Quantum dimension witness with a single repeated operation

Abstract

We present a simple null test of a dimension of a quantum system, using a single repeated operation in the method of delays, assuming that each instance is identical and independent. The test is well-suited to current feasible quantum technologies, with programed gates. We also analyze weaker versions of the test, assuming unitary or almost unitary operations and derive expressions for the statistical error. The feasibility of the test is demonstrated on IBM Quantum. The failure in one of the tested devices can indicate a lack of identity between subsequent gates or an extra dimension in the many worlds/copies model.