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Annalen der Physik

Preparation of Arbitrary High‐Fidelity Decoherence‐Free States for a Four‐Qubit Hybrid System via Whispering‐Gallery‐Mode Microresonator

Fang‐Fang Du, Ming Ma, Wenyao Liu

Published Feb 2, 2025• 1 citation

Abstract

Abstract With the assistance of the practical nonlinear interaction of a nitrogen‐vacancy (NV) center coupled with whispering‐gallery‐mode (WGM) microresonator, a heralded preparation protocol of four‐qubit hybrid decoherence‐free states (logical qubits) is presented, where a single logical qubit encoded on the state of the hybrid system composed of two polarization photons and two NV centers is fully protected against collective decoherence. Compared with the three‐qubit decoherence‐free states, the four‐qubit decoherence‐free states have higher dimensions, stronger collective decoherence resistance, richer quantum coherence and higher fault tolerance. For an ideal photon‐NV interaction, the efficiencies and fidelities of the hybrid decoherence‐free states can, in principle, be close to unity. Otherwise, being directed against a nonideal interaction, the two error‐heralded quantum blocks of the preparation process make their fidelities near‐perfect at the expense of slight reductions of their efficiencies. Moreover, this hybrid decoherence‐free states work in a heralded way and may be experimentally feasible with current technique on regulating the NV‐WGM microresonator system.

DOI: 10.1002/andp.202400435

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Abstract With the assistance of the practical nonlinear interaction of a nitrogen‐vacancy (NV) center coupled with whispering‐gallery‐mode (WGM) microresonator, a heralded preparation protocol of four‐qubit hybrid decoherence‐free states (logical qubits) is presented, where a single logical qubit encoded on the state of the hybrid system composed of two polarization photons and two NV centers is fully protected against collective decoherence. Compared with the three‐qubit decoherence‐free states, the four‐qubit decoherence‐free states have higher dimensions, stronger collective decoherence resistance, richer quantum coherence and higher fault tolerance. For an ideal photon‐NV interaction, the efficiencies and fidelities of the hybrid decoherence‐free states can, in principle, be close to unity. Otherwise, being directed against a nonideal interaction, the two error‐heralded quantum blocks of the preparation process make their fidelities near‐perfect at the expense of slight reductions of their efficiencies. Moreover, this hybrid decoherence‐free states work in a heralded way and may be experimentally feasible with current technique on regulating the NV‐WGM microresonator system.

We investigate the construction of two universal three-qubit quantum gates in a hybrid system. The designed system consists of a flying photon and a stationary negatively charged nitrogen-vacancy (NV) center fixed on the periphery of a whispering-gallery-mode (WGM) microresonator, with the WGM cavity coupled to tapered fibers functioning as an add-drop structure. These gate operations are accomplished by encoding the information both on the spin degree of freedom of the electron confined in the NV center and on the polarization and spatial-mode states of the flying photon, respectively. Compared with previous schemes, our proposed scheme leads to a reduction of time and resource consumption in the processing. Moreover, these gates work in a deterministic way with no extra qubits required, which is feasible with current technologies. Both proposed gate operations could be physically implemented in one step, which provides a promising approach for quantum information processing ranging from distributed quantum computation to long-distance quantum communication.

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We propose an efficient scheme for the realization of quantum information transfer and entanglement with nitrogen-vacancy (N-

V

) centers coupled to a high-

Q

whispering-gallery mode (WGM) microresonator. We show that based on the effective dipole-dipole interaction between the N-

V

centers mediated by the WGM, quantum information can be transferred between the N-

V

centers through Raman transitions combined with laser fields. This protocol may open up promising possibilities for quantum communications with the solid-state quantum electrodynamic cavity system.

We present an efficient scheme for the generation of entangled states of two spatially separated nitrogen-vacancy (NV) centers with two whispering-gallery-mode (WGM) microresonators, which are coupled either by an optical fiber-taper waveguide or by the evanescent fields of the WGM. We show that the steady state of the two NV centers can be steered into a singletlike state through a dissipative quantum dynamical process, where the cavity decay plays a positive role and can help drive the system to the target state. The protocol may open up promising perspectives for quantum communication and computation with this solid-state cavity quantum electrodynamic system.

Entanglement purification is of great importance in long-distance quantum communications and distributed quantum computations. Here we present an efficient scheme for the hyperentanglement purification (HP) of a two-photon system by using a high-dimensional logical gate device which is composed of atoms and a quantized whispering-gallery-mode microresonator. In the present scheme, one can complete the HP and entanglement storage in one step without resorting to additional qubits. Compared with the conventional HP schemes in which the two-qubit two-dimensional parity-checking measurements are used to correct the bit-flip errors, our scheme, which explored the high-dimensional controlled-flip operation, shows a wide distillation range with a higher fidelity. The remaining resources of the failed HP processing can be used to purify the other pair hyperentangled photons. Therefore, the efficiency of our scheme is higher than the previous schemes. The implementation of our HP is assisted by nitrogen-vacancy centers in optical microresonators, which could be achieved with current techniques.

Quantum router is a key element needed for the construction of future complex quantum networks. However, quantum routing with photons, and its inverse, quantum decoupling, are difficult to implement as photons do not interact, or interact very weakly in nonlinear media. In this paper, we investigate the possibility of implementing photonic quantum routing based on effects in cavity quantum electrodynamics, and present a scheme for single-photon quantum routing controlled by the other photon using a hybrid system consisting of a single nitrogen-vacancy (NV) center coupled with a whispering-gallery-mode resonator-waveguide structure. Different from the cases in which classical information is used to control the path of quantum signals, both the control and signal photons are quantum in our implementation. Compared with the probabilistic quantum routing protocols based on linear optics, our scheme is deterministic and also scalable to multiple photons. We also present a scheme for single-photon quantum decoupling from an initial state with polarization and spatial-mode encoding, which can implement an inverse operation to the quantum routing. We discuss the feasibility of our schemes by considering current or near-future techniques, and show that both the schemes can operate effectively in the bad-cavity regime. We believe that the schemes could be key building blocks for future complex quantum networks and large-scale quantum information processing.