Distributed entangled photonic states and applications

自从量子力学诞生以来，人们一直在争论量子系统为什么会有这样的行为。可以在不相互作用的情况下瞬间影响彼此状态的粒子，永远不能确定地测量的量，以及波函数是关于信息而不是具体的物理性质的概念，都是每个物理学家都在思考的难题。然而，无论它有什么神秘之处，新的科学往往会带来新的技术，在过去的25年里，物理学家们已经意识到，量子力学的这些奇怪特性确实可能被用于革命性的新信息处理机器。其中包括：量子密码学、超高速计算、以前所未有的精度进行测量和一种形式的隐形传态。其中有几项依赖于量子纠缠，而量子纠缠现在被认为是实现这些新技术的关键性质。利用纠缠的一个主要问题是，当具有这些特殊关联的粒子通过光、振动或碰撞与环境相互作用时，纠缠很快就会被摧毁。纠缠的迅速丧失降低了它们在上述任务中的表现，令人失望。我们研究的第一部分用一种名为蒸馏的技术来解决这个问题。它包括提纯一组粒子，以获得几个高度相关和孤立的粒子。我们研究的粒子是激光与非线性材料相互作用产生的光子。在专门设计的反射镜、探测器和半反射镜的组合中测量一些光子，可以将退化的纠缠态转换为更干净的纠缠态。在过去的几年里，初步实验已经成功地产生了这种状态，研究了它们的退化，或者试图在不分离它们的情况下提高它们的性能。我们的目标是分离光子群，在本地作用于它们(就像在真实的通信系统中所需要的那样)，并增强它们的有效纠缠。为了实现这一目标，需要开发几种工具。首先，光子具有非常多的可能特性，例如波长或方向。我们需要确保所需的纠缠以正确的方式存在于光的量子态中，以便我们能够利用它。其次，规定状态所需的大量维度通常可能需要同样大量的测量来表征它。我们需要开发数学方法，通过部分测量可以提取纠缠量的严格界限。第三，这些部分测量有些复杂，需要新的探测器。这样的探测器已经建成，显示出令人振奋的结果。这些光子数和光相关探测器的复杂性需要更详细地研究。为此，我们将使用基于最近演示的量子探测器层析成像协议的技术。这一过程类似于医学成像，使我们能够全面了解我们的新探测器的运行情况，从而表明它们确实可以量化我们提取的纠缠。我们项目的另一个方面是测量科学，计量学。挑战在于用有限的资源来测量特定的量，在这种情况下，是光子。众所周知，使用纠缠光子可以提供比使用经典光所能获得的精度更高的精度。因此，我们需要制作特殊的光量子态(类似于项目第一部分中使用的量子态)，使用很少的光子来实现这种超经典测量精度，即使在存在环境干扰的情况下也是如此，以便它们在现实世界中的应用中将是有用的。我们相信，这两个研究项目都将改进和发展量子通信和高精度计量的工具。

Since the birth of Quantum Mechanics, it has been debated exactly why quantum systems behave the way they do. Particles that can instantaneously affect each other's state without interacting, quantities that can never be measured with certainty and the notion that the wavefunction is about information, rather than concrete physicality, are puzzles that every physicist ponders. Whatever its mystery, however, new science often gives rise to new technologies, and in the last 25 years physicists have realized that these strange properties of quantum mechanics may indeed be used for revolutionary new information processing machines. Among these are: quantum cryptography, ultra-fast computation, measurements with unprecedented precision and a form of teleportation. Several of these rely on quantum entanglement, which is now recognized as the crucial property enabling these new technologies. A major problem for exploiting entanglement is that it is quickly destroyed when the particles possessing these special correlations interact with the environment, though light, vibrations or collisions. The rapid loss of entanglement decreases their performance at the aforementioned tasks disappointingly.The first part of our research addresses this problem with a technique called distillation. It involves purifying a collection of particles to obtain a few highly correlated and isolated ones. The particles we study are photons resulting from the interaction between lasers and non-linear materials. Measuring some of the photons in a specifically designed combination of mirrors, detectors and half mirrors transforms degraded entangled states into cleaner ones. Preliminary experiments have succeeded in the last years in producing such states, studying their deterioration or trying to enhance their performance without separating them. Our aim is to separate the groups of photons, act on them locally (as would be required in a real communications system) and enhance their useful entanglement. To achieve this goal several tools need to be developed. First, photons have a very large number of possible characteristics, such as wavelength or direction. We need to ensure that the desired entanglement exists in the quantum state of the light in the right way that we can exploit it. Second, the large number of dimensions required to specify the state might normally require a similarly large number of measurements to characterize it. We need to develop mathematical methods where rigorous bounds on the amount of entanglement can be extracted with partial measurements. Third, these partial measurements are somewhat elaborate and need novel detectors. Such detectors have been built, showing promising results. The complexity of these photon number and photo-correlation detectors needs to be studied in more detail. To do so we will use techniques based on recently demonstrated quantum detector tomography protocols. This process, which has analogies to medical imaging, allows us to build up a full picture of the operation of our new detectors, and to thereby show that they can indeed quantify the entanglement we have distilled. Another aspect of our project is the science of measurements, metrology. The challenge lies in measuring a certain quantity with a limited amount of resources, in this case, photons. It is known that using entangled photons gives a precision beyond what can be obtained using classical light. Therefore we need to craft special quantum states of light (similar to the ones used in the first part of the project) with few photons that are designed to attain this super-classical measurement precision even when there are environmental disturbances, so that they will be useful in real-world applications. We believe that both these research projects will improve and develop the tools for quantum communication and high-precision metrology.