QND measurements for future gravitational-wave detectors

Second-generation interferometric gravitational-wave detectors will be operating at the Standard Quantum Limit (SQL), a sensitivity limitation set by the trade off between measurement accuracy and quantum back action, which is governed by the Heisenberg Uncertainty Principle. We review several schemes that allows the quantum noise of interferometers to surpass the SQL significantly over a broad frequency band. Such schemes may be an important component of the design of third-generation detectors.     

Diamagnetic levitation of a milligram-scale silica using permanent magnets for the use in a macroscopic quantum measurement

Verification of macroscopic quantum mechanics requires that the position measurement accuracy of mirrors of various mass scales reach the Standard Quantum Limit (SQL) derived from Heisenberg's uncertainty principle. At mg-scale, thermal noise of the suspension wire of the mirror is an issue to reach the SQL. We propose to use a magnetic levitation system consisting of permanent magnets and yokes, noting the fact that a silica mirror is diamagnetic, and have succeeded in the experimental verification to levitate a 0.1-1 mg silica mass. This is the first demonstration of the levitation system with this mass scale and this magnetic susceptibility scale using permanent magnets as far as we know. We also estimated major noise sources for a 0.1 mg silica mirror and found the noise level to be lower than the SQL at 400 Hz-18 kHz. In conclusion, the levitation system of a mg-scale mirror for the use in a macroscopic quantum measurement was realized.     

Design of the 10 m AEI prototype facility for interferometry studies

The AEI 10 m prototype interferometer facility is currently being constructed at the Albert Einstein Institute in Hannover, Germany. It aims to perform experiments for future gravitational wave detectors using advanced techniques. Seismically isolated benches are planned to be interferometrically interconnected and stabilized, forming a low-noise testbed inside a 100 m³ ultra-high vacuum system. A well-stabilized high-power laser will perform differential position readout of 100 g test masses in a 10 m suspended arm-cavity enhanced Michelson interferometer at the crossover of measurement (shot) noise and back-action (quantum radiation pressure) noise, the so-called Standard Quantum Limit (SQL). Such a sensitivity enables experiments in the highly topical field of macroscopic quantum mechanics. In this article we introduce the experimental facility and describe the methods employed; technical details of subsystems will be covered in future papers.     

Position and contextuality in Bohm''s causal completion of quantum mechanics

We argue that, in Bohm's formulation, the assumption stipulating the position probability density to be ψ² is both necessary and sufficient for satisfying the requirement of “noncontextuality” (absence of any dependence on the specifics of the measurement procedure) of the observable probabilities at the ensemble level. The reasons as to why position needs to have a special status in a causal completion of quantum mechanics are also discussed.     

Quantum theory of incompatible observations

Quantum theory allows the sequential measurement of incompatible observables in the course of repeated measurements. To get information about the observed system, all observations must be synthesized. This is the main idea of quantum tomographical methods. As shown in this paper, the maximum likelihood principle provides the best measure for relating the experimental data with predictions of quantum theory. Synthesis of incompatible observations appears to be a new quantum measurement described by a positive operator-valued measure. Besides this, the procedure finds the optimal state of the system, which best fits such a measurement.     

Simulating the effect of weak measurements by a phase damping channel and determining different measures of bipartite correlations in nuclear magnetic resonance

Quantum discord is a measure based on local projective measurements which captures quantum correlations that may not be fully captured by entanglement. A change in the measurement process, achieved by replacing rank-one projectors with a weak positive operator-valued measure (POVM), allows one to define weak variants of quantum discord. In this work, we experimentally simulate the effect of a weak POVM on a nuclear magnetic resonance quantum information processor. The two-qubit system under investigation is part of a three-qubit system, where one of the qubits is used as an ancillary to implement the phase damping channel. The strength of the weak POVM is controlled by varying the strength of the phase damping channel. We experimentally observed two weak variants of quantum discord namely, super quantum discord and weak quantum discord, in two-qubit Werner and Bell-diagonal states. The resultant dynamics of the states is investigated as a function of the measurement strength.     

量子非欧姆阻尼环境中的重核熔合概率及热核裂变速率

考虑处于量子非欧姆阻尼环境下的重核熔合及热核裂变系统的动力学,给出了数值模拟相应c数量子广义朗之万方程的方法。其中提出的产生任意关联量子色噪声的数值方法,适用于任意非马尔科夫过程噪声的产生。利用此方法计算了重核熔合概率,结果表明量子涨落对重核熔合具有“低抬高压”的效应:当粒子的初始动能小于（大于）临界初始动能时,量子涨落会增大（减小）粒子鞍点通过概率。非欧姆阻尼环境中粒子稳定通过概率随δ值的变化是非单调的,且当粒子初始动能小于（大于）临界初始动能,量子涨落会使稳定通过概率随δ值变化曲线的极大值位置向右（向左）漂移。此外,在热核裂变系统中,超欧姆阻尼环境会增大裂变速率,而量子涨落不仅显著增大裂变速率,还使裂变速率随δ值变化曲线的极大值位置发生漂移。Dynamics of heavy-ion fusion and nuclear fission system in a quantum non-Ohmic environment have been considered and a numerical simulation method to solve the corresponding c-number quantum generalized Langevin equation is proposed. The method of generating quantum colored noise with arbitrary correlation can be applied to generate noise of arbitrary non-Markov process. Calculating fusion probability of heavy nuclei with this method, the result has shown that the passing probability is enlarged (decreased) by the quantum fluctuation when the initial kinetic energy of the particle is less than (greater than) the critical initial kinetic energy. Steady passing probability of particle in non-Ohmic environment versus is nonmonotonic. Quantum fluctuation makes the maximum position of the curve drift towards right (left), when the initial kinetic energy of the particle is less than (greater than) the critical initial kinetic energy. Furthermore, nuclear fission rate is larger in super-Ohmic environment. Quantum fluctuation enlarges nuclear fission rate and makes the the maximum position of nuclear fission rate versus δ drift.     

Quantization as Selection Problem

Quantum systems exhibit a smaller number of energetic states than classical systems (A. Einstein, 1907, Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme, Ann. Phys. 22, 180ff). We take up the selection criterion for this in two parts. (1) The selection problem between classical and nonclassical mechanical systems is formulated in terms of possible and impossible configurations (among others, this overcomes the difficulties occurring when discussing the behavior of quantum particles in terms of paths). (2) The (nonclassical) selection of the quantum states is formulated, using recurrence relations and the energy law. The reformulation of “quantization as eigenvalue problem” in terms of “quantization as selection problem” allows one to derive Schrödinger’s stationary equation from classical mechanics through a straightforward and unique procedure; the nonstationary and multibody equations are subsequently acquired within the same frame. In contrast to the (classical) eigenvalue problem, the (nonclassical) selection problem can be formulated and solved without any reference to additional a priori assumptions on the nature of the quantum system, such as the wave-corpuscle dualism or an underlying wave equation or the existence of Planck’s finite action parameter. The existence of such an additional parameter—as the only additional one—is inherent in the procedure. Within our axiomatic-deductive approach, we modify classical mechanics only where it itself indicates an inherent limitation.     

基于平衡零拍时间测量的位相问题

文章分析了基于平衡零拍的时间测量的相位问题,给出了以压缩态作为信号场时的量子标准极限,并重点讨论了在实际测量中由于系统不稳定而导致信号场与本底场的相对位相抖动对测量结果的影响.结果表明,利用压缩光的平衡零拍测量,最佳测量结果的压缩度取决于测量系统的相位稳定性.     

Group-theoretical structure of quantum continuous measurements

The group-theoretical structure of continuous measurements is investigated in the framework of the path-integral phenomenological theory of quantum continuous measurements. The “transversal” group transforming alternative measurement results (outputs) into each other and the “longitudinal” semigroup describing the evolution of a quantum system subject to continuous measurement are introduced as well as their unification in a single semigroup. The resulting group-theoretical scheme generalizes the scheme describing the evolution of a nonrelativistic particle in an external field.     

Faithful Multihop Two-Qubit Transmission Through GHZ-GHZ Channel

Quantum teleportation is an important method for transmitting quantum states between two quantum communication nodes. In this paper, we propose a low-latency quantum communication scheme based on Greenberger-Horne-Zeilinger (GHZ) state. To implement two-qubit transmission, the source and all intermediate nodes perform quantum measurements simultaneously and the measurement results are transmitted to the destination node through classical channel independently. The destination node performs appropriate unitary operation on its particles to recover the original two-qubit state based on received measurement results. Our scheme effectively reduces the end-to-end quantum communication delay.

     

Quantum Blobs

Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level sets defined by Fermi for the purpose of representing geometrically quantum states.     

Optimal subsystem approach to multi-qubit quantum state discrimination and experimental investigation

Quantum computing is a significant computing capability which is superior to classical computing because of its superposition feature. Distinguishing several quantum states from quantum algorithm outputs is often a vital computational task. In most cases, the quantum states tend to be non-orthogonal due to superposition; quantum mechanics has proved that perfect outcomes could not be achieved by measurements, forcing repetitive measurement. Hence, it is important to determine the optimum measuring method which requires fewer repetitions and a lower error rate. However, extending current measurement approaches mainly aiming at quantum cryptography to multi-qubit situations for quantum computing confronts challenges, such as conducting global operations which has considerable costs in the experimental realm. Therefore, in this study, we have proposed an optimum subsystem method to avoid these difficulties. We have provided an analysis of the comparison between the reduced subsystem method and the global minimum error method for two-qubit problems; the conclusions have been verified experimentally. The results showed that the subsystem method could effectively discriminate non-orthogonal two-qubit states, such as separable states, entangled pure states, and mixed states; the cost of the experimental process had been significantly reduced, in most circumstances, with acceptable error rate. We believe the optimal subsystem method is the most valuable and promising approach for multi-qubit quantum computing applications.     

Demonstration of quantum zeno effect in a superconducting phase qubit

Quantum Zeno effect is a significant tool in quantum manipulating and computing. We propose its observation in superconducting phase qubit with two experimentally feasible measurement schemes. The conventional measurement method is used to achieve the proposed pulse and continuous readout of the qubit state, which are analyzed by projection assumption and Monte Carlo wavefunction simulation, respectively. Our scheme gives a direct implementation of quantum Zeno effect in a superconducting phase qubit.     

Quantum metrology

The statistical error is ineluctable in any measurement. Quantum techniques, especially with the development of quantum information, can help us squeeze the statistical error and enhance the precision of measurement. In a quantum system, there are some quantum parameters, such as the quantum state, quantum operator, and quantum dimension, which have no classical counterparts. So quantum metrology deals with not only the traditional parameters, but also the quantum parameters. Quantum metrology includes two important parts： measuring the physical parameters with a precision beating the classical physics limit and measuring the quantum parameters precisely. In this review, we will introduce how quantum characters （e.g., squeezed state and quantum entanglement） yield a higher precision, what the research areas are scientists most interesting in, and what the development status of quantum metrology and its perspectives are.     

Event-enhanced quantum theory and piecewise deterministic dynamics

The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating quantum jumps, classical events and histories of single quantum objects. The wave-function Monte Carlo method of Quantum Optics is generalized and promoted to the level of a fundamental process generating all the real events in Nature. The already worked out applications include SQUID-tank model and generalized cloud chamber model with GRW spontaneous localization as a particular case. Differences between the present approach and quantum measurement theories based on environment-induced master equations are stressed. Questions: what is classical, what is time, and what observers are addressed. Possible applications of the new approach are suggested, among them connection between the stochastic commutative geometry and Connes' noncommutative formulation of the Standard Model, as well as potential applications to the theory and practice of quantum computers.     

Classical-Noise-Free Sensing Based on Quantum Correlation Measurement

Quantum sensing,using quantum properties of sensors,can enhance resolution,precision,and sensitivity of imaging,spectroscopy,and detection.An intriguing question is:Can the quantum nature(quantumness)of sensors and targets be exploited to enable schemes that are not possible for classical probes or classical targets?Here we show that measurement of the quantum correlations of a quantum target indeed allows for sensing schemes that have no classical counterparts.As a concrete example,in the case that the second-order classical correlation of a quantum target could be totally concealed by non-stationary classical noise,the higher-order quantum correlations can single out a quantum target from the classical noise background,regardless of the spectrum,statistics,or intensity of the noise.Hence a classical-noise-free sensing scheme is proposed.This finding suggests that the quantumness of sensors and targets is still to be explored to realize the full potential of quantum sensing.New opportunities include sensitivity beyond classical approaches,non-classical correlations as a new approach to quantum many-body physics,loophole-free tests of the quantum foundation,et cetera.     

An overview of quantum error mitigation formulas

Minimizing the effect of noise is essential for quantum computers. The conventional method to protect qubits against noise is through quantum error correction. However, for current quantum hardware in the so-called noisy intermediate-scale quantum (NISQ) era, noise presents in these systems and is too high for error correction to be beneficial. Quantum error mitigation is a set of alternative methods for minimizing errors, including error extrapolation, probabilistic error cancellation, measurement error mitigation, subspace expansion, symmetry verification, virtual distillation, etc. The requirement for these methods is usually less demanding than error correction. Quantum error mitigation is a promising way of reducing errors on NISQ quantum computers. This paper gives a comprehensive introduction to quantum error mitigation. The state-of-art error mitigation methods are covered and formulated in a general form, which provides a basis for comparing, combining and optimizing different methods in future work.     

A Testable Theory for the Emergence of the Classical World

The transition from the quantum to the classical world is not yet understood. Here, we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except on some specific basis. However, we have no established theory for the emergence of a specific basis. Our framework entails the following: (i) Sets of N entangled quantum variables can mutually actualize one another. (ii) Such actualization must occur in only one of the 2^N possible bases. (iii) Mutual actualization progressively breaks symmetry among the 2^N bases. (iv) An emerging “amplitude” for any basis can be amplified by further measurements in that basis, and it can decay between measurements. (v) The emergence of any basis is driven by mutual measurements among the N variables and decoherence with the environment. Quantum Zeno interactions among the N variables mediates the mutual measurements. (vi) As the number of variables, N, increases, the number of Quantum Zeno mediated measurements among the N variables increases. We note that decoherence alone does not yield a specific basis. (vii) Quantum ordered, quantum critical, and quantum chaotic peptides that decohere at nanosecond versus femtosecond time scales can be used as test objects. (viii) By varying the number of amino acids, N, and the use of quantum ordered, critical, or chaotic peptides, the ratio of decoherence to Quantum Zeno effects can be tuned. This enables new means to probe the emergence of one among a set of initially entangled bases via weak measurements after preparing the system in a mixed basis condition. (ix) Use of the three stable isotopes of carbon, oxygen, and nitrogen and the five stable isotopes of sulfur allows any ten atoms in the test protein to be discriminably labeled and the basis of emergence for those labeled atoms can be detected by weak measurements. We present an initial mathematical framework for this theory, and we propose experiments.     

Quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation

Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement. We present a general method based on quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation. As input the method needs only a single entangled state. The feasibility of the technique for the electromagnetic field is shown, and the experimental setup is illustrated based on homodyne tomography of a twin beam.