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Inferring superposition and entanglement from measurements in a single basis
We discuss what can be inferred from measurements on 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 in a coherent oscillation experiment.
Similarly, one can infer that a near maximally entangled state of two qubits
has been created in 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.Comment: Final published versio