Quantum Walks with Encrypted Data

In the setting of networked computation, data security can be a significant concern. Here we consider the problem of allowing a server to remotely manipulate client supplied data, in such a way that both the information obtained by the client about the server’s operation and the information obtained by the server about the client’s data are significantly limited. We present a protocol for achieving such functionality in two closely related models of restricted quantum computation—the boson sampling and quantum walk models. Because of the limited technological requirements of the boson scattering model, small scale implementations of this technique are feasible with present-day technology.

Figure 1

$\log (⟨|⟨a|b⟩{|}^2⟩)$ with $d=1024$, against the number of photons $m$ and the Hamming distance between the strings.

Figure 2

Regions for different levels of confidence in the probability that Bob correctly infers Alice’s state using a randomly chosen basis, $p_{\mathrm{av}}<ϵ$.