We propose a model to perform controlled sign (CS) gate flip in two stages that is free of the use of detectors discriminating between one- and two-photon number states. The CS gate with mode entangled qubits and two-photon quantum channel is used at the first stage to produce a more perfect four-photon quantum channel. A two-photon quantum channel can be constructed using a spontaneous parametric down converter and methods of linear optics. We describe the CS gate performance with the help of a four-photon quantum channel at the second stage. The success probability of the CS gate performance with both two- and four-photon quantum channels is 1/4. The use of usual detectors at the first stage leads to the appearance of a noisy quantum channel that is shown not to have influence on the valid CS gate flip at the second stage whose outcome is characterized by fourfold coincidence registration of photons. The success probability of such a CS gate in two stages is 1/16.
Probabilistic entangling measurements are key operations in linear-optical quantum technologies, enabling the generation and manipulation of high-dimensional quantum states. While prior research has focused predominantly on specific entangled states, notably graph states and Greenberger-Horne-Zeilinger (GHZ) states, broader classes of states with variable entanglement remain underexplored. In this work, we present a linear-optical approach for generating and fusing GHZ-like states, which generalize standard GHZ states to include variable entanglement degrees. We introduce two schemes based on modified fusion gates that allow flexible control over generation efficiency and the entanglement of the output states. These results offer a promising pathway toward resource-efficient entangled-state generation for scalable quantum computing and communication.
Reliable entangling gates for qubits encoded in single-photon states represent a major challenge on the road to scalable quantum computing architectures based on linear optics. In this work, we present two approaches to develop high-fidelity, near-deterministic controlled-sign-shift gates based on the techniques of quantum gate teleportation. On the one hand, teleportation in a discrete-variable setting, i.e., for qubits, offers unit-fidelity operations but suffers from low success probabilities. Here, we apply recent results on advanced linear optical Bell measurements to reach a near-deterministic regime. On the other hand, in the setting of continuous variables, associated with coherent states, squeezing, and, typically, Gaussian states, teleportation can be performed in a deterministic fashion, but the finite amount of squeezing implies an inevitable deformation of a teleported single-mode state. Using a new generalized form of the nonlinear-sign-shift gate for gate teleportation, we are able to achieve fidelities of the resulting controlled-sign gate above
90. A special focus is also put on a comparison of the two approaches, not only with respect to fidelity and success probability, but also in terms of resource consumption.