Measurement-based quantum computation is a quantum computing paradigm that employs single-qubit measurements performed on an entangled resource state in the form of a cluster state. A basic ingredient in the construction of the resource state is the type-II fusion procedure, which probabilistically merges two separate photonic cluster states by a quantum measurement. We generalize the type-II fusion procedure by generalizing the measurement setup, and classify the resulting final states, which also include cluster states up to single-qubit rotations. We prove that the probability for the success of the generalized type-II fusion is bounded by fifty percent and classify all the possibilities to saturate the bound. We analyze the enhancement of the fusion success probability above the fifty percent bound by the reduction of the entanglement entropy of the resulting state. We prove that the only states that can be obtained with a hundred percent probability of success are product states.

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• Quantum computation
• Quantum information processing
• Quantum information theory
• Quantum measurements
• Quantum protocols