Lars M. Johansen, Pier A. Mello
We study successive measurements of two observables using von Neumann's measurement model. The two-pointer correlation for arbitrary coupling strength allows retrieving the initial system state. We recover Luders rule, the Wigner formula and the Kirkwood-Dirac distribution in the appropriate limits of the coupling strength.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Engineering strong interactions between quantum systems is essential for many phenomena of quantum physics and technology. Typically, strong coupling relies on short-range forces or on placing the systems in high-quality electromagnetic resonators, restricting the range of the coupling to small distances. We use a free-space laser beam to strongly couple a collective atomic spin and a micromechanical membrane over a distance of one meter in a room-temperature environment. The coupling is highly tunable and allows the observation of normal-mode splitting, coherent energy exchange oscillations, …
We describe a quantum state tomography scheme which is applicable to a system described in a Hilbert space of arbitrary finite dimensionality and is constructed from sequences of two measurements. The scheme consists of measuring the various pairs of projectors onto two bases --which have no mutually orthogonal vectors--, the two members of each pair being measured in succession. We show that this scheme implies measuring the joint quasi-probability of any pair of non-degenerate observables having the two bases as their respective eigenbases. The model Hamiltonian underlying the scheme makes u…
Semiclassical approximations to quantum dynamics are almost as old as quantum mechanics itself. In the approach pioneered by Wigner, the evolution of his quasiprobability density function on phase space is expressed as an asymptotic series in increasing powers of Planck's constant, with the classical Liouvillean evolution as leading term. Successive semiclassical approximations to quantum dynamics are defined by successive terms in the series. We consider a complementary approach, which explores the quantum-clssical interface from the other direction. Classical dynamics is formulated in Hilber…
Wigner function is a quasi-distribution that provides a representation of the state of a quantum mechanical system in the phase space of position and momentum. In this paper we find a relation between Wigner function and appropriate measurements involving the system position and momentum which generalize the von Neumann model of measurement. We introduce two probes coupled successively in time to projectors associated with the system position and momentum. We show that one can relate Wigner function to Kirkwood joint quasi-distribution of position and momentum, the latter, in turn, being a par…
A method is proposed for generating and discriminating Bell states of high fidelity from consecutive single-photons generated in a semiconductor quantum dot. The use of a non-symmetric beam splitter is found to be essential and sufficient, and no nonlinear optical process such as SPDC is required at any stage. This should be of considerable importance for testing the foundations of quantum mechanics.
Q-based, objective-field model for wave-function collapse: Analyzing measurement on a macroscopic superposition state
本文提出基于Q的客观场模型，通过分析宏观叠加态测量过程，揭示波函数坍缩为两个阶段：幅值放大和信息丢失。
In the history of quantum mechanics, various types of uncertainty relationships have been introduced to accommodate different operational meanings of Heisenberg uncertainty principle. We derive an optimized entropic uncertainty relation (EUR) that quantifies an amount of quantum uncertainty in the scenario of successive measurements. The EUR characterizes the limitation in the measurability of two different quantities of a quantum state when they are measured through successive measurements. We find that the bound quantifies the information between the two measurements and imposes a condition …
We describe how to obtain information on a quantum-mechanical system by coupling it to a probe and detecting some property of the latter, using a model introduced by von Neumann, which describes the interaction of the system proper with the probe in a dynamical way. We first discuss single measurements, where the system proper is coupled to one probe with arbitrary coupling strength. The goal is to obtain information on the system detecting the probe position. We find the reduced density operator of the system, and show how Lüders rule emerges as the limiting case of strong coupling. The von N…
A real two-particle experiment is proposed in which one of the particles undergoes two successive impacts on beam-splitters. It is shown that the standard quantum mechanical superposition principle implies the possibility of influences acting backward in time ("retrocausation"), in striking contrast with the principle of causality. It is argued that nonlocality and retrocausation are not necessarily entangled.
An inconsistency is pointed out within Quantum Mechanics as soon as successive joint measurements are involved on entangled states. The resolution of the inconsistency leads to a refutation of the use of entangled states as eigenvectors. Hence, the concept of quantum teleportation, which is based on the use of such entangled states--the Bell states--as eigenvectors, is demonstrated to be irrelevant to Quantum Mechanics.
We study the relativistic quantum mechanical problem of a Dirac particle tunneling through two successive electrostatic barriers. Our aim is to study the emergence of the so-called \emph{Generalized Hartman Effect}, an effect observed in the context of nonrelativistic tunneling as well as in its electromagnetic counterparts, and which is often associated with the possibility of superluminal velocities in the tunneling process. We discuss the behavior of both the phase (or group) tunneling time and the dwell time, and show that in the limit of opaque barriers the relativistic theory also allows…
When you measure an observable, A, in Quantum Mechanics, the state of the system changes. This, in turn, affects the quantum-mechanical uncertainty in some non-commuting observable, B. The standard Uncertainty Relation puts a lower bound on the uncertainty of B in the initial state. What is relevant for a subsequent measurement of B, however, is the uncertainty of B in the post-measurement state. We re-examine this problem, both in the case where A has a pure point spectrum and in the case where A has a continuous spectrum. In the latter case, the need to include a finite detector resolution, …
Quantum correlations between imprecision and back-action are a hallmark of continuous linear measurements. Here we study how measurement-based feedback can be used to improve the visibility of quantum correlations due to the interaction of a laser field with a nano-optomechanical system. Back-action imparted by the meter laser, due to radiation pressure quantum fluctuations, gives rise to correlations between its phase and amplitude quadratures. These quantum correlations are observed in the experiment both as squeezing of the meter field fluctuations below the vacuum level in a homodyne measu…
We describe a system composed of two coupled optical cavity modes with a coupling modulated by a bulk mechanical resonator. In addition, one of the cavity modes is irreversibly coupled to a single photon source. Our scheme is an opto-mechanical realisation of the Jaynes-Cummings model where the qubit is a dual rail optical qubit while the bosonic degree of freedom is a matter degree of freedom realised as the bulk mechanical excitation. We show the possibility of engineering phonon number states of the mechanical oscillator in such a system by computing the conditional state of the mechanics a…
Dependence of measurement outcomes on the dynamics of quantum coherent interactions between the system and the meter
本文研究了量子测量结果对系统与测量仪间量子相干相互作用动力学的依赖，表明测量值源于反作用动力学的量子相干特性，而非独立于测量的实在要素。
Quantum back action imposes fundamental sensitivity limits to the majority of quantum measurements. The effect results from the unavoidable contamination of the measured parameter with the quantum noise of a meter. Back action evading measurements take advantage of the quantum correlations introduced by the system under study to the meter and allow overcoming the fundamental limitations. The measurements are frequently restricted in their bandwidth due to a finite response time of the system components. Here we show that probing a mechanical oscillator with a dichromatic field with frequencies…
We implemented a joint weak measurement of the trajectories of two photons in a photonic version of Hardy's experiment. The joint weak measurement has been performed via an entangled meter state in polarization degrees of freedom of the two photons. Unlike Hardy's original argument in which the contradiction is inferred by retrodiction, our experiment reveals its paradoxical nature as preposterous values actually read out from the meter. Such a direct observation of a paradox will give us a new insight into the spooky action of quantum mechanics.
We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work [1]. We begin with a brief recall about the so called phase space representation. We give the definition of linear canonical transformation with the transformation law of coordinate and momentum operators. We establish successively the transformation laws of mean values, dispersions, basis state and wave functions.Then we introduce the concept of isodispersion linear canonical transformation.
Standard Quantum Limit (SQL) of a classical mechanical force detection results from quantum back action impinged by the meter on a probe mechanical transducer perturbed by the force of interest. In this paper we introduce a technique of continuous \vy{broadband} back action avoiding measurements for the case of a resonant signal force acting on a linear mechanical oscillator supporting one of mirrors of an optical Michelson-Sagnac Interferometer (MSI). The interferometer with the movable mirror is an opto-mechanical transducer able to support polychromatic probe field. The method involves a di…
We study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $\hat{A}$ and $\hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension of the von Neumann model of measurement, in which two probes interact with the same system proper at two successive times, so we can exhibit how the disturbing effect of the first interaction affects the second measurement. Detecting the statistical properties of the second {\em probe} variable $Q_2$ conditioned on the first {\em probe} measurement yielding $…
Emergence of classical realism under successive noncommuting measurements
本文提出一种新机制，通过连续监测非对易可观测量确立实在性元素，证明足够多次不相容测量可使一般系统涌现经典性，无需依赖大储库退相干。
As shown in the \emph{EPR} paper (Einstein, Podolsky e Rosen, 1935), Quantum Mechanics is a non-local Theory. The Bell theorem and the successive experiments ruled out the possibility of explaining quantum correlations using only local hidden variables models. Some authors suggested that quantum correlations could be due to superluminal communications that propagate isotropically with velocity \emph{$v_{t}>c$} in a preferred reference frame. For finite values of \emph{$v_{t}$} and in some special cases, Quantum Mechanics and superluminal models lead to different predictions. So far, no deviati…
We propose a method for finding an initial state vector which by ordinary Hamiltonian time evolution follows a single branch of many-worlds quantum mechanics. The resulting deterministic system appears to exhibit random behavior as a result of the successive emergence over time of information present in the initial state but not previously observed.
We introduce a two-qubit engine that is powered by entangling operations and projective local quantum measurements. Energy is extracted from the detuned qubits coherently exchanging a single excitation. This engine, which uses the information and back-action of the measurement, is generalized to an N-qubit chain. We show that by gradually increasing the energy splitting along the chain, the initial low energy of the first qubit can be up-converted deterministically to an arbitrarily high energy at the last qubit by successive neighbor swap operations and local measurements. Modeling the local …
The experimental realization of successive non-demolition measurements on single microscopic systems brings up the question of ergodicity in Quantum Mechanics (QM). We investigate whether time averages over one realization of a single system are related to QM averages over an ensemble of similarly prepared systems. We adopt a generalization of von Neumann model of measurement, coupling the system to $N$ "probes" --with a strength that is at our disposal-- and detecting the latter. The model parallels the procedure followed in experiments on Quantum Electrodynamic cavities. The modification of …
In this paper, without any priori assumption about the post-measurement state of system, we will examine how this state is restricted by assuming each of these following assumptions. First, by using this reasonable assumption that two successive measurements should be describable as one measurement. Second, by assuming the impossibility of faster than light signaling, "No-signaling condition". However, only by using these assumptions it is not possible to obtain the usual projection postulate. Instead, by means of a simple lemma, we will show that the density operator of system after a measure…
Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement. We show that this generalized concept of weak measurements displays a symmetry under reversal of measurement order. We show that the conditions for order symmetry are the same as in classical mechanics. We also find that the imaginary part of the weak value has a counterpart in classical mechanics. This scheme suggests new experimental possibilities.
The interplay between quantum-mechanical and classical evolutions in a chirped driven Rydberg atom is discussed. It is shown that the system allows two continuing resonant excitation mechanisms, i.e., a successive two-level transitions (ladder climbing) and a continuing classical-like nonlinear phase locking (autoresonance). The persistent $1:1$ and $2:1$ resonances between the driving and the Keplerian frequencies are studied in detail and characterized in terms of two dimensionless parameters $P_{1,2}$ representing the driving strength and the nonlinearity in the problem, respectively. The q…
Intersubjectivity and value reproducibility of outcomes of quantum measurements
该研究针对量子测量结果仅具个人意义的怀疑论观点，通过量子力学分析证明两名观测者测量同一可观测量时结果必然一致，且测量会建立类时与类空纠缠，同时指出该结论不适用于广义可观测量，为量子力学基础研究提供了新视角。
The continuous fuzzy measurement of energy of a single two-level system driven by a resonant external field is studied. An analysis is given in the framework of the phenomenological restricted path integral approach (RPI) (which reduces effectively to a Schrodinger equation with a complex Hamiltonian) as well as with reference to the microphysical details of a class of concrete physical realizations. Within the RPI approach it is demonstrated that for appropriately adjusted fuzziness, information about the evolution of the state of the system can be read off from the measurement readout E(t). …
Quantum interference between distant creation processes
本研究提出生成宏观量子系统的新方法，通过产生相距最远70米的相干叠加态光子对，验证量子系统产生过程可跨宏观距离，为量子基础实验及分布式特性高精度测量提供新可能。
We discuss the scattering of a quantum particle by two independent successive point interactions in one dimension. The parameter space for two point interactions is given by $U(2)\times U(2)$, which is described by eight real parameters. We perform an analysis of perfect resonant transmission on the whole parameter space. By investigating the effects of the two point interactions on the scattering matrix of plane wave, we find the condition under which perfect resonant transmission occurs. We also provide the physical interpretation of the resonance condition.
Several relatively small-scale experimental setups aimed on prototyping of future laser gravitational-wave detectors and testing of new methods of quantum measurements with macroscopic mechanical objects, are under development now. In these devices, not devoted directly to the gravitational-wave detection, Mach-Zehnder interferometer with pass-through Fabry-Perot cavities in the arms can be used instead of the standard Michelson/Fabry-Perot one. The advantage of this topology is that it does not contain high-reflectivity end mirrors with multilayer coatings, which Brownian noise could constitu…
The temporal evolution of an unstable quantum mechanical system undergoing repeated measurements is investigated. In general, by changing the time interval between successive measurements, the decay can be accelerated (inverse quantum Zeno effect) or slowed down (quantum Zeno effect), depending on the features of the interaction Hamiltonian. A geometric criterion is proposed for a transition to occur between these two regimes.
An idea for an application of the quantum annealing mechanism to construct a projection measurement in a collective space is proposed. We use the annealing mechanism to drive the pointer degree of freedom associated with the measurement process. The parameters in its problem Hamiltonian is given not as classical variables but as quantum variables (states). By additionally introducing successive short interactions so that the back reaction to the quantum state (to be measured) can be controlled, we invent a quantum mechanically parametrized quantum annealing process. Applying to a particular pr…
Quantum mechanics sets severe limits on the sensitivity and required circulating energy in traditional free-mass gravitational-wave antennas. One possible way to avoid these restrictions is the use of intracavity QND measurements. We analyze a new QND observable, which possesses a number of features that make it a promising candidate for such measurements and propose a practical scheme for the realization of this measurement. In combination with an advanced coordinate meter, this scheme makes it possible to lower substantially the requirements on the circulating power.
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We demonstrate that there are only two ways to resolve this problem. The first solution places emphasis on the precise use of the concept of conditional probability for successive measurements. The physically correct conditional probabilities define additive probabilities for two-time measurements. These probabilities depend explicitly on the resolution of the…
Long sequences of successive direct (projective) measurements or observations of a few "uninteresting" physical quantities of a quantum system may reveal indirect, but precise and unambiguous information on the values of some very "interesting" observables of the system. In this paper, the mathematics underlying this claim is developed; i.e., we attempt to contribute to a mathematical theory of indirect and, in particular, non-demolition measurements in quantum mechanics. Our attempt leads us to make novel uses of classical notions and results of probability theory, such as the "algebra of fun…
The stochastic evolution of quantum systems during measurement is arguably the most enigmatic feature of quantum mechanics. Measuring a quantum system typically steers it towards a classical state, destroying any initial quantum superposition and any entanglement with other quantum systems. Remarkably, the measurement of a shared property between non-interacting quantum systems can generate entanglement starting from an uncorrelated state. Of special interest in quantum computing is the parity measurement, which projects a register of quantum bits (qubits) to a state with an even or odd total …
The main challenge in deterministic quantum state transfer in long-distance quantum communications is the transmission losses in the communication channel. To overcome this limitation, here we use the adiabatic theorem and find a lossless evolution path between two remote mechanical modes. By adiabatic variation of the effective coupling strengths between the two nodes and the intermediate optical channel modes, we engineer a transmission path for the quantum state transfer that is decoupled from the decaying fiber modes. Using our proposed method we show that one obtains a quantum state trans…
The two-photon ladder climbing (successive two-photon Landau-Zener-type transitions) in a chirped quantum nonlinear oscillator and its classical limit (subharmonic autoresonance) are discussed. An isomorphism between the chirped quantum-mechanical one and two-photon resonances in the system is used in calculating the threshold for the phase-locking transition in both the classical and quantum limits. The theory is tested by solving the Schrodinger equation in the energy basis and illustrated via the Wigner function in phase space.
Entropic Dynamics approach to Relational Quantum Mechanics
本文利用熵动力学框架，从概率、熵与信息几何原理构建部分关系性的非相对论量子模型，提出适配量子相空间的状态失配测度，并将关系性约束施加于期望值，从而规避量子引力中的时间问题。
Most educational literature on conceptual change concerns the process by which introductory students acquire scientific knowledge. However, with modern developments in science and technology, the social significance of learning successive theories is steadily increasing, thus opening new areas of interest to discipline-based education research, e.g., quantum logic, quantum information and communication. Here we present an initial proposal for modeling the transition from the understanding of a theory to the understanding of its successor and explore its generative potential by applying it to a…
A major question in our understanding of the fabric of the world is where the randomness of some quantum phenomena comes from and how to represent it in a rational theory. The statistical interpretation of quantum mechanics made its way progressively since the early days of the theory. We summarize the main historical steps and then we outline how the randomness gains to be depicted by using tools adapted to Markov processes. We consider a model system corresponding to experimental situations, namely a single two-level atom submitted to a monochromatic light triggering transitions from the gro…
A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle relative to the von Neumann chain. For the basis of the theory, the local measurement theorem provides the joint probability distribution for the outcomes of local successive measurements on a noninteracting entangled system without assuming the projection postulate, and the quantum Bayes principle enables us to determine operationally the quantum state from a …
A numerical thought experiment with two momentum correlated particles is presented, in which particle A passes through a series of zig-zagging slits and particle B moves unobstructedly. It is shown that, if particle A's meandering path is monitored by successive non-detections, particle B will loosely adhere to a similar trajectory without violating momentum conservation. The discussion relates this apparent telekinetic influence, which is a standard quantum mechanical result, to supposedly real telekinesis and to Stapp's hypothesis on intention in quantum physics.
The non-commutativity of position and momentum observables is a hallmark feature of quantum physics. However this incompatibility does not extend to observables which are periodic in these base variables. Such modular-variable observables have been suggested as tools for fault-tolerant quantum computing and enhanced quantum sensing. Here we implement sequential measurements of modular variables in the oscillatory motion of a single trapped ion, using state-dependent displacements and a heralded non-destructive readout. We investigate the commutative nature of modular variable observables by de…
Beginning with the Everett-DeWitt many-worlds interpretation of quantum mechanics, there have been a series of proposals for how the state vector of a quantum system might be split at any instant into orthogonal branches, each of which exhibits approximately classical behavior. Here we propose a decomposition of a state vector into branches by finding the minimum of a measure of the net quantum complexity of the branch decomposition. We then propose a method for finding an ensemble of possible initial state vectors from which a randomly selected member, if evolved by ordinary Hamiltonian time …
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically recast the basics of quantum mechanics - dynamics, observables, and measurement theory - in terms of two-states as the elementary quantities. We find a simple and suggestive formulation, that ``unifies'' two complementary observables: probabilistic observables and non-probabilistic `weak' observables. Probabilities are relevant for measurements in the `strong co…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。