  We report the results of an experiment that searches for causal non-linear
state-dependent terms in quantum field theory. Our approach correlates a binary
macroscopic classical voltage with the outcome of a projective measurement of a
quantum bit, prepared in a coherent superposition state. Measurement results
are recorded in a bit string, which is used to control a voltage switch.
Presence of a non-zero voltage reading in cases of no applied voltage is the
experimental signature of a non-linear state-dependent shift of the
electromagnetic field operator. We implement blinded measurement and data
analysis with three control bit strings. Control of systematic effects is
realized by producing one of the control bit strings with a classical
random-bit generator. The other two bit strings are generated by measurements
performed on a superconduting qubit in an IBM Quantum processor, and on a
$^{15}$N nuclear spin in an NV center in diamond. Our measurements find no
evidence for electromagnetic quantum state-dependent non-linearity. We set a
bound on the parameter that quantifies this non-linearity
$|\epsilon_{\gamma}|<4.7\times 10^{-11}$, at 90% confidence level. Within the
Everett many-worlds interpretation of quantum theory, our measurements place
limits on the electromagnetic interaction between different branches of the
universe, created by preparing the qubit in a superposition state.
