Fidelity of dynamical maps

Discrete Dynamical Systems: Maps

Many physical systems displaying chaotic behavior are accurately described by mathematical models derived from well-understood physical principles. For example, the fundamental equations of fluid dynamics, namely the Navier–Stokes equations, are obtained from elementary mechanical and thermodynamical considerations. The simplest laser models are built from Maxwell’s laws of electromagnetism and...

Continuous iteration of dynamical maps

High fidelity quantum memory via dynamical decoupling

Quantum information processing requires overcoming decoherence—the loss of ‘quantumness’ due to the inevitable interaction between the quantum system and its environment. One approach towards a solution is quantum dynamical decoupling—a method employing strong and frequent pulses applied to the qubits. Here we report on the first experimental test of the concatenated dynamical decoupling (CDD) ...

High fidelity quantum gates via dynamical decoupling.

Realizing the theoretical promise of quantum computers will require overcoming decoherence. Here we demonstrate numerically that high fidelity quantum gates are possible within a framework of quantum dynamical decoupling. Orders of magnitude improvement in the fidelities of a universal set of quantum gates, relative to unprotected evolution, is achieved over a broad range of system-environment ...

Fidelity Preserving Maps on Density Operators

We prove that any bijective fidelity preserving transformation on the set of all density operators on a Hilbert space is implemented by an either unitary or antiunitary operator on the underlying Hilbert space. Let H be a Hilbert space. The set of all density operators on H, that is, the set of all positive self-adjoint operators on H with finite trace is denoted by C 1 (H). (We note that one m...