The Basics of Perfect Communication through Quantum Networks

Abstract

Perfect transfer of a quantum state through a one-dimensional chain is now well understood, allowing one not only to decide whether a fixed Hamiltonian achieves perfect transfer, but to design a suitable one. We are particularly interested in being able to design, or understand the limitations imposed upon, Hamiltonians subject to various naturally arising constraints such as a limited coupling topology with low connectivity (specified by a graph) and type of interaction. In this paper, we characterise the necessary and sufficient conditions for transfer through a network, and describe some natural consequences such as the impossibility of routing between many different recipients for a large class of Hamiltonians, and the limitations on transfer rate. We also consider some of the trade-offs that arise in uniformly coupled networks (both Heisenberg and XX models) between transfer distance and the size of the network as a consequence of the derived conditions.

v2: 9 pages, 1 figure, published version

References in corpus (16)

• Perfect Transfer of Arbitrary States in Quantum Spin Networks
• Mirror Inversion of Quantum States in Linear Registers
• Spin Chains as Perfect Quantum State Mirrors
• Perfect state transfer on a spin-chain without state initialization
• Perfect State Transfer: Beyond Nearest-Neighbor Couplings
• Electron wavepacket propagation and entanglement in a chain of coupled quantum dots
• Quantum Networks on Cubelike Graphs
• Perfect Quantum Routing in Regular Spin Networks
• State Transfer and Spin Measurement
• Perfect state transfer in networks of arbitrary topology and coupling configuration
• The Non-Equilibrium Reliability of Quantum Memories
• Statics and Dynamics of Quantum XY and Heisenberg Systems on Graphs
• Communication in quantum networks of logical bus topology
• Quantum Control Theory for State Transformations: Dark States and their Enlightenment
• Quantum state transfer in a q-deformed chain
• The 3-dimensional cube is the only periodic, connected cubic graph with perfect state transfer

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