Inferring superposition and entanglement in evolving systems from measurements in a single basis

We discuss what can be inferred from measurements on evolving one- and two-qubit systems using a single measurement basis at various times. We show that, given reasonable physical assumptions, carrying out such measurements at quarter-period intervals is enough to demonstrate coherent oscillations of one or two qubits between the relevant measurement basis states. One can thus infer from such measurements alone that an approximately equal superposition of two measurement basis states has been created during a coherent oscillation experiment. Similarly, one can infer that a near-maximally entangled state of two qubits has been created part way through an experiment involving a putative SWAP gate. These results apply even if the relevant quantum systems are only approximate qubits. We discuss applications to fundamental quantum physics experiments and quantum-information processing investigations