Alas, a rather dry month for property testing. We did find one quantum computing result based on the classic linearity testing theorem.
Robust Self-Testing of Many-Qubit States, by Anand Natarajan and Thomas Vidick (arXiv). (Frankly, my understanding of quantum computation is poor, and this summary may reflect that. Then again, some searching on Google and Wikipedia have definitely broadened my horizons.) One of the key concepts in quantum computation is the notion of entanglement. This allows for correlations between (qu)bits of information beyond what can be classically achieved. Given some device with supposed quantum properties (such as sets of entangled bits), is there a way of verification by measuring various outcomes of the device? This is referred to as self-testing of quantum states. This paper proves such a result for a set of \(n\) EPR pairs, which one can think of \(n\) pairs of “entangled” qubits. The interest to us property testers is the application of a quantum version of the seminar Blum, Luby, Rubinfeld linearity test.