We present a scheme of two-photon quantum Fourier transform at first, where the controlled π/2 phase gate and the Hadamard gates are applied. The indirect interaction between two photons can be realized through a coupling bus provided by a coherent state in Kerr media. Employing photon-number measurements and the corresponding classical feed-forward techniques, the task of low-error quantum Fourier transform can be fulfilled. With revision and modulation on the optical elements, controlled π/2n (n=2,3,…) phase gates are constructed, and the multiphoton quantum Fourier transform can be achieved by integrating these controlled phase gates and Hadamard gates.
Quantum Fourier transform is realized by the Hadamard gate in a quantum computer, which can also be considered as a Hadamard transform. We introduce the Hadamard transformed photon-added coherent state (HTPACS), which is obtained by letting the photon-added coherent state (PACS) across the quantum Hadamard gate, from this result. It is found that the HTPACS can be considered as a coordinate—momentum mutual exchanging followed by a squeezing transform of the PACS. In addition, the non-classical statistical properties of HTPACS, such as squeezing coefficient, Mandel parameter, etc., are also discussed.
Consider the problem: Alice wishes to send the same key to
n−1 users (Bob, Carol,. . . , Nathan), while preventing eavesdropper Eve from acquiring information without being detected. The problem has no solution in the classical cryptography but in quantum telecommunication there are some codes to solve the problem. In the paper \cite{zengetall}, Guo-Jyun Zeng, Kuan-Hung Chen, Zhe-Hua Chang, Yu-Shan Yang, and Yao-Hsin Chou from one side and Cabello in \cite{cabello} from other side, used Hadamard gates, Pauli gates in providing the quantum communication code for two-partity telecommunication with 3 persons and then generalized it to the case of arbitrary number of participants, indicating the position of measurements of participants. We remark that the Hadamard gate with precising the position of measurement is the same as Fourier transform for two qubits and hence use the general Fourier transform for
n entangled qubits, in place of Hadamard gates. The result is more natural for arbitrary
n qudits.