Journal of Quantum Optics, Volume. 28, Issue 2, 96(2022)
Nonlocal Correlations for Hybrid Entanglement with Discrete and Continuous Variables
Nonlocal correlations between discrete-variable and continuous-variable systems in an entangled state are not only of fundamental interest but also having applications in quantum information processing. These correlations are well manifested by violation of the Bell inequality imposed by theories of local realism. Based on the entanglement state of the hybrid system, which consists of the qubit of the discrete variable and the harmonic oscillator of the continuous variable system. We constructed a special operator, the rotated quantum number parity operator, that distinguishes between the displaced parity operator in previous studies. In this case, we investigated Bell inequality tests with entanglement between aqubit and coherent states of a harmonic oscillator based on joint measurements on the qubit’s spin and the oscillator’s rotated quantum number parity. Results showed that the obtained correlations nearly maximally violated the Bell inequality when the qubit-oscillator entanglement approaches its maximum value. Comparing to the displaced quantum number parity operator, the violate of Bell inequality in rotated quantum number parity operator increased rapidly to the maximal value as the amplitude increased. This result showed that the Bell signal of spin-rotated parity operator is simpler in terms of the varying scales and the experimental conditions in two-partite hybrid entangled state. We further explored the nonlocal correlations for the system with one or more qubits entangled with coherent states of two oscillators, evidenced by violation of the Mermin-Klyshko inequality. The results showed that the nonlocality was quickly strengthened as the amplitudes of the coherent state components increase, and the Mermin-Klyshko inequality can be nearly maximally violated for quite moderate values of the amplitudes of the coherent state components. It showed that the MK signal of spin-rotated parity operator had more obvious effect and and the simpler condition requirements in multi-partite hybrid entangled states. That enhanced the feasibility in experimental.
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YANG Shou-bang, SHEN Li-tuo, LIN Li-hua, YANG Zhen-biao, ZHONG Zhi-rong, ZHENG Shi-biao. Nonlocal Correlations for Hybrid Entanglement with Discrete and Continuous Variables[J]. Journal of Quantum Optics, 2022, 28(2): 96
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Received: Mar. 4, 2022
Accepted: --
Published Online: Oct. 14, 2022
The Author Email: YANG Shou-bang (ysbscuphy@163.com)