Computational self-testing of multi-qubit states and measurements

Abstract

Self-testing is a fundamental technique within quantum information theory 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 [MV21] showed that a single EPR pair of a single quantum device can be self-tested under standard computational assumptions. In this work, we generalize their techniques to give the first protocol that self-tests N EPR pairs and measurements 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 ǫ must be poly(N, ǫ)-close to being honest in the appropriate sense. In particular, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a cloud quantum computer, on which we cannot enforce spatial separation, using only classical communication.

Efficient Certifiable Randomness from a Single Quantum Device

“…The small change that we make, which is described below, allows us to greatly simplify the proof of correctness while achieving a nearly optimal rate of randomness generation as a function of the total number of bits sent from the quantum device to the verifier, thereby also providing a way of certifying that the quantum device has roughly n bits of quantum memory. We note that a quantum dimension test was recently obtained in [FWZ22] by performing parallel repetition of (a variant of) the protocol from [BCM + 18]. In contrast, our protocol is more efficient (constant rounds, linear communication) and our analysis far more direct.…”

“…However,[FWZ22], see also[GMP22], proves a stronger rigidity result for their protocol, which extends the qubit test to certain n-qubit states.…”