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.

Perfect state transfer in a spin chain without mirror symmetry

“…This is in fact necessary to have PST between the extremities of the chain [8]. While a five-site example was given in [19,Section IV.B] with asymmetric transfer, we here present a system where PST occurs in the absence of this mirror symmetry for an arbitrary (even) number of sites.…”

Spin Guides and Spin Splitters: Waveguide Analogies in One-Dimensional Spin Chains

“…In general, a spin chain is a one-dimensional array of spins that are closely spaced to facilitate strong spin-spin interactions, perhaps via dipole-dipole or exchange coupling. As the inter-spin spacing is typically on the atomic or near atomic scale, individual addressability of the spins is either impossible, or unscalable [2][3][4][5]. As a consequence of the restriction on local control, many innovative schemes have been studied to realise spin transport including schemes with uniform spins and control over just the ends of the chains (see Refs.…”

“…As a consequence of the restriction on local control, many innovative schemes have been studied to realise spin transport including schemes with uniform spins and control over just the ends of the chains (see Refs. [1,[3][4][5][6][7]), or with carefully designed coupling schemes [8,9]. There has also been related work in transport in coupled cavity systems [10][11][12].…”

Routing quantum information in spin chains

“…Actually, a setup admitting QST from a sender to a single receiver may not be trivially extended to implement a routing scheme: By way of example, in Ref. [24], it is explicitly demonstrated that perfect quantum state routing is forbidden unless experimentally demanding operations or severe Hamiltonian engineering is performed. Even by relaxing the request of perfect QST, the problem still remains nontrivial, especially in the huge class of QST protocols based on mirror symmetry where a pivotal role is played by matrices being both persymmetric and centrosymmetric [23].…”