Abstract
Self-testing allows classical referees to verify the quantum behaviour of some untrusted devices. Recently we developed a framework for building large self-tests by repeating a smaller self-test many times in parallel. However, the framework did not apply to the CHSH test, which tests a maximally entangled pair of qubits. CHSH is the most well known and widely used test of this type. Here we extend the parallel self-testing framework to build parallel CHSH self-tests for any number of pairs of maximally entangled qubits. Our construction achieves an error bound which is polynomial in the number of tested qubit pairs.
Highlights
The most basic self-testing problem is this: given two non-communicating quantum devices, verify through classical interaction alone that they share a maximally entangled pair of qubits
As a step in our construction we show that it is possible to self-test many maximally entangled pairs of qubits using a modified parallel repetition of CHSH with only a logarithmic number of questions
We have shown that the CHSH game can be used for testing many pairs of maximally entangled qubits, and that the error bound scales polynomially
Summary
The most basic self-testing problem is this: given two non-communicating quantum devices, verify through classical interaction alone that they share a maximally entangled pair of qubits. This problem can be phrased in the language of non-local games. While it is interesting that it is possible to self-test a single pair of maximally entangled qubits, many more applications are possible if many pairs can be tested. The CHSH game [CHSH69] is arguably the most wellknown non-local game and has seen wide application It is distinguished by its simplicity, with only single-bit questions and answers for both Alice and Bob. It is distinguished by its simplicity, with only single-bit questions and answers for both Alice and Bob Because of this simplicity, the CHSH game is widely used, both in theory and experiment.
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