Fidelity of dynamical maps

TL;DR

This paper introduces a fidelity measure for dynamical maps in open quantum systems, establishing an inequality that constrains these maps based solely on environmental states and system dynamics, with applications in quantum programming and probing.

Contribution

It presents a novel fidelity concept for dynamical maps and derives an inequality linking it to environmental state distinguishability, independent of microscopic Hamiltonians.

Findings

Derived bounds on quantum processor dimension for approximate unitary programming.

Demonstrated environmental information extraction via quantum probing without prior Hamiltonian assumptions.

Established constraints on dynamical maps based solely on environmental states and system dynamics.

Abstract

We introduce the concept of fidelity for dynamical maps in an open quantum system scenario. We derive an inequality linking this quantity to the distinguishability of the inducing environmental states. Our inequality imposes constraints on the allowed set of dynamical maps arising from the microscopic description of system plus environment. Remarkably, the inequality involves only the states of the environment and the dynamical map of the open system and, therefore, does not rely on the knowledge of either the microscopic interaction Hamiltonian or the environmental Hamiltonian characteristic parameters. We demonstrate the power of our result by applying it to two different scenarios: quantum programming and quantum probing. In the first case we use it to derive bounds on the dimension of the processor for approximate programming of unitaries. In the second case we present an intriguing proof-of-principle demonstration of the ability to extract information on the environment via a quantum probe without any a priori assumption on the form of the system-environment coupling Hamiltonian.