A quantum linearity test for robustly verifying entanglement

Abstract

We introduce a simple two-player test which certifies that the players apply tensor products of Pauli σ X and σ Z observables on the tensor product of n EPR pairs. The test has constant robustness: any strategy achieving success probability within an additive ǫ of the optimal must be poly(ǫ)-close, in the appropriate distance measure, to the honest n-qubit strategy. The test involves 2n-bit questions and 2-bit answers. The key technical ingredient is a quantum version of the classical linearity test of Blum, Luby, and Rubinfeld.As applications of our result we give (i) the first robust self-test for n EPR pairs; (ii) a quantum multiprover interactive proof system for the local Hamiltonian problem with a constant number of provers and classical questions and answers, and a constant completenesssoundness gap independent of system size; (iii) a robust protocol for delegated quantum computation.

Maximal violation of a broad class of Bell inequalities and its implication on self-testing

“…(6). Interestingly, there are Bell inequalities whose maximal quantum violation alone is sufficient to self-test the quantum state (and the measurement operators) [28,34,36,37,[49][50][51][52]. Since then, identifying Bell inequalities which can be used for the task of self-testing has received considerable attention.…”

Parallel Self-Testing of the GHZ State with a Proof by Diagrams

“…This condition allows the computations to be performed in polynomial time. The works[26,11] go further, and prove an error term that is independent of the number of copies of the state.…”

“…Such games are a resource not only for cryptography, but also for quantum computation: these games can be manipulated to force untrusted devices to perform measurements on copies of the Bell state which carry out complex circuits. This idea originated in [32] and has seen variants and improvements since then [21,26,11]. For such applications, it is important that the result include an error term which is (at most) bounded by some polynomial function of the number of copies of the state.…”

Accrediting outputs of noisy intermediate-scale quantum computing devices

“…Inspired by cryptographic protocols [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], our accreditation protocol is trap-based, meaning that the target circuit being accredited is implemented together with a number v of classically simulable circuits (the 'trap' circuits) able to detect all types of noise subject to conditions N1 and N2 above. A single run of our protocol requires implementing the target circuit being accredited and v trap circuits.…”

“…measure [34-38] single qubits, however recently a protocol for a fully classical verifier was devised that relies on the widely believed intractability of a computational problem for quantum computers [39]. Other protocols for classical verifiers have also been devised, but they require interaction with multiple entangled and noncommunicating provers [40][41][42][43][44]. Cryptographic protocols show that with minimal assumptions, verification of the outputs of quantum computations of arbitrary size can be done efficiently, in principle.In practice, implementing cryptographic protocols in experiments remains challenging, especially in the near term.…”