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Mesure faible, Valeur Faible et Interférométrie
Abstract
La théorie de la mesure, basée sur la mesure projective, constitue un aspect fondamental de la mécanique quantique. La mesure faible diffère de la mesure projective traditionnelle sur laquelle les axiomes élémentaires de la physique quantique sont bâtis. Bien que définies dans le cadre de la théorie quantique standard, les mesures faibles sont encore mal comprises. Le travail de thèse s'inscrit dans une large démarche qui vise à comprendre les implications conceptuelles et pratiques d'une telle mesure et à la comprendre dans le cadre de la théorie quantique.Le chapitre 1 est une introduction détaillée à la mesure faible et à la valeur faible. Ensuite, nous étudierons les "trajectoires faibles" dans un interféromètre à fentes d'Young. Nous abordons au chapitre 3 les implications de l'annulation d'une valeur faible au regard de l'apparition de trajectoires faibles dans des interféromètres de Mach-Zender imbriqués. Enfin, le chapitre 4 traite des critiques théoriques et expérimentales présentes dans la littérature concernant l'effet du Chat du Cheshire quantique qui est défini dans le cadre de mesures faibles.
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We investigate in this work the meaning of weak values through the prism of property ascription in quantum systems. Indeed, the weak measurements framework contains only ingredients of the standard quantum formalism, and as such weak measurements are from a technical point of view uncontroversial. However attempting to describe properties of quantum systems through weak values—the output of weak measurements—goes beyond the usual interpretation of quantum mechanics, that relies on eigenvalues. We first recall the usual form of property ascription, based on the eigenstate-eigenvalue link and the existence of “elements of reality”. We then describe against this backdrop the different meanings that have been given to weak values. We finally argue that weak values can be related to a specific form of property ascription, weaker than the eigenvalues case but still relevant to a partial description of a quantum system.
Weak measurement allows one to empirically determine a set of average trajectories for an ensemble of quantum particles. However, when two particles are entangled, the trajectories of the first particle can depend nonlocally on the position of the second particle. Moreover, the theory describing these trajectories, called Bohmian mechanics, predicts trajectories that were at first deemed “surreal” when the second particle is used to probe the position of the first particle. We entangle two photons and determine a set of Bohmian trajectories for one of them using weak measurements and postselection. We show that the trajectories seem surreal only if one ignores their manifest nonlocality.
The Quantum Cheshire Cat [New J. Phys. 15, 113015, 2013] (QCC) is an effect defined within the Weak Measurements framework by which a property of a quantum particle appears to be spatially separated from its position. The status of this effect has however remained unclear, as claims of experimental observation of the QCC have been disputed by strong criticism of the experimental as well as the theoretical aspects of the effect. In this paper we clarify in what precise sense the QCC can be regarded as an unambiguous consequence of the standard quantum mechanical formalism applied to describe quantum pointers weakly coupled to a system. In light of this clarification, the raised criticisms of the QCC effect are rebutted. We further point out that the limitations of the experiments performed to date imply that a loophole-free experimental demonstration of the QCC has not yet been achieved.
Huw Price has proposed an argument that suggests a time-symmetric ontology for quantum theory must necessarily be retrocausal, i.e. it must involve influences that travel backwards in time. One of Price's assumptions is that the quantum state is a state of reality. However, one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no-go theorems, including recent proofs of the reality of the quantum state. Here, we show that this assumption can be replaced by a different assumption, called -mediation, that plausibly holds independently of the status of the quantum state. We also reformulate the other assumptions behind the argument to place them in a more general framework and pin down the notion of time symmetry involved more precisely. We show that our assumptions imply a timelike analogue of Bell's local causality criterion and, in doing so, give a new interpretation of timelike violations of Bell inequalities. Namely, they show the impossibility of a (non-retrocausal) time-symmetric ontology.
Bartkiewicz et al. [Phys. Rev. A 91, 012103 (2015)] provided an alternative
analysis of experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402
(2013)] which presented surprising evidence regarding the past of photons
passing through an interferometer. They argued that the quantity used by Danan
et al. is not a suitable which-path witness, and proposed an alternative. It is
argued that the quantum and classical analyses of Bartkiewicz et al. are
inconsistent and both are inappropriate for describing the past of photons in a
properly working interferometer.
The interpretational problems of quantum mechanics are considered. The way in which the standard Copenhagen interpretation of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the transactional interpretation, is presented. The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereby consistent with recent tests of the Bell inequality, yet is relativistically invariant and fully causal. A detailed comparison of the transactional and Copenhagen interpretations is made in the context of well-known quantum-mechanical Gedankenexperimente and "paradoxes." The transactional interpretation permits quantum-mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the Copenhagen interpretation. The transactional interpretation is shown to provide insight into the complex character of the quantum-mechanical state vector and the mechanism associated with its "collapse." It also leads in a natural way to justification of the Heisenberg uncertainty principle and the Born probability law (P=ψψ*), basic elements of the Copenhagen interpretation.
The question: "Where was a quantum particle between pre- and postselection
measurements?" is analyzed in view of a recent proposal that it was in the
overlap of the forward and backward evolving wave functions. It is argued that
this proposal corresponds not only to the criterion of where the particle
leaves a weak trace, but also where the local interactions can affect the
probability of postselection and where finding the particle in a strong
nondemolition measurement is possible. The concept of a "secondary presence" of
a pre- and postselected particle where local interactions affect the weak trace
in the overlap region is introduced.
We study the quantum slit diffraction problem in three dimensions. In the
treatment of diffraction of particles by a slit, it is usually assumed that the
motion perpendicular to the slit is classical. Here we take into account the
effect of the quantum nature of the motion perpendicular to the slit using the
Green function approach [18]. We treat the diffraction of a Gaussian wave
packet for general boundary conditions on the shutter. The difference between
the standard and our three-dimensional slit diffraction models is analogous to
the diffraction in time phenomenon introduced in [16]. We derive corrections to
the standard formula for the diffraction pattern, and we point out situations
in which this might be observable. In particular, we discuss the diffraction in
space and time in the presence of gravity.
Linear-optical interferometers play a key role in designing circuits for quantum information processing and quantum communications. Even though nested Mach-Zehnder interferometers appear easy to describe, there are occasions when they provide unintuitive results. This paper explains the results of a highly discussed experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013).] using a standard approach. We provide a simple and intuitive one-state vector formalism capable of interpreting their experiment. Additionally, we cross-checked our model with a classical-physics-based approach and found that both models are in complete agreement. We argue that the quantity used in the mentioned experiment is not a suitable which-path witness, producing seemingly contraintuitive results. To circumvent this issue, we establish a more reliable which-path witness and show that it yields well-expected outcomes of the experiment.
We reexamine the thought experiment and real experiment of Vaidman et al., by
placing Dove prisms in the nested Mach-Zehnder interferometer arms. In those
previous works, the criterion of whether a single photon was present, or not,
was the presence of a "weak trace", indicating the presence of a nonzero weak
value. This was verified by slightly varying the mirror angle at a given
frequency, which was then detected on a position sensitive detector at the
oscillation frequency. We show the presence of the Dove prisms gives identical
weak values everywhere to the previous configuration because the prisms change
neither the path difference, nor the mode profile in the aligned case.
Nevertheless, the same slight variations of the interferometer mirrors now give
a signal at the first mirror of the nested interferometer. We can interpret
this result as a misaligned optical interferometer, whose detailed response
depends on the stability of the elements, or as the detector coupling to a
nonzero effective weak value.
The notion of the trajectory of an individual particle is strictly inhibited in quantum mechanics because of the uncertainty
principle. Nonetheless, the weak value, which has been proposed as a novel and measurable quantity definable to any quantum
observable, can offer a possible description of trajectory on account of its statistical nature. In this paper, we explore
the physical significance provided by this “weak trajectory” by considering various situations where interference takes place
simultaneously with the observation of particles, that is, in prototypical quantum situations for which no classical treatment
is available. These include the double slit experiment and Lloyd's mirror, where in the former case it is argued that the
real part of the weak trajectory describes an average over the possible classical trajectories involved in the process, and
that the imaginary part is related to the variation of interference. It is shown that this average interpretation of the weak
trajectory holds universally under the complex probability defined from the given transition process. These features remain
essentially unaltered in the case of Lloyd's mirror where interference occurs with a single slit.
A recent neutron interferometry experiment claims to demonstrate a paradoxical phenomenon dubbed the “quantum Cheshire cat” [ Nat. Commun. 5, 4492 (2014)]. We have reproduced and extended these results with an equivalent optical interferometer. The results suggest that the photon travels through one arm of the interferometer, while its polarization travels through the other. However, we show that these experimental results belong to the domain where quantum and classical wave theories coincide; there is nothing uniquely quantum about the illusion of this Cheshire cat.
Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.
In a recent work, Aharonov et al. suggested that a photon could be separated
from its polarization in an experiment involving pre- and post-selection [New
J. Phys 15, 113015 (2013)]. They named the effect 'quantum Cheshire Cat', in a
reference to the cat that is separated from its grin in the novel Alice's
Adventures in Wonderland. Following these ideas, Denkmayr et al. performed a
neutron interferometric experiment and interpreted the results suggesting that
neutrons were separated from their spin [Nat. Commun. 5, 4492 (2014)]. Here we
show that these results can be interpreted as simple quantum interference, with
no separation between the quantum particle and its internal degree of freedom.
We thus hope to clarify the phenomenon with this work, by removing these
apparent paradoxes.
We present surprising experimental evidence regarding the past of photons passing through an interferometer. The information about the positions through which the photons pass in the interferometer is retrieved from modulations of the detected signal at the vibration frequencies of mirrors the photons bounce off. From the analysis we conclude that the past of the photons is not represented by continuous trajectories, although a "common sense" analysis adopted in various welcher weg measurements, delayed-choice which-path experiments, and counterfactual communication demonstrations yields a single trajectory. The experimental results have a simple explanation in the framework of the two-state vector formalism of quantum theory.
From its very beginning quantum theory has been revealing extraordinary and
counter-intuitive phenomena, such as wave-particle duality, Schr\"odinger cats
and quantum non-locality. In the study of quantum measurement, a process
involving pre- and postselection of quantum ensembles in combination with a
weak interaction was found to yield unexpected outcomes. This scheme, usually
referred to as "weak measurements", can not only be used as an amplification
technique and for minimal disturbing measurements, but also for the exploration
of quantum paradoxes. Recently the quantum Cheshire Cat has attracted
attention: a quantum system can behave as if a particle and its property (e.g.
its polarization) are spatially separated. Up to now most experiments studying
weak measurements were done with photonic setups. To reveal the peculiarities
of a quantum Cheshire Cat the use of non-zero mass particles is most appealing,
since no classical description is possible. Here, we report an experiment using
a neutron interferometer to create and observe a purely quantum mechanical
Cheshire Cat. The experimental results suggest that the system behaves as if
the neutrons went through one beam path, while their spin travelled along the
other.
The ability to post-select the outcomes of an experiment is a useful
theoretical concept and experimental tool. In the context of weak measurements
post-selection can lead to surprising results such as complex weak values
outside the range of eigenvalues. Usually post-selection is realized by a
projective measurement, which is hard to implement in ensemble systems such as
NMR. We demonstrate the first experiment of a weak measurement with
post-selection on an NMR quantum information processor. Our setup is used for
measuring complex weak values and weak values outside the range of eigenvalues.
The scheme for overcoming the problem of post-selection in an ensemble quantum
computer is general and can be applied to any circuit-based implementation.
This experiment paves the way for studying and exploiting post-selection and
weak measurements in systems where projective measurements are hard to realize
experimentally
That quantum mechanics is a probabilistic theory was, by 1964, an old but still troubling story. The fact that identical measurements of identically prepared systems can yield different outcomes seems to challenge a basic tenet of science and philosophy. Frustration with the indeterminacy intrinsic to quantum mechanics was famously expressed in Albert Einstein's assertion that "God doesn't play dice."
We investigate general differential relations connecting the respective behaviors of the phase and modulus of probability amplitudes of the form 〈ψf∣ψ〉, where ∣ψf〉 is a fixed state in Hilbert space and ∣ψ〉 is a variable state, treated as a section of a U(1) bundle over a complex subspace of the corresponding ray space R = Pn. Amplitude functions on such holomorphic line bundles, while not strictly holomorphic, nevertheless satisfy generalized Cauchy–Riemann conditions involving the U(1) Berry–Simon connection on the parameter space. These conditions entail invertible relations between the gradients of the phase and modulus, therefore allowing for the reconstruction of the phase from the modulus (or vice versa) and other conditions on the behavior of either polar component of the amplitude. As a special case, we consider amplitude functions valued on the space of pure states, the ray space R = Pn, where transition probabilities have a geometric interpretation in terms of geodesic distances as measured with the Fubini–Study metric. In conjunction with the generalized Cauchy–Riemann conditions, this geodesic interpretation leads to additional relations, in particular, a novel connection between the modulus of the amplitude and the phase gradient, somewhat reminiscent of the WKB formula. Finally, a connection with geometric phases is established.
The technical merits of weak value amplification techniques are analyzed. We
consider models of several different types of technical noise in an optical
context and show that weak value amplification techniques (which only use a
small fraction of the photons) compare favorably with standard techniques
(which uses all of them). Using the Fisher information metric, we demonstrate
that weak value techniques can put all of the Fisher information about the
detected parameter into a small portion of the events and show how this fact
alone gives technical advantages. We go on to consider a time correlated noise
model, and find that a Fisher information analysis indicates that while the
standard method can have much larger information about the detected parameter
than the postselected technique. However, the estimator needed to gather the
information is technically difficult to implement, showing that the inefficient
(but practical) signal-to-noise estimation of the parameter is usually
superior. We also describe other technical advantages unique to imaginary weak
value amplification techniques, focusing on beam deflection measurements. In
this case, we discuss combined noise types (such as detector transverse jitter,
angular beam jitter before the interferometer and turbulence) for which the
interferometric weak value technique gives higher Fisher information over
conventional methods. We go on to calculate the Fisher information of the
recently proposed photon recycling scheme for beam deflection measurements, and
show it further boosts the Fisher information by the inverse postselection
probability relative to the standard measurement case.
In a recent paper [Phys. Rev. A 95, 032110 (2017)2469-992610.1103/PhysRevA.95.032110], Duprey and Matzkin investigated the meaning of vanishing weak values and their role in the retrodiction of the past of a preselected and postselected quantum system in the presence of interference. Here we argue that any proposition regarding the weak values should be understood as a statement about the probability amplitudes. With this in mind, we revisit some of the conclusions reached in Duprey and Matzkin's work.
We discuss the preceding Comment and conclude that the arguments given there against the relevance of null weak values as representing the absence of a system property are not compelling. We give an example in which the transition matrix elements that make the projector weak values vanish are the same ones that suppress detector clicks in strong measurements. Whether weak values are taken to account for the past of a quantum system or not depend on general interpretional commitments of the quantum formalism itself rather than on peculiarities of the weak measurements framework.
We analyze Vaidman's three-path interferometer with weak path marking [L. Vaidman, Phys. Rev. A 87, 052104 (2013)] and find that common sense yields correct statements about the particle's path through the interferometer. This disagrees with the original claim that the particles have discontinuous trajectories at odds with common sense. In our analysis, “the particle's path” has operational meaning as acquired by a path-discriminating measurement. For a quantum-mechanical experimental demonstration of the case, one should perform a single-photon version of the experiment by Danan et al. [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, Phys. Rev. Lett. 111, 240402 (2013)] with unambiguous path discrimination. We present a detailed proposal for such an experiment.
Griffiths [Phys. Rev. A 94, 032115 (2016)] analyzed, in the framework of a consistent histories interpretation, the controversy regarding the approach to the past of a quantum particle introduced by Vaidman [Phys. Rev. A 87, 052104 (2013)]. I argue that Griffith's criticism of my approach using an analysis of experiments with weak probes is unfounded.
Quantum mechanics, one of the keystones of modern physics, exhibits several peculiar properties, differentiating it from classical mechanics. One of the most intriguing is that variables might not have definite values. A complete quantum description provides only probabilities for obtaining various eigenvalues of a quantum variable. These and corresponding probabilities specify the expectation value of a physical observable, which is known to be a statistical property of an ensemble of quantum systems. In contrast to this paradigm, we demonstrate a unique method allowing to measure the expectation value of a physical variable on a single particle, namely, the polarisation of a single protected photon. This is the first realisation of quantum protective measurements.
Recently, a scheme based on the method of weak measurements to register the trajectories of photons passing through a nested Mach–Zehnder interferometer was proposed [L. Vaidman, Phys. Rev. A 87, 052104 (2013)] and then realized [A. Danan, D. Farfurnik, S. Bar-Ad, et al., Phys. Rev. Lett. 111, 240402 (2013)]. Interpreting the results of the experiment, the authors concluded that “the photons do not always follow continuous trajectories.” It is shown in this work that these results can be easily and clearly explained in terms of traditional classical electrodynamics or quantum mechanics implying the continuity of all possible paths of photons. Consequently, a new concept of disconnected trajectories proposed by the authors of work [Phys. Rev. Lett. 111, 240402 (2013)] is unnecessary.
Non-destructive weak measurements (WM) made on a quantum particle allow to extract information as the particle evolves from a prepared state to a finally detected state. The physical meaning of this information has been open to debate, particularly in view of the apparent discontinuous trajectories of the particle recorded by WM. In this work we investigate the properties of vanishing weak values for projection operators as well as general observables. We then analyze the implications when inferring the past of a quantum particle. We provide a novel (non-optical) example for which apparent discontinuous trajectories are obtained by WM.\ Our approach is compared to previous results.
The authors of Phys.Rev.Lett. \textbf{111}, 240402 (2013) conclude that "the past of the photons is not represented by continuous trajectories". A simple analysis by standard quantum mechanics shows that this claim is false.
We report an experimental realization of the quantum paradox of the separation of a single photon from one of its properties (the so-called “quantum Cheshire cat”). We use a modified Sagnac interferometer with displaced paths to produce appropriately pre- and postselected states of heralded single photons. Weak measurements of photon presence and circular polarization are performed in each arm of the interferometer by introducing weak absorbers and small polarization rotations and analyzing changes in the postselected signal. The absorber is found to have an appreciable effect only in one arm of the interferometer, while the polarization rotation significantly affects the signal only when performed in the other arm. We carry out both sequential and simultaneous weak measurements and find good agreement between measured and predicted weak values. In the language of Aharonov et al. and in the sense of the ensemble averages described by weak values, the experiment establishes the separation of a particle from one its properties during the passage through the interferometer.
In our recent paper [Phys. Rev. A 91, 012103 (2015)10.1103/PhysRevA.91.012103] we have provided an alternative description of a highly debated experiment by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)10.1103/PhysRevLett.111.240402]. The former paper has been recently commented on by Vaidman [Phys. Rev. A 93, 036103 (2016)10.1103/PhysRevA.93.036103]. In this Reply we demonstrate that the comments are either invalid or, where valid, do not affect the results of our original paper.
Possible paths of a photon passing through a nested Mach-Zehnder interferometer on its way to a detector are analyzed using the consistent histories formulation of quantum mechanics, and confirmed using a set of weak measurements (but not weak values). The results disagree with an analysis by Vaidman [ Phys.\ Rev.\ A 87 (2013) 052104 ], and agree with a conclusion reached by Li et al.\ [ Phys.\ Rev.\ A 88 (2013) 046102 ]. However, the analysis casts serious doubt on the claim of Salih et al.\ (whose authorship includes Li et al.) [ Phys.\ Rev.\ Lett.\ 110 (2013) 170502 ] to have constructed a protocol for counterfactual communication: a channel which can transmit information even though it contains a negligible number of photons.
We present a procedure to completely determine the complex modular values of arbitrary observables of pre- and postselected ensembles, which works experimentally for all measurement strengths and all postselected states. This procedure allows us to discuss the physics of modular and weak values in interferometric experiments involving a qubit meter. We determine both the modulus and the argument of the modular value for any measurement strength in a single step, by simultaneously controlling the visibility and the phase in a quantum eraser interference experiment. Modular and weak values are closely related. Using entangled qubits for the probed and meter systems, we show that the phase of the modular and weak values has a topological origin. This phase is completely defined by the intrinsic physical properties of the probed system and its time evolution. The physical significance of this phase can thus be used to evaluate the quantumness of weak values.
Recently, A. Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.240402] performed a much-discussed experiment in which which-way information was obtained from the light in a nested Mach-Zehnder interferometer by weak measurement. The presented analysis using the two-state vector formalism drew the conclusions that the photons followed disconnected paths. We analyze this experiment using standard quantum optical methods and arrive at analytical expressions that match the experimental results without the need for such disconnected photon paths. We also propose a simple amendment to the experiment capable of displaying new phenomena, highlighting the advantages of our description. © 2015 American Physical Society.
"Protective measurement" refers to two related schemes for finding the
expectation value of an observable without disturbing the state of a quantum
system, given a single copy of the system that is subject to a "protecting"
operation. There have been several claims that these schemes support
interpreting the quantum state as an objective property of a single quantum
system. Here we provide three counter-arguments, each of which we present in
two versions tailored to the two different schemes. Our first argument shows
that the same resources used in protective measurement can be used to
reconstruct the quantum state in a different way via process tomography. Our
second argument is based on exact analyses of special cases of protective
measurement, and our final argument is to construct explicit "-epistemic"
toy models for protective measurement, which strongly suggest that protective
measurement does not imply the reality of the quantum state. The common theme
of the three arguments is that almost all of the information comes from the
"protection" operation rather than the quantum state of the system, and hence
the schemes have no implications for the reality of the quantum state.
The recent single-photon double-slit experiment of Steinberg et al., based on a weak measurement method proposed by Wiseman, showed that, by encoding the photon's transverse momentum behind the slits into its polarization state, the momentum profile can subsequently be measured on average, from a difference of the separated fringe intensities for the two circular polarization components. They then integrated the measured average velocity field, to obtain the average trajectories of the photons enroute to the detector array. In this paper, we propose a modification of their experiment, to demonstrate that the average particle velocities and trajectories change when the mode of detection changes. The proposed experiment replaces a single detector by a pair of detectors with a given spacing between them. The pair of detectors is configured so that it is impossible to distinguish which detector received the particle. The pair of detectors is then analogous to the simple pair of slits, in that it is impossible to distinguish which slit the particle passed through.To establish the paradoxical outcome of the modified experiment, the theory and explicit three-dimensional formulas are developed for the bilocal probability and current densities, and for the average velocity field and trajectories as the particle wavefunction propagates in the volume of space behind the Gaussian slits. Examples of these predicted results are plotted. Implementation details of the proposed experiment are discussed.
We examine some surprising results that have been obtained for pre- and postselected quantum systems. We show that these results depend on a counterfactual interpretation of the rule of Aharonov, Bergmann, and Lebowitz [Phys. Rev. 134, B1410 (1964)] (the ABL rule) and that this interpretation is not valid in general. We then argue, with the help of the consistent histories interpretation of quantum mechanics, that there is a special class of situations where application of the counterfactual interpretation of the ABL rule can be justified. We then reexamine the aforementioned surprising results.
The weak value, introduced by Aharonov et al. to extend the conventional
scope of physical observables in quantum mechanics, is an intriguing concept
which sheds new light on quantum foundations and is also useful for precision
measurement, but it poses serious questions on its physical meaning due to the
unconventional features including the complexity of its value. In this paper we
point out that the weak value has a direct connection with the wave-particle
duality, in the sense that the wave nature manifests itself in the imaginary
part while the particle nature in the real part. This is illustrated by the
double slit experiment, where we argue, with no conflict with complementarity,
that the trajectory of the particle can be inferred based on the weak value
without destroying the interference.
The average result of a weak measurement of some observable A can, under
post-selection of the measured quantum system, exceed the largest eigenvalue of
A. The nature of weak measurements, as well as the presence of post-selection
and hence possible contribution of measurement-disturbance, has led to a
long-running debate about whether or not this is surprising. Here, it is shown
that such "anomalous weak values" are non-classical in a precise sense: a
sufficiently weak measurement of one constitutes a proof of contextuality. This
clarifies, for example, which features must be present (and in an experiment,
verified) to demonstrate an effect with no satisfying classical explanation.
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In an recent work with the title "Asking Photons Where They Have Been," Danan et al. experimentally demonstrate an intriguing behavior of photons in an interferometer [Phys. Rev. Lett. 111, 240402 (2013), 10.1103/PhysRevLett.111.240402]. In their words: "The photons tell us that they have been in the parts of the interferometer through which they could not pass." They interpret the results using the two-state vector formalism of quantum theory and say that, although an explanation of the experimental results in terms of classical electromagnetic waves in the interferometer is possible (and they provide a partial description), it is not so intuitive. Here we present a more detailed classical description of their experimental results, showing that it is actually intuitive. The same description is valid for the quantum wave function of the photons propagating in the interferometer. In particular, we show that it is essential that the wave propagates through all parts of the interferometer to describe the experimental results. We hope that our work helps to give a deeper understanding of these interesting experimental results.
Why is the future so different from the past? Why does the past affect
the future and not the other way around? What does quantum mechanics
really tell us about the world? In this important and accessible book,
Huw Price throws fascinating new light these great mysteries of modern
physics, and connects them in a wholly original way. Price begins with
the mystery of the arrow of time. Price shows that, for over a century,
most physicists have thought about problems of time in the wrong way.
Misled by the human perspective from within time, which distorts and
exaggerates the differences between past and future, they have fallen
victim to what Price calls the "double standard fallacy": proposed
explanations of the difference between the past and the future turn out
to rely on a difference which has been slipped in at the beginning, when
the physicists themselves treat the past and future in different ways.
To avoid this fallacy, Price argues, we need to overcome our natural
tendency to think about the past and the future differently. We need to
imagine a point outside time--an Archimedean "view from nowhen"--from
which to observe time in an unbiased way. Time's Arrow and
Archimedes'Point presents an innovative and controversial view of time
and contemporary physics. In this exciting book, Price urges physicists,
philosophers, and anyone who has ever pondered the mysteries of time to
look at the world from the fresh perspective of Archimedes' Point and
gain a deeper understanding of ourselves, the universe around us, and
our own place in time.
We present an analysis of a nested Mach-Zehnder interferometer in which an ensemble of identical pre- and postselected particles leaves a weak trace. A knowledge of the weak value partially destroys the quantum interference. The results, contrary to some recent claims [Vaidman, Phys. Rev. A 87, 052104 (2013)], are in accordance with the usual quantum-mechanical expectations.
A simple classical probabilistic system (a simple card game) classically exemplifies Aharonov and Vaidman's 'three-box 'paradox'' (1991 J. Phys. A: Math. Gen. 24 2315), implying that the three-box example is neither quantal nor a paradox and leaving one with less difficulty to busy the interpreters of quantum mechanics. An ambiguity in the usual expression of the retrodiction formula is shown to have misled Albert et al (1985 Phys. Rev. Lett. 54 5) to a result not, in fact, 'curious'; the discussion illustrates how to avoid this ambiguity.
"... the energy tensor can be regarded only as a provisional means of representing matter. In reality, matter consists of electrically charged particles...."3
This book presents the first, comprehensive exposition of the interpretation of quantum mechanics pioneered by Louis de Broglie and David Bohm. The purpose is to explain how quantum processes may be visualized without ambiguity or confusion, in terms of a simple physical model. Developing the theme that a material system, such as an electron, is a particle guided by a surrounding quantum wave, an examination of the classic phenomena of quantum theory is presented to show how the spacetime orbits of an ensemble of particles can reproduce the statistical quantum predictions. The mathematical and conceptual aspects of this theory are developed carefully from first principles. The book thus provides a comprehensive overview of an approach which brings clarity to a subject notorious for its conceptual difficulties. It will, therefore, appeal to all physicists with an interest in the foundations of their subject.