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In order to fulfill quantum information processing tasks such as quantum computation and scalable quantum networks, quantum logic gates are indispensable parts. A multiqubit logic gate can efficiently reduce the cost of physical resources and complicated operations that are necessary in the combination of fewer-qubit (e.g., two-qubit) logic gates to fulfill the same tasks. However, the construction of multiphoton quantum logic gates is a large challenge. Assisted by spatial and temporal degrees of freedom, a polarization multiphoton controlled one-photon unitary gate is proposed, which can be realized with three processes including the control-path process based on weak cross-Kerr nonlinearities, the unitary transformation process, and the output process. In the control-path process, the control-path modules are applied, where the entanglement between polarization, spatial and temporal degrees of freedom is generated by beam splitters, time delayers, and nonlinear interaction in cross-Kerr media. The scheme presented here, assisted by spatial and temporal degrees of freedom reduces the experimental complexity of the schemes assisted by only spatial degree of freedom. Moreover, it will also be a useful reference in optimally constructing multiqubit quantum logic gates with other multiple degrees of freedom in many physical systems.variety of physical systems in the theoretical aspect [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and experimental aspect. [21][22][23][24][25][26] Photons are the promising carriers of quantum information due to their advantages, fast propagation, low decoherence, ease to manipulate, etc. [27] However, owing to weak photon-photon interaction, quantum logic gates at the single-photon level had made slow progress. [22] The linear optics standard model proposed by Knill et al. [28] had changed this unclear situation, while its upper limitation of success probability is less than unity. [29] Furthermore, by using nonlinear optical interaction such as cross-Kerr interaction, the threshold on the success probability imposed by the linear optics standard model could be broken through. [30] Due to tiny strength of nonlinear interaction, the direct applications of cross-Kerr nonlinearities have not been easily realized. To achieve feasibility of deterministic quantum logic gates, weak cross-Kerr nonlinearities were applied first in the two-photon controllednot gate using an auxiliary photon, [31] which approaches the success probability nearly close to unity. After that, many construction schemes of twophoton logic gates based on weak cross-Kerr nonlinearities were proposed, for instance, the controlled-not gate with half unity success probability without an auxiliary photon, [32] the controllednot gate, [33] and the controlled-phase gate [34] with nearly unity success probability without the auxiliary photon, quantum logic gates [35] composed by control-path gate and merging gate. On the other hand, weak cross-Kerr nonlinearities were also used in the Bell states analys...

Hyper‐entangled states that encode qubits in multiple degrees of freedom of a quantum system can provide a decisive advantage in quantum information processing, such as improving the capacity of communication and speeding up the computation. Assisted by quantum dots in single‐sided optical microcavities, nonlinear interaction of optical circular polarizations is induced and a deterministic scheme for preparing a three‐photon hyper‐entangled asymmetric W state with polarization degree of freedom and spatial degree of freedom is proposed. The preparing process is composed of three steps: the preparation of a three‐photon polarization entangled asymmetric W state; the preparation of a three‐photon spatial entangled asymmetric W state; the preparation of a three‐photon hyper‐entangled asymmetric W state. It can be generalized to generate a three‐photon general W state according to practical requirement.