We propose a scheme for preparing multiple-photon GHZ state via cavity-assisted interaction. There are n -pair single-photon pulses successively injected and reflected from two sides of the cavity, which traps one atom. After the atomic state is measured, a 2 n -photon GHZ state is produced. In the ideal case, the successful probability of the scheme is close to unity.

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International Journal of Theoretical Physics

Flexible for Multiple Equations about GHZ States and a Prototype Case

Chaonan Wang, Zexi Li, Hongfeng Zhu

Published Sep 14, 2021• 5 citations

Publisher

DOI: 10.1007/s10773-021-04948-0

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z

-type (Pauli

z

matrix on different qubits) and

x

-type (Pauli

x

matrix on all qubits) measurements and one control Hamiltonian, we provide general conditions on the feedback controller and the control Hamiltonian ensuring almost sure exponential convergence to a predetermined Greenberger–Horne-Zeilinger (GHZ) state, which is assumed to be a common eigenstate of the measurement operators. We provide explicit expressions of feedback controllers satisfying such conditions. We also consider the case of only

z

-type measurements and multiple control Hamiltonians. We show that local stability in probability holds true, however due to the absence of random displacements generated by

x

-type measurements, the reachability of a neighborhood of a predetermined GHZ state is not clear. In this case, we provide a heuristic discussion on some conditions which may ensure asymptotic convergence toward the target state. Finally, we demonstrate the effectiveness of our methodology for a three-qubit system through numerical simulations.