Stefano Olivares
In this tutorial, we introduce the basic concepts and mathematical tools needed for phase-space description of a very common class of states, whose phase properties are described by Gaussian Wigner functions: the Gaussian states. In particular, we address their manipulation, evolution and characterization in view of their application to quantum information.
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Gaussian states -- or, more generally, Gaussian operators -- play an important role in Quantum Optics and Quantum Information Science, both in discussions about conceptual issues and in practical applications. We describe, in a tutorial manner, a systematic operator method for first characterizing such states and then investigating their properties. The central numerical quantities are the covariance matrix that specifies the characteristic function of the state, and the closely related matrices associated with Wigner's and Glauber's phase space functions. For pedagogical reasons, we restrict …
Tutorial: Optical quantum metrology
本教程围绕光学量子计量学展开，介绍非经典光为量子光子传感带来的性能优势，讲解参数估计基本原理并综述领域研究现状，帮助理解量子效应在测量领域的应用价值。
A Tutorial on Quantum Master Equations: Tips and tricks for quantum optics, quantum computing and beyond
本文是一份面向跨学科读者的量子主方程教程，系统讲解 Lindblad、Redfield、Floquet 等方法并辅以代码示例。
Two-photon absorption (TPA) and other nonlinear interactions of molecules with time-frequency-entangled photon pairs (EPP) has been predicted to display a variety of fascinating effects. Therefore, their potential use in practical quantum-enhanced molecular spectroscopy requires close examination. This paper presents in tutorial style a detailed theoretical study of one- and two-photon absorption by molecules, focusing on how to treat the quantum nature of light. We review some basic quantum optics theory, then we review the density-matrix (Liouville) derivation of molecular optical response, …
Tutorial: projector approach to master equations for open quantum systems
本教程系统介绍投影算符方法，展示如何从Nakajima-Zwanzig方程的不同微扰展开推导Brownian主方程、Born-Markov主方程和绝热消除，并通过四个具体例子说明其在开放量子系统中的应用。
Optomechanics of optically-levitated particles: A tutorial and perspective
本文以教程形式综述光悬浮粒子光力学的关键概念、实验与理论方法及当前研究进展，并展望新兴实验平台与未来理论发展方向，为初学者提供入门参考。
Gaussian states have played on important role in the physics of continuous-variable quantum systems. They are appealing for the experimental ease with which they can be produced, and for their compact and elegant mathematical description. Nevertheless, many proposed quantum technologies require us to go beyond the realm of Gaussian states and introduce non-Gaussian elements. In this Tutorial, we provide a roadmap for the physics of non-Gaussian quantum states. We introduce the phase-space representations as a framework to describe the different properties of quantum states in continuous-variab…
Tutorial: Hong-Ou-Mandel interference with Structured Photons
本教程系统分析结构光子中的HOM干涉效应，推导不同测量条件下的可见度闭式表达式，填补任意空间模式测量下理论综述空白，助力AI驱动新量子实验发现。
How to find optimal quantum states for optical micromanipulation and metrology in complex scattering problems: tutorial
本教程提出基于量子算符的综合框架，通过散射矩阵利用光的空间和量子自由度，实现复杂介质中的最优微操控与参数估计，并连接波控制、量子光学与真空物理等领域。
These notes, intended to be self contained and tutorial, present a direct, macroscopic approach to quantizing light inside a linear-response dielectric material when both spectral dispersion and spatial nonuniformity are present, but the spectral region of interest is optically transparent so that explicit treatment of the underlying physics of the medium is not needed. The approach taken is based on the macroscopic Maxwell equations and a corresponding Hamiltonian, without the use of Lagrangians or any dynamical model for the medium, and uses a standard mode-based quantization method. The tre…
We discuss the unique capabilities of programmable logic devices (PLD's) for experimental quantum optics and describe basic procedures of design and implementation. Examples of advanced applications include optical metrology and feedback control of quantum dynamical systems. As a tutorial illustration of the PLD implementation process, a field programmable gate array (FPGA) controller is used to stabilize the output of a Fabry-Perot cavity.
The purpose of this short tutorial paper is to review various criteria that have been used to characterize the quantum character of correlations in optical systems, such as "gemellity", QND correlation, intrication, EPR correlation and Bell correlation, to discuss and compare them. This discussion, restricted to the case of measurements of continuous optical variables, includes also an extension of known criteria for "twin beams" to the case of imbalanced correlations.
The purpose of this tutorial is to give a brief introduction to linear quantum control systems. The mathematical model of linear quantum control systems is presented first, then some fundamental control-theoretic notions such as stability, controllability and observability are given, which are closely related to several important concepts in quantum information science such as decoherence-free subsystems, quantum non-demolition variables, and back-action evasion measurements. After that, quantum Gaussian states are introduced, in particular, an information-theoretic uncertainty relation is pre…
We discuss recent developments in measurement protocols that generate quantum entanglement between two remote qubits, focusing on the theory of joint continuous detection of their spontaneous emission. We consider a device geometry similar to that used in well-known Bell-state measurements, which we analyze using a conceptually transparent model of stochastic quantum trajectories; we use this to review photodetection, the most straightforward case, and then generalize to the diffusive trajectories from homodyne and heterodyne detection as well. Such quadrature measurement schemes are a realist…
We introduce a protocol that maps finite-dimensional pure input states onto approximately Gaussian states in an iterative procedure. This protocol can be used to distill highly entangled bi-partite Gaussian states from a supply of weakly entangled pure Gaussian states. The entire procedure requires only the use of passive optical elements and photon detectors that solely distinguish between the presence and absence of photons.
Quantum imaging and metrology with undetected photons: a tutorial
本教程介绍了无诱导发射的诱导相干现象及其在量子成像与计量学中的应用，阐明如何利用未探测光子成像，并为研究人员提供理论基础、实验搭建指南及该子领域的全面概述。
Trapping, manipulating and probing ultracold atoms: a quantum technologies tutorial
本教程综述超冷原子的捕获、操控与探测关键技术，涵盖激光冷却、光镊、干涉测量及多种成像方法，旨在为初学者提供实验工具包的全面概览。
We show how to implement the optimal Gaussian $N$-to-$M$ cloning with linear optics and homodyne detection. We also show that the Gaussian $N$-to-$M$ cloning of known-phase coherent states can be performed with the fidelity $\sqrt \frac{2 M N}{2M N+M -N}$ by linear optics and homodyne detection, and with $\frac{2}{\sqrt{1+\frac{1}{N}}+\sqrt {1-\frac{1}{M}}}$ by utilizing quadrature squeezing. From the classical limit of the cloning (1-to-$\infty$ cloning), a necessary condition of continuous variable quantum key distribution using known-phase coherent states is provided.
Transforming Traditional Neural Networks into Neuromorphic Quantum-Cognitive Models: A Tutorial with Applications
本文通过教程形式展示如何用普通笔记本电脑将前馈、循环、储备池和贝叶斯神经网络转化为量子启发模型，以优化训练并赋予类人认知特性，从而降低量子技术的使用门槛。
The linear optical creation of Gaussian cluster states, a potential resource for universal quantum computation, is investigated. We show that for any Gaussian cluster state, the canonical generation scheme in terms of QND-type interactions, can be entirely replaced by off-line squeezers and beam splitters. Moreover, we find that, in terms of squeezing resources, the canonical states are rather wasteful and we propose a systematic way to create cheaper states. As an application, we consider Gaussian cluster computation in multiple-rail encoding. This encoding may reduce errors due to finite squ…
Laser-light (coherent-state) modulation is sufficient to achieve the ultimate (Holevo) capacity of classical communication over a lossy and noisy optical channel, but requires a receiver that jointly detects long modulated codewords with highly nonlinear quantum operations, which are near-impossible to realize using current technology. We analyze the capacity of the lossy-noisy optical channel when the transmitter uses coherent state modulation but the receiver is restricted to a general quantum-limited Gaussian receiver, i.e., one that may involve arbitrary combinations of Gaussian operations…
Implementing arbitrary multi-mode continuous-variable quantum gates with fixed non-Gaussian states and adaptive linear optics
针对多模高阶非高斯量子门高效实现研究不足的问题，提出仅用固定非高斯辅助态和自适应线性光学的测量式实现方法，资源效率与实验可行性更高，助力光量子容错计算发展。
Time-domain programmable beam-splitter operations for an optical phase-sensitive non-Gaussian state
本文提出一种基于环路的光学处理器，实现对相位敏感非高斯态的时域可编程分束器操作，并验证其高质量存储能力，为大规模通用量子信息处理奠定基础。
We analyze in details a scheme for cloning of Gaussian states based on linear optical components and homodyne detection recently demonstrated by U. L. Andersen et al. [PRL 94 240503 (2005)]. The input-output fidelity is evaluated for a generic (pure or mixed) Gaussian state taking into account the effect of non-unit quantum efficiency and unbalanced mode-mixing. In addition, since in most quantum information protocols the covariance matrix of the set of input states is not perfectly known, we evaluate the average cloning fidelity for classes of Gaussian states with the degree of squeezing and …
Linear canonical transformations of bosonic modes correspond to Gaussian unitaries, which comprise passive linear-optical transformations as effected by a multiport passive interferometer and active Bogoliubov transformations as effected by a nonlinear amplification medium. As a consequence of the Bloch-Messiah theorem, any Gaussian unitary can be decomposed into a passive interferometer followed by a layer of single-mode squeezers and another passive interferometer. Here, it is shown how to circumvent the need for active transformations. Namely, we provide a technique to simulate sampling fro…
Sequential and Programmable Squeezing Gates for Optical Non-Gaussian Input States
本研究整合高斯门与非高斯态生成技术，开发出可扩展可编程的光学量子计算平台，通过环形光路与时间同步实现非高斯态上的序列压缩门，保留Wigner函数负性，为大规模通用光量子计算提供基础。
We prove that a classical computer can efficiently sample from the photon-number probability distribution of a Gaussian state prepared by using an optical circuit that is shallow and local. Our work generalizes previous known results for qubits to the continuous-variable domain. The key to our proof is the observation that the adjacency matrices characterizing the Gaussian states generated by shallow and local circuits have small bandwidth. To exploit this structure, we devise fast algorithms to calculate loop hafnians of banded matrices. Since sampling from deep optical circuits with exponent…
We present an implementation of quantum logic gates via internal state dependent displacements of ions in a linear Paul trap caused by optical dipole forces. Based on a general quantum analysis of the system dynamics we consider specific implementations with alkaline earth ions. For experimentally realistic parameters gate infidelities as low as $10^{-4}$ can be obtained.
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