Quantum interference experiments, modular variables and weak measurements

Tollaksen, Jeff; Aharonov, Yakir; Casher, A.; Kaufherr, T.; Nussinov, S.

doi:10.1088/1367-2630/12/1/013023

Cited by 81 publications

(123 citation statements)

References 44 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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“…Eventually, quantum mechanical calculations including these effects will be performed, as it is clear that in time scales much shorter than neuronal firings Ca 2+ wave packets spread over distances the size of typical synapses [29]. Note that gauge of A is not specified here, and this can lead to important effects especially at quantum scales [18].…”

Section: Vector Potential Of Eeg Dipolesmentioning

confidence: 99%

“…An early discussion of SMNI-VP contained in a review of short-term memory as calculated by SMNI was not as detailed [16]. Note that gauge of A is not specified here, and this can lead to important effects especially at quantum scales [18]. Current research is directed to more detailed interactions of SMNI-VP firing states with Ca 2+ waves.…”

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confidence: 99%

Influence of Macrocolumnar EEG on Ca Waves

Ingber¹

2012

SSRN Journal

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Abstract-A "smoking gun" for explicit top-down neocortical mechanisms that directly drive bottom-up processes that describe memory, attention, etc. The top-down mechanism considered are macrocolumnar EEG firings in neocortex, as described by a statistical mechanics of neocortical interactions (SMNI), developed as a magnetic vector potential A. The bottom-up process considered are Ca 2+ waves prominent in synaptic and extracellar processes that are considered to greatly influence neuronal firings. Here, the complimentary effects are considered, i.e., the influence of A on Ca 2+ momentum, p. The canonical momentum of a charged particle in an electromagnetic field, Π = p + qA (SI units), is calculated, where the charge of Ca 2+ is q = 2e, e is the magnitude of the charge of an electron, valid in both classical and quantum mechanics. It is shown that A is large enough to influence p. This suggests that, instead of the common assumption that Ca 2+ waves contribute to neuronal activity, they may in fact at times be caused by the influence of A of larger-scale EEG.Index Terms-short-term memory, astrocytes, neocortical dynamics, vector potential I. SMOKING GUN FOR TOP-DOWN PROCESSESThere is a growing awareness of the importance of multiple scales in many physical and biological systems, including neuroscience [1], [2]. As yet, there does not seem to be any "smoking gun" for explicit top-down mechanisms that directly drive bottom-up processes that describe memory, attention, etc. Of course, there are many top-down type studies demonstrating that neuromodulator [3] and neuronal firing states, e.g., as defined by EEG frequencies, can modify the milieu or context of individual synaptic and neuronal activity, which is still consistent with ultimate bottom-up paradigms. However, there is a logical difference between top-down milieu as conditioned by some prior external or internal conditions, and some direct top-down processes that direct cause bottom-up interactions specific to STM. Here, the operative word is "cause". A. Magnetism Influences in Living SystemsThere is a body of evidence that suggests a specific topdown mechanism for neocortical STM processing.An example of a direct physical mechanism that affects neuronal processing not part of "standard" sensory influences is the strong possibility of magnetic influences in birds at quantum levels of interaction [4]- [6]. It should be noted that this is just a proposed mechanism [7].The strengths of magnetic fields in neocortex may be at a threshold to directly influence synaptic interactions with astrocytes, as proposed for long-term memory (LTM) [ rise to even stronger magnetic fields. Columnar excitatory and inhibitory processes largely take place in different neocortical laminae, providing possibilities for more specific mechanisms. II. SMNI CONTEXTSince 1981 about 30 papers on a statistical mechanics of neocortical interactions (SMNI) has been detailed properties of short-term memory, long-term memory, EEG analyses, and other properties of neocortex [11]-[16].This disc...

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“…On the other hand, if they decide to only mark the atoms which left photons behind, neglecting the others, the screen will exhibit a classical pattern without interference. This analysis enforces the idea that post-selected ensembles are "purer" and contain more information than ensembles that are only preselected [17,18].…”

Section: Post-selectionmentioning

confidence: 61%

Complementarity and post-selection in an atomic double-slit interferometer

Bernardo¹

2013

Open Physics

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Abstract:This paper analyzes, theoretically, an atomic double-slit interferometer in order to probe the extent to which complementary properties affect quantum interference. It is shown that if the energy eigenstates of a two-level atom are one-to-one correlated with its particle and wave behaviors, complementary phenomena can be measured simultaneously, indicating a reinterpretation of the complementarity principle. We also demonstrate that these complementary properties can be further distinguished by using a post-selection process.

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Quantum interference experiments, modular variables and weak measurements

Cited by 81 publications

References 44 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

Influence of Macrocolumnar EEG on Ca Waves

Complementarity and post-selection in an atomic double-slit interferometer

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