Thermodynamics of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mtext>O</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>antiferromagnets in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>dimensions

Hofmann, Christoph P.

doi:10.1103/physrevb.81.014416

Cited by 57 publications

(106 citation statements)

References 53 publications

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“…It seems timely, not only for conceptual purposes but to help the development of realistic experiments, to work out further models, in particular for such quantum measurements in which the whole history of the process is used to gather information. In this context we should mention the so-called weak measurements [365] that (in a sense) minimize the back-action of the measurement device on the measured system, and -although they have certain counterintuitive features -can reveal the analogues of classical concepts in quantum mechanics; e.g., state determination with the minimal disturbance, classical causality [366,367,368,369,370,371], and even mapping out of the complete wave function [372] or of the average trajectories of single photons in a double-slit experiment [373].…”

Section: Other Types Of Measurementsmentioning

confidence: 99%

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N 1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrixD(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final stateD(t f ) that involves correlations between the system and the indications of the pointer, thus ensuring registration. AlthoughD(t f ) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrixD(t f ) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on m...

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Section: Other Types Of Measurementsmentioning

confidence: 99%

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…On the basis of the above property, recent works have theoretically shown that weak measurement can be used for observing the quantum wave function [8][9][10][11][12]. In contrast to conventional quantum-state tomography [13], this scheme records the complex-valued weak values describing the wave function of the quantum state and requires less postprocessing.…”

Section: Introductionmentioning

confidence: 99%

Stereographical visualization of a polarization state using weak measurements with an optical-vortex beam

2014

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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 Poincaré sphere. We experimentally perform single-setup weak measurement to validate the stereographical relationship between the polarization state on the Poincaré sphere and the location of the zero-intensity point.

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“…It has also been used to amplify small experimental effects [22] and as feedback for control of a quantum system [23]. Weak measurements have been demonstrated in both classical [24] and non-classical systems [25].The concept of weak measurement is universally applicable to all types of measurement [26][27][28] but here we introduce it with a standard model of measurement, the von Neumann model [29]. In it, a measurement apparatus has a pointer, in an initial position wavefunction…”

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confidence: 99%

“…The concept of weak measurement is universally applicable to all types of measurement [26][27][28] but here we introduce it with a standard model of measurement, the von Neumann model [29]. In it, a measurement apparatus has a pointer, in an initial position wavefunction…”

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confidence: 99%

Procedure for Direct Measurement of General Quantum States Using Weak Measurement

2012

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Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. 'strong') measurement of the complementary variable. We generalize this method to mixed states by considering the weak measurement of various products of these observables, thereby providing the density matrix an operational definition in terms of a procedure for its direct measurement. The method only requires measurements in two bases and can be performed 'in situ', determining the quantum state without destroying it.PACS numbers: 03.65. Ta, 03.65.Wj, 42.50.Dv, The wavefunction Ψ is at the heart of quantum mechanics, yet its nature has been debated since its inception. It is typically relegated to being a calculational device for predicting measurement outcomes. Recently, Lundeen et al. proposed a simple and general operational definition of the wavefunction based on a method for its direct measurement: "it is the average result of a weak measurement of a variable followed by a strong measurement of the complementary variable [1,2]." By 'direct' it is meant that a value proportional to the wavefunction appears straight on the measurement apparatus itself without further complicated calculations or fitting. The 'wavefunction' referred to here is a special case of a general quantum state, known as a 'pure state.' The general case is represented by the density operator ρ, which can describe both pure and 'mixed' states. The latter incorporates both the effects of classical randomness (e.g., noise) and entanglement with other systems (e.g., decoherence). The density operator plays an important role in quantum statistics, quantum information, and the study of decoherence. Because of its generality and because it follows naturally from classical concepts of probability and measures, some consider ρ, rather than Ψ, to be the fundamental quantum state description. In this letter, we propose two methods to directly measure general quantum states, one of which directly gives the matrix elements of ρ.The standard method for experimentally determining the density operator is Quantum State Tomography [3]. In it, one makes a diverse set of measurements on an ensemble of identical systems and then determines the quantum state that is most compatible with the measurement results. An alternative is our direct measurement method, which may have advantages over tomography, such as simplicity, versatility, and directness. A quantitative comparison of measures such as the signal to noise ratio, resolution, and fidelity, has not been undertaken but some limitations of the direct method have been identified in [4]. As compared to tomography, which works with mixed states, the most significant limitation of the direct measurement of the wavefunction is that it has only been shown to work with pure states.Previous works have developed direct methods to measure quasi-probability distributions, such as the Wigner function [5], Husimi Q-function [6], and the GlauberSudarshan P-function [7]...

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Thermodynamics ofO(N)antiferromagnets in2+1dimensions

Cited by 57 publications

References 53 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

Stereographical visualization of a polarization state using weak measurements with an optical-vortex beam

Procedure for Direct Measurement of General Quantum States Using Weak Measurement

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