Parallel self-testing of EPR pairs under computational assumptions

TL;DR

This paper presents a parallel self-testing protocol for multiple EPR pairs in a single quantum device under computational assumptions, enabling efficient certification of quantum states and measurements with classical communication.

Contribution

It extends previous work to parallel self-testing of multiple EPR pairs in a single device, under computational assumptions, with applications in quantum cryptography and cloud quantum computing.

Findings

Achieves high success probability with polynomial resources

Any device failing the test is close to honest in the appropriate sense

Enables certification of multiple qubits with only classical communication

Abstract

Self-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Quantum, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of $N$ EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to $1$ by an honest quantum device using poly$(N)$ resources. Moreover, we show that any quantum device that fails our protocol with probability at most $\epsilon$ must be poly$(N,\epsilon)$-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.