Quantum Control Theory for State Transformations: Dark States and their Enlightenment

TL;DR

This paper introduces a new framework for quantum control focusing on accessible state pairs, providing bounds on fidelity, analyzing dark states, and demonstrating how to access them using catalytic excitations in spin networks.

Contribution

It proposes the concept of accessible pairs, derives fidelity bounds based on system symmetries, and characterizes dark states and their accessibility in spin networks.

Findings

Fidelity bounds depend on system symmetries.

Dark states can be calculated and accessed with catalytic excitations.

Single excitation subspace analysis is insufficient for state transfer.

Abstract

For many quantum information protocols such as state transfer, entanglement transfer and entanglement generation, standard notions of controllability for quantum systems are too strong. We introduce the weaker notion of accessible pairs, and prove an upper bound on the achievable fidelity of a transformation between a pair of states based on the symmetries of the system. A large class of spin networks is presented for which this bound can be saturated. In this context, we show how the inaccessible dark states for a given excitation-preserving evolution can be calculated, and illustrate how some of these can be accessed using extra catalytic excitations. This emphasises that it is not sufficient for analyses of state transfer in spin networks to restrict to the single excitation subspace. One class of symmetries in these spin networks is exactly characterised in terms of the underlying graph properties.