Quantum metrology utilizes entanglement to improve the sensitivity of measurements(1-3). To date, the focus has been on the measurement of a single observable. Its orthogonal observable, however, may contain additional information, the knowledge of which can be used to further improve the measurement result beyond what is possible with state-of-the-art quantum metrology. Here we demonstrate a laser interferometer that provides information about two non-commuting observables, with uncertainties below the meter's quantum ground state. Our experiment is a proof of principle of what we call 'quantum-dense metrology', referring to its increased measurement information and its analogy to quantum-dense coding in quantum information science. We propose to use the additional information to discriminate between the actual science signal and parasitic signals originating from scattered photons. Our approach can be readily applied to improve squeezed-light enhanced gravitational-wave detectors at non-quantum noise-limited detection frequencies by providing a sub-shot-noise veto trigger against stray-light-induced signals.