基于离散与连续变量系统的混合纠缠态的非局域关联性

Nonlocal Correlations for Hybrid Entanglement with Discrete and Continuous Variables

研究离散变量与连续变量系统在纠缠态下的非局域关联性是量子信息处理中的基本理论与应用课题。对于局域隐变量理论的Bell不等式的违背可以很好地体现这些关联。在本文中,我们对量子比特自旋操作与谐振子旋转宇称操作进行联合测量,研究了量子比特与谐振子相干态的纠缠对Bell不等式的影响,并且证明,当量子比特与谐振子之间的纠缠接近最大值时,二者的非局域关联几乎最大限度地违背了Bell不等式。之后通过对Mermin-Klyshko不等式的违背,进一步研究了一个或多个比特与两个谐振子相干态纠缠的系统的非局域关联性。结果表明随着谐振子相干态的振幅增大,非局域性也会快速增强,同时,相干态振幅取值适中,就能使Mermin-Klyshko不等式接近最大违背。

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 a qubit 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.