Secure two-party quantum evaluation of unitaries against specious adversaries

TL;DR

This paper presents a method for securely evaluating any two-party quantum unitary operation against specious adversaries, using ideal functionalities like SWAP and AND-box, with efficiency depending on the unitary's Clifford group membership.

Contribution

It introduces a private quantum evaluation protocol utilizing ideal functionalities, distinguishing between Clifford and non-Clifford unitaries, and analyzes the minimal requirements for privacy.

Findings

Clifford group unitaries require only one SWAP call for privacy.

Non-Clifford unitaries need an AND-box per R-gate for privacy.

SWAP cannot be privately implemented in the bare model.

Abstract

We describe how any two-party quantum computation, specified by a unitary which simultaneously acts on the registers of both parties, can be privately implemented against a quantum version of classical semi-honest adversaries that we call specious. Our construction requires two ideal functionalities to garantee privacy: a private SWAP between registers held by the two parties and a classical private AND-box equivalent to oblivious transfer. If the unitary to be evaluated is in the Clifford group then only one call to SWAP is required for privacy. On the other hand, any unitary not in the Clifford requires one call to an AND-box per R-gate in the circuit. Since SWAP is itself in the Clifford group, this functionality is universal for the private evaluation of any unitary in that group. SWAP can be built from a classical bit commitment scheme or an AND-box but an AND-box cannot be constructed from SWAP. It follows that unitaries in the Clifford group are to some extent the easy ones. We also show that SWAP cannot be implemented privately in the bare model.