that every quadratic system-environment interaction can be suppressed with two simple operations acting only on the system. Using a random dynamical decoupling or homogenization scheme, we develop bounds that characterize how fast we have to work in order to achieve the desired uncoupled dynamics. This allows us to identify how well homogenization can be achieved and decoherence can be suppressed in continuous variable systems.

14 pages

References in corpus (7)

• Universal dynamical decoupling of a single solid-state spin from a spin bath
• Optimized Dynamical Decoupling in a Model Quantum Memory
• Decoherence-protected quantum gates for a hybrid solid-state spin register
• Macroscopicity of Mechanical Quantum Superposition States
• Universality of Uhrig dynamical decoupling for suppressing qubit pure dephasing and relaxation
• Optomechanical sensing of spontaneous wave-function collapse
• A continuous-time diffusion limit theorem for dynamical decoupling and intrinsic decoherence

Cited by in corpus (9)

• Dynamical Decoupling of Unbounded Hamiltonians
• Amplification of quadratic Hamiltonians
• State-dependent Trotter Limits and their approximations
• Universal Uhrig dynamical decoupling for bosonic systems
• Operational Markovianization in Randomized Benchmarking
• Control of quantum noise: on the role of dilations
• Locally optimal control of continuous variable entanglement
• An upper bound on the time required to implement unitary operations
• Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories