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We propose a new method, "counter-factual" carving, that uses the "no-jump"evolution of a probe to generate entangled many-body states of high fidelity.The probe is coupled to a target ensemble of qubits and engineered toexponentially decay at a rate depending on the target collective spin, suchthat post-selecting on observing no probe decay precisely removes selectfaster-decaying spin components. When probe and $N$-qubit target interact via acavity mode of cooperativity $C$, counter-factual carving generates entangledstates with infidelities of $e^{-C/N}$, an exponential improvement overprevious carving schemes. Counter-factual carving can generate complexentangled states for applications in quantum metrology and quantum computing.

Counter-factual carving exponentially improves entangled-state fidelity