State Transfer in Latent-Symmetric Quantum Networks

The transport of states is a fundamental task in quantum information processing systems, enabling operations such as quantum key distribution and inter-component communication within quantum computers. A straightforward approach to the design of state transfer networks are spatial symmetries such as permutation or reflection symmetry. Instead of strictly confining the design space in this fashion, our work takes a novel path by harnessing photonic networks that lack any conventional spatial symmetries, while nevertheless supporting an efficient transfer of quantum states [1], [2]. Key to this approach are so-called latent symmetries [3], which are embodied exclusively in the spectral properties of the network, thereby remaining hidden in the spatial domain. Two network sites <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$u$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$v$</tex> are considered latent-symmetric if there is no permutation symmetry between them, but the two sites are cospectral, i.e. the sets of eigenvalues of the networks obtained upon removal of either site are identical (fig. 1a). One of the hallmark features of latent symmetry is the existence of so-called singlet sites [4] at which these networks can be arbitrarily extended without breaking the latent symmetry (e.g. for sites <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$a, b, c$</tex> in fig. 1a). Anti-symmetric excitations at the two latent-symmetric sites will always interfere destructively at those singlet sites and hence will never leave the initial network. Latent symmetries significantly improve the flexibility in designing quantum networks and hold great potential for applications in quantum cryptography and secure state transfer.