基于双模波导中光场横向模式的量子纠缠的经典模拟

【作者】 张汛；

【导师】 符建；

【作者基本信息】 浙江大学 ， 光通信技术， 2006， 硕士

【摘要】 量子纠缠是量子力学中最基本也是最独特的性质之一,由于它是实现量子计算和量子隐形传态的关键,在国际上得到了广泛关注和深入研究。 本文首先介绍了以量子计算为代表的量子信息学,量子纠缠的基本性质以及量子纠缠在量子信息学中的重要性。然后介绍了一种基于双模波导中光场横向模式的量子计算方案,该方案将波导中光场的横向模式编码为量子比特,并基于非线性光学实现了控制非门。在此基础上,本文提出了一种利用光场横向模式实现量子纠缠的经典模拟的思想,利用控制非门或线性光学器件实现的模式纠缠态作为量子纠缠态的经典模拟,并对这种模式纠缠态的性质进行了研究。这篇论文主要的工作如下: 首先,利用有限差分光束传播方法(FD-BPM)对基于非线性光学实现模式纠缠态的方案进行计算机模拟,通过基于Bell不等式的相关测量,得到模式纠缠态中两个场的相关函数,这个相关函数能够对Bell不等式产生破坏,证明模式纠缠态中的两个光场之间存在一种非局域的关联,可以作为量子纠缠态的经典模拟。进一步,本文建立了一个由随机相位差标定的系综模型来对模式纠缠态进行描述。 然后本文提出一种全新的基于线性光学的方案来实现两个光场的模式纠缠态。对这个方案进行的计算机模拟结果表明,这种模式纠缠态可以产生和量子纠缠态完全类似的相关函数,同样能够对Bell不等式产生破坏。这种方案更清晰地说明随机相位系综能够对模式纠缠态所显示的非局域性质进行准确的刻画,非局域性质很有可能就来源于这种随机相位机制。 接下来对线性光学方案进行推广,利用三个光场实现三粒子GHZ态的经典模拟。由GHZ定理可知,三粒子的完全关联可以给出量子纠缠存在的非统计判据,这种判据比基于统计性质的Bell不等式更为可靠。进一步的计算机模拟结果显示三个经典光场实现的模式纠缠态的相关函数与量子GHZ态完全类似,并且得到了模式纠缠态中非局域关联的非统计判据。这进一步证明了利用波导中横向模式来实现量子纠缠的可行性。 本文提出的实现量子纠缠的经典模拟方案在现有的实验条件下是完全可以实现的,因此我们进行了一些实验方面的工作,为进一步的实验验证作准备。文章的结尾给出了讨论和总结。更多还原

【Abstract】 Quantum entanglement is one of the most fundamental and most special properties of quantum mechanics;it attracts wide attentions and in-depth researches due to the importance of quantum entanglement in quantum information.In this paper, we first introduce quantum information, the properties of quantum entanglement and the importance of quantum entanglement in quantum information. Then we introduce a quantum computation scheme based on optical transverse modes in multimode waveguide. In the scheme, quantum bits are encoded by using optical transverse modes, and CNOT gate is implemented by using nonlinear optics. Based on this, we propose a new conception of the so-called "mode-entangled states" to realize the classical simulation of quantum entangled states, which can be produced by CNOT gate or linear optical components. Further, we study some properties of the mode-entangled states. The main work of this paper is as follow:First, we simulate the nonlinear optical scheme using finite difference beam propagation method, and obtain correlation function of the two fields in mode entangled states based on correlation measurement of Bell inequality, the correlation function violate the Bell inequality, which proves there is nonlocal correlation between the two fields. Thus, the mode entangled states can be regarded as the classical simulation of the quantum entangled states. Further, we use an ensemble labeled by phase difference to describe mode entangled states.After that, we proposed a new scheme based on linear optics to realize mode entangled states. The numerical simulation results show that the correlation function of mode entangled states is quite similar to quantum entangled states, which can violate the Bell inequality. This scheme has proved that the phase difference ensemble can be used to describe the nonlocal correlation, and the nonlocal properties may originate from the random phase mechanism.And then we generalize the linear optical scheme to realize the GHZ states of three particles using three classical fields. According to GHZ theorem, the full correlation of three particles can give the nonstatistical criterion of quantum entanglement, which is more reliable than Bell inequality, which is based on statistical property. Further, we obtain the nonstatistical criterion of nonlocal correlation of mode entangled states, which again prove the validity of using classical fields to realize the classical simulation of quantum entanglement.The nonlinear and linear optical schemes proposed in the paper can be carried out in current condition;hence we have some experimental research to prepare the experimental verification. At last we give some discussion and conclusion.更多还原