Abstract
Reliable qubits are difficult to engineer. What can we do with just a few of them? Here are some ideas:
1. Dimension test. An n-qubit system should have 2^n dimensions, but systems with just polynomial(n) dimensions can look like they have n qubits. Is nature really exponential? We give a test for verifying that your system has 2^n dimensions.
2. Entanglement and nonlocality tests. A Bell-inequality violation establishes that your systems share some entanglement. We give a test to show that your systems share lots of entanglement. Additionally, we give a test to eliminate non-signaling correlations (like the Popescu-Rohrlich nonlocal box), giving a way to check whether multi-party entanglement breaks down.
3. Error test. Error correction will be needed for scalable quantum computers. But high qubit overhead makes it impractical for small devices. We show that a seven-qubit computer can fault tolerantly correct errors on one encoded qubit, and that a 17-qubit computer can protect and compute fault tolerantly on seven encoded qubits.