Generation of Bell, W and GHZ states via exceptional points in non-Hermitian quantum spin systems

Abstract

We study quantum phase transitions in non-Hermitian XY and transverse-field Ising spin chains, in which the non-Hermiticity arises from the imaginary magnetic field. Analytical and numerical results show that at exceptional points, coalescing eigenstates in these models close to W, distant Bell and GHZ states, which can be steady states in dynamical preparation scheme proposed by T. D. Lee et. al. (Phys. Rev. Lett. 113, 250401 (2014)). Selecting proper initial states, numerical simulations demonstrate the time evolution process to the target states with high fidelity.

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• PT-symmetric Rabi model: Perturbation theory
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• Bare-Excitation Ground State of a Spinless-Fermion -- Boson Model and $W$-State Engineering in an Array of Superconducting Qubits and Resonators
• Conversion from $W$ to Greenberger-Horne-Zeilinger states in the Rydberg-blockade regime of neutral-atom systems: Dynamical-symmetry-based approach
• Scalable $W$-type entanglement resource in neutral-atom arrays with Rydberg-dressed resonant dipole-dipole interaction
• Dicke-state preparation through global transverse control of Ising-coupled qubits
• Long-range entangled zero-mode state in a non-Hermitian lattice
• Quantum-brachistochrone approach to the conversion from $W$ to Greenberger-Horne-Zeilinger states for Rydberg-atom qubits
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• Shortcut-to-adiabaticity for coupled harmonic oscillators
• Quantum speed limit time of a qubit system with non-Hermitian detuning