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

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.

14 pages, 3 figures v3: rewritten for increased clarity

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• Reference frames, superselection rules, and quantum information
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• Control by quantum dynamics on graphs
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Cited by in corpus (12)

• Long quantum channels for high-quality entanglement transfer
• Perfect Quantum Routing in Regular Spin Networks
• The Basics of Perfect Communication through Quantum Networks
• Symmetry & Controllability for Spin Networks with a Single-Node Control
• Capacitively coupled double quantum dot system in the Kondo regime
• A coherent router for quantum networks
• Cospectrality preserving graph modifications and eigenvector properties via walk equivalence of vertices
• Chiral quantum router with Rydberg atoms
• How to Suppress Dark States in Quantum Networks and Bio-Engineered Structures
• Characterization and Control of Quantum Spin Chains and Rings
• Which weighted circulant networks have perfect state transfer?
• Incorporating Encoding into Quantum System Design