State Transfer in Highly Connected Networks and a Quantum Babinet Principle

Abstract

The transfer of a quantum state between distant nodes in two-dimensional networks, is considered. The fidelity of state transfer is calculated as a function of the number of interactions in networks that are described by regular graphs. It is shown that perfect state transfer is achieved in a network of size N, whose structure is that of a N/2-cross polytope graph, if N is a multiple of 4. The result is reminiscent of the Babinet principle of classical optics. A quantum Babinet principle is derived, which allows for the identification of complementary graphs leading to the same fidelity of state transfer, in analogy with complementary screens providing identical diffraction patterns.

5 pages, 3 figures; Replaced with published version

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• Transport of Quantum Correlations across a spin chain
• Spin systems dynamics and faults detection in threshold networks
• Quantum walks on complex networks with connection instabilities and community structure
• Relationship between probabilities of the state transfers and entanglements in spin systems with simple geometrical configurations
• Quantum state transfer in spin chains with q-deformed interaction terms
• Robustness of spin-chain state-transfer schemes
• Continuous-Time Quantum Walks on Directed Bipartite Graphs
• Quantum transport efficiency in noisy random-removal and small-world networks
• Enhancing quantum state transfer efficiency in binary-tree spin networks by partially collapsing measurements
• Perfect state transfer, integral circulants and join of graphs