  A measurement of the time between quantum jumps implies the capability to
measure the next jump. During the time between jumps the quantum system is not
evolving in a closed or unitary manner. While the wave function maintains phase
coherence it evolves according to a non-Hermitian effective Hamiltonian. So
under null measurement the timing of the next quantum jump can change by very
many orders of magnitude when compared to rates obtained by multiplying
lifetimes with occupation probabilities obtained via unitary transformation.
The theory developed in 1987 for atomic fluorescence is here extended to
transitions in transmon qubits. These systems differ from atoms in that they
are read out with a harmonic cavity whose resonance is determined by the state
of the qubit. We extend our analysis of atomic fluorescence to this infinite
level system by treating the cavity as a quantum system. We find that next
photon statistics is highly non exponential and when implemented will enable
faster readout, such as on time scales shorter than the decay time of the
cavity. Commonly used heterodyne measurements are applied on time scales longer
than the cavity lifetime. The overlap between the next photon theory and the
theory of heterodyne measurement which are described according to the
Stochastic Schroedinger Equation is elucidated. In the limit of large
dispersion the intrinsic error for next jump detection -- at short time --
tends to zero. Whereas for short time dyne detection the error remains finite
for all values of dispersion.
