A. Aiello, J. P. Woerdman
We review a few useful concepts about polarization measurements in the quantum domain. Using a perfectly general formalism, we show how to build the quantum counterpart of some classical quantities like Stokes parameters and Mueller matrices, which are well known in classical polarization-measurement theory.
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An example of a coherent measurement for the direct evaluation of the degree of polarization of a single-mode optical beam is presented. It is applied to the case of great practical importance where depolarization is caused by polarization mode dispersion. It is demonstrated that coherent measurement has the potential of significantly increasing the information gain, compared to standard incoherent measurements.
Sequential unsharp measurement of photon polarization
本文提出基于部分偏振分束器二叉树的实验方案实现光子偏振序列非锐利测量，建立通用形式体系，并推导了后选择与再选择下的反常平均值和二阶关联函数。
We demonstrate a coherent quantum measurement for the determination of the degree of polarization (DOP). This method allows to measure the DOP in the presence of fast polarization state fluctuations, difficult to achieve with the typically used polarimetric technique. A good precision of the DOP measurements is obtained using 8 type II nonlinear crystals assembled for spatial walk-off compensation.
We produce polarization entangled states with variable degree of entanglement for twin photons. Entanglement in polarization is coupled to entanglement in position that produces transverse coincidence interference fringes. We show both theoretically and experimentally that, due to this coupling, we can use the interference pattern to measure the polarization degree of entanglement.
We consider a photon beam incident on a stack of polarizers as an example of a von Neumann projective measurement, theoretically leading to the quantum Zeno effect. The Maxwell theory (which is equivalent to the single photon Schrödinger equation) describes measured polarization phenomena, but without recourse to the notion of a projective measurement.
Recent theoretical and experimental studies have given raise to new aspects in quantum measurements and error-disturbance uncertainty relations. After a brief review of these issues, we present an experimental test of the error-disturbance uncertainty relations in photon polarization measurement. Using generalized, strength-variable measurement of a single photon polarization state, we experimentally evaluate the error and disturbance in the measurement process and demonstrate the validity of recently proposed uncertainty relations.
Protective measurements of photon polarization using a temporal pointer
该研究利用光子到达时间作测量指针，通过光学环实现1-9个可控的保护测量阶段，在无需初始态信息的情况下测得光子偏振期望值，证明保护性测量可提供非先验的真实信息增益。
Here we propose an implementation of all possible Positive Operator Value Measures (POVMs) of two-photon polarization states. POVMs are the most general class of quantum measurements. Our setup requires linear optics, Bell State measurements and an entangled three-photon ancilla state, which can be prepared separately and in advance (or 'off-line'). As an example we give the detailed settings for a simultaneous measurement of all four Bell States for an arbitrary two-photon polarization state, which is impossible with linear optics alone.
A protocol of measurements providing direct, complete and single-valued recover of all a-priori unknown parameters of biphoton polarization qutrits
该研究提出一种测量协议，利用测量结果概率构造显式表达式，以完整恢复双光子偏振 qutrit 的所有先验未知参数。
We study repeated (noncontinuous) measurements on the electron spin in a quantum dot and find that the measurement technique may lead to a different met$ or mechanism to realize nuclear spin polarization. While it may be used in any case, the method is aimed at the further polarization, providing that nuclear spins have been polarized by the existent electrical or optical methods. The feasibility of the method is analyzed. The existing techniques in electron spin measurements are applicable to this scheme. The repeated measurements \emph{deform} the structures of the nuclear wave function and …
Features of biphoton polarization-frequency ququarts are considered. Their wave functions are defined as functions of both polarization and frequency variables of photons with the symmetry obligatory for two-boson states taken into account. In experiments, biphoton ququarts can display different features in dependence on whether experiments involve purely polarization or (alternatively) polarization-frequency measurements. If in experiments one uses only polarization measurements, the originally pure states of ququarts can be seen as mixed biphoton polarization states. Features of such states …
A sequential measurement of two non-commuting quantum observables results in a joint probability distribution for all output combinations that can be explained in terms of an initial joint quasi-probability of the non-commuting observables, modified by the resolution errors and back-action of the initial measurement. Here, we show that the error statistics of a sequential measurement of photon polarization performed at different measurement strengths can be described consistently by an imaginary correlation between the statistics of resolution and back-action. The experimental setup was design…
Non-classical joint measurements can hugely improve the efficiency with which certain figures of merit of quantum systems are measured. We use such a measurement to determine a particular figure of merit, the purity, for a polarization qubit. In the process we highlight some of subtleties involved in common methods for generating decoherence in quantum optics.
Active polarization stabilization of fields in an optical fiber for protective measurements
通过在双折射光纤中主动稳定偏振，利用光子计数实现更高信号和更低背景的Zeno保护测量
We propose a new scheme for measuring the quantum efficiency of photon counting detectors by using correlated pho-tons. The measurement technique is based on a 90 rotation of the polarization of one photon member of a correlated pair produced by parametric down-conversion, conditioned on the detection of the other correlated photon after polarization selection. We present experimental results obtained with this scheme.
The essential feature of weak measurements on quantum systems is the reduction of measurement back-action to negligible levels. To observe the non-classical features of weak measurements, it is therefore more important to avoid additional back-action errors than it is to avoid errors in the actual measurement outcome. In this paper, it is shown how an optical weak measurement of diagonal (PM) polarization can be realized by path interference between the horizontal (H) and vertical (V) polarization components of the input beam. The measurement strength can then be controlled by rotating the H a…
Quantum measurements that use the entangled photons' polarization to encode quantum information require calibration and alignment of the measurement bases between spatially separate observers. Because of the changing birefringence in optical fibers arising from temperature fluctuations or external mechanical vibrations, the polarization state at the end of a fiber channel is unpredictable and time-varying. Polarization tracking and stabilization methods originally developed for classical optical communications cannot be applied to polarization-entangled photons, where the separately detected p…
A novel method for the direct measurement of the degree of polarization is described. It is one of the first practical implementations of a coherent quantum measurement, the projection on the singlet state. Our first results demonstrate the successful operation of the method. However, due to the nonlinear crystals used presently, its application is limited to spectral widths larger than ~8nm.
Polarization of light is one of the fundamental concepts in optics. There are many ways to measure and characterise this feature of light but at the fundamental level it is quantum mechanics that imposes ultimate limits to such measurements. Here, I calculate the quantum limit to a precision of a polarization measurement of classical coherent light. This is a multiparameter estimation problem with a crucial feature of noncommuting optimal observables corresponding to each parameter which prohibits them to be measured at the same time. I explicitly minimize the quantum Holevo-Cramer-Rao bound w…
We perform a proof-of-principle demonstration of the measurement-device-independent quantum key distribution (MDI-QKD) protocol using weak coherent states and polarization-encoded qubits over two optical fiber links of 8.5 km each. Each link was independently stabilized against polarization drifts using a full-polarization control system employing two wavelength-multiplexed control channels. A linear-optics-based polarization Bell-state analyzer was built into the intermediate station, Charlie, which is connected to both Alice and Bob via the optical fiber links. Using decoy-states, a lower bo…
We propose a nuclear-spin-polarization protocol in a general evolution-and-measurement framework. The protocol works in a spin-star configuration, where the central spin is coupled to the surrounding bath (nuclear) spins by flip-flop interaction of equal strength and is subject to a sequence of projective measurements on its ground state. Then a nondeterministic nuclear spin polarization could be implemented by entropy reduction through measurement. The optimized measurement-interval $τ_{\rm opt}$ is analytically obtained in the near-resonant condition, which is relevant to the nuclear spins' …
The sets of after-measurement states for standard and generalized quantum measurements are compared. It is shown that for a SIC-POVM generalized measurement, the ratio of the volume of the set of after-measurement states and the volume of the simplex generated by individual outcomes quickly tends to zero with increase of the number of dimensions. The volumes used are based on the Hilbert-Schmidt norm. Some consequences on actual realizations, having finite collections of systems are discussed.
The idea that wave-function collapse is a physical process stems from a misunderstanding of probability and the role it plays in quantum mechanics.
Aiming the construction of quantum computers and quantum communication systems based on optical devices, in this work we present possible implementations of quantum and classical CNOTs gates, as well an optical setup for generation and distribution of bipartite entangled states, using linear optical devices and photon number quantum non-demolition measurement.
A one-way quantum key distribution scheme based on intrinsically stable Faraday-mirror type Michelson interferometers with four-port polarizing beampslitters has been demonstrated which can compensate for birefringence effects automatically. The encoding is performed with phase modulators, but decoding is accomplished through measurement of the polarization state of Bob's photons. An extinction ratio of about 30dB was maintained for several hours over 50km of fiber at 1310nm without any adjustment to the setup, which shows its good potential for practical systems
The emerging strategy to overcome the limitations of bulk quantum optics consists of taking advantage of the robustness and compactness achievable by the integrated waveguide technology. Here we report the realization of a directional coupler, fabricated by femtosecond laser waveguide writing, acting as an integrated beam splitter able to support polarization encoded qubits. This maskless and single step technique allows to realize circular transverse waveguide profiles able to support the propagation of Gaussian modes with any polarization state. Using this device, we demonstrate the quantum …
The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets. By using the approach of adding noises to measurement operators we present a complete classification of the incompatibility of a given measurement assemblage with $n$ members. Detailed examples are given to the incompatibility for unbiased qubit measurements based on semidefinite programm.
We propose a feasible scheme to create $n$-party ($n\geq 2$) polarization-entangled photon states in a controllable way. The scheme requires only single-photon sources, single-photon quantum non-demolition measurement (SP-QNDM) and simple linear optical elements, usually with high perfections. The SP-QNDM acts as a non-destructive projection measurement onto the wanted entangled states and filters out the unwanted terms. Our scheme in fact realizes entanglement of non-interacting photons; the interaction occurs only implicitly in the optical elements and SP-QNDM. We also briefly consider purif…
Assessment of Polarization Entanglement Source: Photon Counting and Correlation Measurement
本文提出了一个全面的光子计数和相关性测量测试框架，用于可扩展且可重复地表征缺乏第三方认证的电信波长偏振纠缠商用源，通过严格的概率方法讨论了真实和虚假符合的界限，并对三种商用源进行了QST、偏振可见度测量等最先进水平的比较分析。
Estimation of nuclear polarization via discrete measurement of NV center spin evolution
提出一种通过测量NV中心自旋相干性演化来估计13C核极化的方法，利用离散测量点获取信息，无需直接干预环境，具有简单且资源消耗少的优势，并在八核自旋环境中验证了其准确性。
The wave plate is a basic device for transforming and measuring the polarization states of light. It is known that the transformation of light by means of two wave plates makes it possible to measure the state of polarization in an arbitrary basis. The finite spectral width of the light, however, leads to a chromatic aberration of the polarization quantum transformation caused by the parasitic dispersion of the birefringence of the plate material. This causes systematic errors in the tomography of quantum polarization states and significantly reduces its accuracy. This study is a development o…
We present a set of notes, meant for quick reference, on radiative spin polarization, computer algorithms and spin matching in electron storage rings.
By limiting the resolution of quantum measurements, the measurement induced changes of the quantum state can be reduced, permitting subsequent measurements of variables that do not commute with the initially measured property. It is then possible to experimentally determine correlations between non-commuting variables. The application of this method to the polarization statistics of entangled photon pairs reveals that negative conditional probabilities between non-orthogonal polarization components are responsible for the violation of Bell's inequalities. Such negative probabilities can also b…
We propose a stereographical-visualization scheme for a polarization state by two-dimensional imaging of a weak value with a single setup. The key idea is to employ Laguerre-Gaussian modes or an optical vortex beam for a probe state in weak measurement. Our scheme has the advantage that we can extract information on the polarization state from the single image in which the zero-intensity point of the optical vortex beam corresponds to a stereographic projection point of the Poincare sphere. We experimentally perform single-setup weak measurement to validate the stereographical relationship bet…
Modification of Hanle and polarization recovery curves under interplay of hopping and quantum measurement back action
该研究考虑电子跳跃与量子测量反作用的相互作用，分析定域化电子自旋极化对磁场的依赖性，发现二者在不同几何结构中效应相似或竞争，有助于解释实验结果和研究量子测量基本效应。
The problem considered is how to map the concepts of Quantum Theory (QT) to elements of a psychological experiment. The QT concepts are "measurement," "state," and "observable". The elements of a psychological experiment are trial, stimulus, instructions, questions, and responses.
Generation of particular polarization states of light, encoding information in polarization degree of freedom, and efficient measurement of unknown polarization are the key tasks in optical metrology, optical communications, polarization-sensitive imaging, and photonic information processing. Liquid crystal devices have proved to be indispensable for these tasks, though their limited precision and the requirement of a custom design impose a limit of practical applicability. Here we report fast preparation and detection of polarization states with unprecedented accuracy using liquid-crystal cel…
We present a general formulation of the ground state binding energy of a shallow hydrogenic impurity in spherical quantum dot with parabolic confinement, considering the effects of polarization and self energy. The variational approach within the effective mass approximation is employed here. The binding energy of an on-center impurity is computed for a $\mathrm{GaAs}$/ $\mathrm{{Al}_{x}{Ga}_{1-x}As}$ quantum dot as a function of the dot size with the dot barrier as parameter. The influence of polarization and self energy are also treated separately. Results indicate that the binding energy in…
This paper has been withdrawn by the author. In this paper I present some reasons to adopt an holistic point of wiev, eliminating a boundary subject/object in the measurement. I review shortly Everett's and Cramer's positions, casting light on their flaws, to introduce a logical motivation to thinking to an experiment as a totality in which everything is entangled.
The polarization emerging in the subsequent scattering processes can never exceed $1$ which corresponds to the fully polarized pure state. This property is shown to be provided by the addition rule similar to that for relativistic velocities never exceeding the speed of light. The cases of spin $1/2$ and $1$ are considered. The photon linear polarization in Thomson scattering is monotonically increasing. This directness is shown to be a consequence of spin measurement procedure and may be the particular example of ithe anticipated relation between quantum measurement and time irreversibility. …
We consider the bipartite state of a two-photon polarization system and obtain the exact analytical expression for the von Neumann entropy in the particular case of a 5-parameter polarization density matrix. We investigate and graphically illustrate the dependence of the entropy on these five parameters, in particular, the existence of exotic, transition from exotic to non-exotic, and non-exotic states, where the quantum conditional entropy is negative, both positive and negative, and positive, respectively. We study the "cooling" or "heating" effect that follows from the reduced density of ph…
We demonstrate the use of cylindrical vector beams - beams with spatially varying polarization - for detecting and preparing the spin of a warm rubidium vapor in a spatially dependent manner. We show that a modified probe vector beam can serve as an atomic spin analyzer for an optically pumped medium, which spatially modulates absorption of the beam. We also demonstrate space-variant atomic spin by optical pumping with the vector beams. The beams are thus beneficial for making singleshot polarization-dependent measurements, as well as for providing a means of preparing samples with position-de…
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