Privacy in Quantum Communication Complexity

TL;DR

This paper explores the complexities of defining and achieving privacy in two-party quantum communication protocols, highlighting the differences between classical and quantum input assumptions and proposing new protocols for specific functions.

Contribution

It introduces new quantum protocols for the Inner Product function and Private Information Retrieval, and clarifies the appropriate privacy definitions based on input register assumptions.

Findings

Privacy bounds differ exponentially between classical and quantum input assumptions.

Classical input register privacy is more suitable for protocol security.

New protocols demonstrate practical privacy considerations in quantum communication.

Abstract

In two-party quantum communication complexity, Alice and Bob receive some classical inputs and wish to compute some function that depends on both these inputs, while minimizing the communication. This model has found numerous applications in many areas of computer science. One question that has received a lot of attention recently is whether it is possible to perform such protocols in a private way. We show that defining privacy for quantum protocols is not so straightforward and it depends on whether we assume that the registers where Alice and Bob receive their classical inputs are in fact classical registers (and hence unentangled with the rest of the protocol) or quantum registers (and hence can be entangled with the rest of the protocol or the environment). We provide new quantum protocols for the Inner Product function and for Private Information Retrieval, and show that the privacy assuming classical input registers can be exponentially smaller than the privacy assuming quantum input registers. We also argue that the right notion of privacy of a communication protocol is the one assuming classical input registers, since otherwise the players can deviate considerably from the protocol.