Efficient Fault-Tolerant Quantum Protocol for Differential Privacy in the Shuffle Model

TL;DR

A quantum protocol is presented which securely and implicitly implements a random shuffle to realize differential privacy in the shuffle model and can be efficiently implemented using fault-tolerant computation.

Abstract

We present a quantum protocol which securely and implicitly implements a random shuffle to realize differential privacy in the shuffle model. The shuffle model of differential privacy amplifies privacy achievable via local differential privacy by randomly permuting the tuple of outcomes from data contributors. In practice, one needs to address how this shuffle is implemented. Examples include implementing the shuffle via mix-networks, or shuffling via a trusted third-party. These implementation specific issues raise non-trivial computational and trust requirements in a classical system. We propose a quantum version of the protocol using entanglement of quantum states and show that the shuffle can be implemented without these extra requirements. Our protocol implements k-ary randomized response, for any value of k > 2, and furthermore, can be efficiently implemented using fault-tolerant computation.

Figures (8)

• Figure 1: The shuffle model of differential privacy. Each client's input $x_i$ is locally randomized, before being shuffled. Shuffling in this case is implemented via a mix network. The server then combines the shuffled and locally randomized values to produce a differentially private estimate $\widehat{f}$ of the function $f$ of the original inputs $x_1, \ldots, x_n$.
• Figure 2: The two types of channels between each client and the server. The arrows indicate the direction in which information flows in our protocol using the respective channel.
• Figure 3: Circuit for creating the generalized Bell state from Eq \ref{['eq:bell']}.
• Figure 4: Circuit for creating the initial GHZ state $\ket{\psi_0} = \frac{1}{\sqrt{d}} \sum_{j = 0}^{d-1} \ket{j}^{\otimes n}$ from Eq \ref{['eq:ghz']}.
• Figure 5: Teleportation circuit for teleporting an individual qudit $\ket{j}_T$ of the GHZ state to a client using generalized Bell pairs $\ket{\beta}$. Here, the server has the top two qudits, and the client the bottom.

Theorems & Definitions (16)

• Definition 1: Differential Privacy
• Proposition 1: Post-processing dwork2006calibrating
• Proposition 2: Sequential composition dwork2014dp-book
• Definition 2: Local Differential Privacy
• Proposition 3
• proof
• Proposition 4
• proof
• Proposition 5
• proof