Quantum optics routinely uses beam splitters to generate entanglement, including in pioneering experiments conducted by Hanbury-Brown and Twiss and Hong, Ou, and Mandel. The quantum interference at beam splitters lies at the heart of what makes boson sampling hard to emulate by classical computers and is a vital component of quantum computation with light. Yet, despite overwhelming positive evidence, the conjecture that beam splitters with equal reflection and transmission probabilities generate the most entanglement for any state interfered with the vacuum has remained unproven for almost two decades [Asbóth et al., Phys. Rev. Lett. 94, 173602 (2005)]. We prove this conjecture for ubiquitous entanglement monotones including mixed-state generalizations of entanglement entropy and purity by uncovering monotonicity and convexity with respect to photon loss for these monotones. At the same time, we highlight an infinite class of lesser-used monotones for which the conjecture fails. Because beam splitters are so fundamental, our results yield numerous corollaries for quantum optics, including proof of a recent conjecture for the evolution of a measure of quantumness through loss and a more efficient computational strategy for optimizing entanglement generation over linear optics. These results justify the value of seeking mathematical rigour behind commonly accepted facts and the danger of trusting them unconditionally.
Beam splitters are routinely used for generating entanglement between modes in the optical and microwave domains, requiring input states that are not convex combinations of coherent states. This leads to the ability to generate entanglement at a beam splitter as a notion of quantumness. A similar, yet distinct, notion of quantumness is the amount of entanglement generated by two-mode squeezers (i.e., four-wave mixers). We show that squeezed-vacuum states, paradoxically, both minimize and maximize these notions of quantumness, with the crucial resolution of the paradox hinging upon the relative…
Quantum Beam Splitter as a Deterministic Entanglement Source: Exact Photon-Number Statistics, Hong-Ou-Mandel Interference, and von Neumann Entropy Scaling from Balanced Inputs
Increasing relative nonclassicality quantified by standard entanglement potentials by dissipation and unbalanced beam splitting
如果单模非经典光在分束器上与真空结合，则输出态是纠缠的。如[Phys. Rev. Lett. 94，173602（2005）]，通过测量平衡无损分束器的输出态纠缠，可以量化输入态的非经典性。这些非经典性的度量（称为纠缠势）原则上可以基于各种纠缠度量，导致负性（NP）和并发（CP）势，以及纠缠的相对熵（REEP）势。我们寻找最大的非经典性，这可以通过比较任意两个量子比特态的纠缠度量和那些可以通过平衡无损分束器从光子数量子比特产生的纠缠度量来实现，其中量子比特基态是真空和单光子态。令人惊讶的是，我们发现，最大的非经典性，测量的REEP为一个给定的NP值，可以增加（如果NP<0.527）通过使用可调分束器或通过振幅阻尼的平衡分束器的输出状态。我们还表明，最大的非经典性，测量的NP为一个给定的值的REEP，可以通过移相增加。纠缠本身并没有增加这些本地损失，但不同的措施可能的比例受到影响。此外，我们表明，部分混合态可以比纯态和完全混合态更非经典，通过比较NP对于一个给定的值的REEP。这意味着并非所有的纠缠度量都可以作为纠缠势。另外，一个平衡的无损分束器并不总是将其输入态的全部非经典性转换为其输出模的纠缠。至少在本文分析的情况下，应用有耗分束器可以解决这个问题。
In this paper we address the problem of optimizing an unbalanced Mach-Zehnder interferometer, for a given pure input state and considering a specific detection scheme. While the optimum transmission coefficient of the first beam splitter can be uniquely determined via the quantum Fisher information only [Phys. Rev. A 105, 012604 (2022)], the second beam splitter transmission coefficient is detection-scheme dependent, too. We systematically give analytic solutions for the optimum transmission coefficient of the second beam splitter for three types of widely used detection schemes. We provide de…
The double-slit interferometer and the Mach-Zehnder interferometer (MZI) with balanced beam splitters are prototypical setups for investigating the quantum wave-particle duality. These setups induced a quantitative association of interferometric visibility (IVI) with the wave aspect of a single quantum system (WAQ). Recently, it was realized that quantum coherence (QC) can be better suited than IVI for quantifying the WAQ in complementarity relations. In this article, we investigate a MZI with biased beam splitters both in the input and the output, and we show that in some cases the IVI is not…
Passing a photon number state through a balanced beam splitter will produce an entangled state in which the phases of the two output beams are highly correlated. This entangled state can be viewed as a generalized form of a Schrodinger cat state where there is an equal probability amplitude for all possible phases. We show that Bell's inequality can be violated using this entangled state and two distant measuring devices that consist of a single-photon interferometer with a Kerr medium in one path, a set of single-photon detectors, and postselection based on a homodyne measurement. These entan…
In this paper we provide the answer to the following question: given an arbitrary pure input state and a general, unbalanced, Mach-Zehnder interferometer, what transmission coefficient of the first beam splitter maximizes the quantum Fisher information (QFI)? We consider this question for both single- and two-parameter QFI, or, in other words, with or without having access to an external phase reference. We give analytical results for all involved scenarios. It turns out that, for a large class of input states, the balanced (50/50) scenario yields the optimal two-parameter QFI, however this is…
Programmable Hong--Ou--Mandel interference in a giant-atom beam splitter
Center for Theoretical Physics & School of Physics and Optoelectronic Engineering, Hainan University（海南大学理论物理中心与物理光电工程学院）；Department of Microtechnology and Nanoscience, Chalmers University of Technology（查尔姆斯理工大学微技术与纳米科学系）
The cross-correlation sensitivity of two identical balanced photodiode heterodyne receivers is characterized. Both balanced photodiodes receive the same weak signal split up equally, a situation equivalent to an astronomical spatial interferometer. A common local oscillator (LO) is also split up equally and its phase difference between both receivers is stabilized. We show by semi-classical photon deletion theory that the post-detection laser shot noise contributions on both receivers must be completely uncorrelated in this case of passing three power splitters. We measured the auto- and cross…
Wigner entropy conjecture and the interference formula in quantum phase space
Wyant College of Optical Sciences, The University of Arizona（亚利桑那大学怀特光学科学学院）；DIENS, École Normale Supérieure, PSL University, CNRS, INRIA (QAT)（巴黎高等师范学院，PSL大学，法国国家科学研究中心，INRIA（QAT））
Twisted Gaussian Schell States in Quantum Optics: Twist-Assisted Nonclassicality and Entanglement
Universidade Federal do Rio de Janeiro（里约热内卢联邦大学）；Universidad del Bío-Bío（比奥比奥大学）；Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）；Universidade Federal de Santa Catarina（圣卡塔琳娜联邦大学）；Universidad de Concepción（孔塞普西翁大学）；Millennium Institute for Research in Optics, Universidad de Concepción（孔塞普西翁大学光学研究千年研究所）
Quantum optical effective-medium theory for layered metamaterials
超材料的量子光学始于一个问题，即有效介质理论是否适用于经典光学。总的来说，答案是否定的。对于主动等离子体，但也为一些被动的超材料，我们表明，一个额外的有效介质参数是必不可少的，除了有效的指数，即有效的噪声光子分布。只有有了这个额外的参数，人们才能预测超材料中光的量子态保持得有多好。在超材料的量子光学中，单独的有效折射率并不总是足够的，而一个附加的有效参数就足够了，这一事实既具有基础性又具有实际意义。本文从具有线性增益和损耗的介质的量子电动力学的拉格朗日描述出发，计算了量子光在层状超材料中沿任意方向传播的有效噪声-光子分布，从而详细和推广了我们最近的工作[ E. Amooghorban等人，物理修订版信函${\bf 110}$，153602（2013）]。有效折射率及其方向和偏振依赖性与经典有效介质理论相同。作为我们的主要结果，我们推导出被动和主动介质的有效噪声光子分布的值也取决于光的偏振和传播方向。有趣的是，对于TE-偏振光入射到无源超材料上，噪声光子分布减少到热分布，但对于TM-偏振光，它不是。我们说明了我们的量子光学有效介质理论的鲁棒性的准确预测功率谱和平衡零差检测的超材料的输出量子态。
The coherent one-way (COW) quantum key distribution (QKD) is a highly practical quantum communication protocol that is currently deployed in off-the-shelves products. However, despite its simplicity and widespread use, the security of COW-QKD is still an open problem. This is largely due to its unique security feature based on inter-signal phase distribution, which makes it very difficult to analyze using standard security proof techniques. Here, to overcome this problem, we present a simple variant of COW-QKD and prove its security in the infinite-key limit. The proposed modifications only in…
High-fidelity entangled photon pairs from a quantum-dot-based single-photon source
University of Basel（巴塞尔大学）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Ruhr-Universität Bochum（波鸿鲁尔大学）
