Testing quantum nonlocality of two-qubit entangled states under decoherence

Quantum nonlocality is one of the most fundamental characteristics of quantum theory. As a commonly used quantum state generated in experiments, the "X" state is a typical one in the research of open quantum systems, since it still maintains the stability of the "X" shape during the evolution. Using the Clauser-Horne-Harmony-Holt (CHSH) inequality, the quantum nonlocality testing of two "X" states associated with local transformation operations is studied under the Markov environment. The results show that in the phase damping environment, the two "X" states have the same CHSH inequality testing results with the increasing of the evolution time. Moreover, the maximum of quantum nonlocality test of the two "X" states will decrease nonlinearly. When 0.78<F<1, the maximum value Sm of testing quantum nonlocality will gradually transition from Sm>2 to Sm<2 with the increasing of the evolution time of the two "X" states, and the research on the quantum nonlocality test cannot be successfully carried out. In the amplitude damping environment, using the "X" state obtained by the local transformation operation have a longer evolution time for the successfully quantum nonlocality testing when F>1. In particular, when F=1, the "X" state with the density matrix $\rho _W$ cannot successfully perform the quantum nonlocality testing after the evolution time $\Gamma t > 0.22$. For the "X" state with density matrix ${\tilde \rho _W}$, the quantum nonlocality testing cannot be performed until the evolution time $\Gamma t > 0.26$. This results show that the local transformation operation of the "X" state is more conducive to the quantum nonlocality testing based on the CHSH inequality. Finally, the fidelity ranges of successfully testing the quantum nonlocality of the two "X" states in phase and amplitude damping environments are given in detail. The results show that, on the premise of quantum nonlocality testing successfully, the two types of "X" states evolving in the phase damping environment have the large range of valid fidelity. Meanwhile, at the same evolution time, the local transformation operation is helpful to improve the fidelity range of quantum nonlocality test in amplitude damping environment for "X" state with density matrix ${\rho _W}$.

unclassified

Quantum nonlocality testing of the “X” state based on the CHSH inequality in Markov environment

Bai-yun¹,

Gu²,

Shi-min³

et al. 2023

High-fidelity storage and on-demand retrieval of quantum states via a microwave waveguide

Dao-Quan¹,

Sun²,

He³

2022

On-demand quantum memory is an important step towards practical applications in various quantum information tasks such as long-distance entanglement distribution, quantum computation, and quantum networks. In this work, based on stimulated Raman adiabatic passage (STIRAP) protocol, we introduce a controllable delay between the reading and writing puleses so that the quantum state can be stored in the superconducting waveguide and finlly retrieved on demand with high fidelity. Through systematic numerical simulations, we find that if the duration of the writing pulse is set within a certain range, the readout unit is capable of retrieving the quantum state stored in the waveguide with high fidelity at any moment after a critical time. Moreover, we also investigate the robustness of our protocol, and find that the fidelity is robust against both the average number of thermal photons in the waveguide and the duration of the reading pulse. The numerical results also show that the area of the pulse in our protocol is only about one third of the pulse area in the original STIRAP protocol. This protocol might be uselful for sharing the entangled pairs between distant nodes, which is crucial to build quantum network.

Decoherence suppression for N-qubit states via weak measurement and environment-assisted measurement

Zhang¹,

Cong²,

Wang³

et al. 2022

All open quantum systems are affected by environmental noises due to their interactions with the external environment and inevitably suffer from decoherence. Hence, it is fundamentally important and necessary to investigate decoherence suppression for open quantum systems via proper control strategies. Inspired by feed-forward control in the classical control theory, this paper proposes a novel decoherence suppression scheme via weak measurement and environment-assisted measurement. We first take the single-qubit system as an example to illustrate steps of the proposed scheme. To be specific, the single-qubit system is transferred to a state that is more robust to environmental noises via pre-weak measurement operators and feed-forward control operators before the decoherence channel, a measurement is performed on the environment coupled to the protected qubit during the decoherence channel, and the initial state is recovered via reversed feed-forward control operators and post-weak measurement operators after the decoherence channel. The optimum post-weak measurement strength is derived by setting the normalized final state equal to the initial state. By considering the optimum post-weak measurement strength, analytical formulas of the total success probability and the total fidelity are deduced. The proposed scheme is applicable for protecting quantum states from arbitrary decoherence channels with at least one invertible Kraus operator although only the amplitude damping channel and the phase damping channel are taken into account. Provided that the decay rate of the amplitude or phase damping channel is completely known, one can always achieve unit fidelity even for heavy damping cases, which is the biggest advantage of the proposed scheme. Influences of several parameters including strengths of weak measurements, the initial state and the decay rate of the decoherence channel on the performance of decoherence suppression are analyzed, and detailed procedures of a single-qubit pure and mixed state protection are presented on the Bloch sphere, respectively. Subsequently, the Kronecker product is employed to construct operators of dimension $2^N \times 2^N$, the proposed scheme is extended to the general $N$-qubit case, and unified analytical formulas of the total success probability and the total fidelity are deduced. By applying the proposed scheme to the protection of two-qubit entangled states, it is demonstrated that post-weak measurement operators are not necessary sometimes because of the particular structure of two-qubit entangled states. Furthermore, two numerical simulations are designed to enhance the concurrence of two-qubit entangled states and improve the average fidelity of the standard quantum teleportation in a noisy environment. Analytical formulas of the improvement of concurrence and the average teleportation fidelity are deduced, and the superiority of the proposed scheme is highlighted in comparison with unprotected scenarios.