  Quantum control of a linear oscillator using a static dispersive coupling to
a nonlinear ancilla underpins a wide variety of experiments in circuit QED.
Extending this control to more than one oscillator while minimizing the
required connectivity to the ancilla would enable hardware-efficient multi-mode
entanglement and measurements. We show that the spectrum of an ancilla
statically coupled to a single mode can be made to depend on the joint photon
number in two modes by applying a strong parametric beamsplitter coupling
between them. This `joint-photon number-splitting' regime extends
single-oscillator techniques to two-oscillator control, which we use to realize
a hardware-efficient erasure check for a dual-rail qubit encoded in two
superconducting cavities. By leveraging the beamsplitter coupling already
required for single-qubit gates, this scheme permits minimal connectivity
between circuit elements. Furthermore, the flexibility to choose the pulse
shape allows us to limit the susceptibility to different error channels. We use
this scheme to detect leakage errors with a missed erasure fraction of $(9.0
\pm 0.5)\times10^{-4}$, while incurring an erasure rate of $2.92 \pm 0.01\%$
and a Pauli error rate of $0.31 \pm 0.01\%$, both of which are dominated by
cavity errors.
