Carving entangled multiparticle states with exponentially improved fidelity

We propose a method that uses the ``no-jump'' evolution of a probe to generate entangled multiparticle states of high fidelity. The probe is coupled to a target ensemble of qubits and engineered to exponentially decay at a rate depending on the target collective spin, such that postselecting on observing no probe decay precisely removes select faster-decaying spin components. When a probe and $N$-qubit target interact via a cavity mode of cooperativity $C$, our procedure generates entangled states with infidelities of ${e}^{\ensuremath{-}C/N}$, an exponential improvement over previous carving schemes. This scheme, which we call ``counterfactual'' carving, can generate complex entangled states for applications in quantum metrology and quantum computing.