Quantum Advantage in Continuous Variable Sensing

Quantum systems of infinite-dimension such as bosonic oscillators provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing is unknown. We present such a framework for algorithmic quantum sensing at the fundamental limits of quantum mechanics, i.e. the Heisenberg sensing limit. We manipulate the bosonic system by performing arbitrary polynomial transformations on the bosonic phase space using quantum signal processing (QSP) in a qubit+oscillator system. For continuous variable parameter estimation, we generalize Ramsey-like sensing sequences and our protocol achieves a sensitivity scaling with the Heisenberg limit, as is the case in state-of-the-art phase and displacement sensing. Furthermore, we use our bosonic QSP sensing framework to make binary decisions about signals affecting the oscillator. The sensing accuracy of a single shot qubit measurement can outperform the Heisenberg scaling as one bit of information may encode our yes/no question without violating any physical laws. We expect our algorithmic quantum sensing protocol to unify different approaches for optimal sensing and offer a new way of sensing with various applications in chemistry and physics.