Quantum Computation and Information Seminar 

11/09/2015, 14:00 — 15:00 — Room P9, Mathematics Building
Rúben Sousa, Instituto Superior Técnico

Pretty good state transfer of entangled states through quantum spin chains

Since the transfer of quantum states from one site to another is a key task in quantum information processing, the one-dimensional spin-$1/2$ chain has been extensively studied as a quantum wire for the transfer of qubit states. The ideal scenario is that where we have unit fidelity of transfer, but unfortunately it has been demonstrated that such perfect transfer cannot be achieved within chains with basic nearest-neighbor couplings.

In this talk, I will address the notion of pretty good state transfer, where the requirement is only slightly relaxed: here the requirement is that the fidelity of transfer gets arbitrarily close to one. Then, I will show that any multi-qubit state can be transferred with arbitrarily large fidelity through the uniform XX quantum spin chain if and only if the length of the chain is $n = p − 1$, $n = 2p − 1$, where $p$ is prime, or $n = 2^k − 1$. This result highlights the link between quantum dynamics and primality, and opens the way to using uniformly coupled spin chains as short-distance quantum channels for the transfer of arbitrary states of any dimension. I will discuss how the experimental implementation of this transfer protocol can be carried out with current technology.