On the quantum theory of sequential measurements

Busch, Paul; Cassinelli, Gianni; Lahti, Pekka

doi:10.1007/bf01889690

Cited by 44 publications

(59 citation statements)

References 9 publications

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“…The total mass of the box before and after a photon passes is measured. Bohr showed that the process of weighting introduces a quantum uncertainty (in the gravitational field) leading to an uncertainty in time τ , which is the time needed to pass out of the box that usually called the time of passage [6,7], in accordance with the TEUR, eq (1) below. Aharonov and Rezinik [5] offer a similar interpretation, that the weighing leads, due to the back reaction of the system underlying a perturbation (energy measurement), to an uncertainty in the time of the internal clock relative to the external time [5].…”

Section: Introductionmentioning

confidence: 99%

Tunneling time in attosecond experiments and the time-energy uncertainty relation

Kullie

2015

Phys. Rev. A

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In this work we present a theoretical model supported with a physical reasoning leading to a relation which performs an excellent estimation for the tunneling time in attosecond and strong field experiments, where we address the important case of the He-atom [1,2]. Our tunneling time estimation is found by utilizing the time-energy uncertainty relation and represents a quantum clock. The tunneling time is also featured as the time of passage through the barrier similarly to the Einstein's photon box Gedanken experiment. Our work tackles an important study case for the theory of time in quantum mechanics, and is very promising for the search for a (general) time operator in quantum mechanics. The work can be seen as a new fundamental step in dealing with the tunneling time in strong field and ultra-fast science, and is appealing for more elaborate treatments using quantum wave packet dynamics and especially for complex atoms and molecules.Keywords: Tunneling time in strong field and ultra-fast science, time measurement in attosecond experiments, quantum clock, time-energy uncertainty relation, time and time-operator in quantum mechanics, photon box Gedanken experiment.

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Section: Introductionmentioning

confidence: 99%

Tunneling time in attosecond experiments and the time-energy uncertainty relation

Kullie

2015

Phys. Rev. A

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“…Indeed, since the appearance of QM time was controversial, the famous example is the Bohr-Einstein weighing photon box Gedanken experiment (BE-photon-box-GE). In [10] I showed with a simple tunneling model that the tunneling in the attosecond experiment is intriguingly similar to the BE-photon-box-GE, where the former can be seen as a realization to the later, with the electron as a particle (instead of the photon) and an uncertainty in the energy being determined from the (Coulomb) atomic potential due to the electron being disturbed by the field F , instead of (the photon) being disturbed by the weighting process and, as a result, an uncertainty in the gravitational potential [24], as shown by the famous proof of Bohr (see for example [25] p. 132) to the uncertainty (or indeterminacy) of time in the BE-photon-box-GE [15,16,24].…”

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confidence: 99%

How to understand the tunneling in attosecond experiment?

Kullie

2018

Annals of Physics

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The measurement of the tunneling time (T-time) in today's attosecond and strong field (low-frequency) experiments, despite its controversial discussion, offers a fruitful opportunity to understand time measurement and the time in quantum mechanics. In addition, as we will see in this work, a related controversial issue is the particulate nature of the radiation. Different models used to calculate the T-time will be discussed in this work in relation to my model of real T-time, Phys. Rev. 92, 052118 (2015), where an intriguing similarity to the Bohr-Einstein photon box Gedanken experiment was found. The tunneling process itself is still not well understood, but I am arguing that a scattering mechanism (by the laser wave packet) offers a possibility to understand the tunneling process in the tunneling region. This is related to the question about the corpuscular nature of light which is widely discussed in modern quantum optics experiments.Keywords: Attosecond physics, tunneling time and time measurement in attosecond experiments, timeenergy uncertainty relation, time and time-operator in quantum mechanics, Bohr-Einstein's photon box Gedanken experiment, multiphoton processing, Compton scattering, wave-particle duality. I. INTRODUCTIONThere is no doubt that the advent of 'attophysics' opens new perspectives in the study of time resolved phenomena in atomic and molecular physics [1][2][3][4][5] A similar controversial issue to the time issue (and the T-time and TEUR) is the wave-matter duality and the partic-

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“…However, in general theory of quantum measurements which is mathematically formalized in the framework of theory of quantum instruments [1][2][3][4][5] this constraint is nontrivial [6,8]. In the present paper, as [6,8], in we restrict our consideration to atomic instruments.…”

Section: Introductionmentioning

confidence: 99%

“…[5] and, especially, [6]. In the latter article it was shown that in the finite dimensional case and for atomic instruments adjacent reproducibility is equivalent to the projector type of quantum operations, i.e., M = P, where P is an orthogonal projector.…”

Section: Introductionmentioning

confidence: 99%

On the Possibility to Combine the Order Effect with Sequential Reproducibility for Quantum Measurements

Basieva

Khrennikov

2015

Found Phys

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In this paper we study the problem of a possibility to use quantum observables to describe a possible combination of the order effect with sequential reproducibility for quantum measurements. By the order effect we mean a dependence of probability distributions (of measurement results) on the order of measurements. We consider two types of the sequential reproducibility: adjacent reproducibility ( A − A) (the standard perfect repeatability) and separated reproducibility(A − B − A). The first one is reproducibility with probability 1 of a result of measurement of some observable A measured twice, one A measurement after the other. The second one, A − B − A, is reproducibility with probability 1 of a result of A measurement when another quantum observable B is measured between two A's. Heuristically, it is clear that the second type of reproducibility is complementary to the order effect. We show that, surprisingly, this may not be the case. The order effect can coexist with a separated reproducibility as well as adjacent reproducibility for both observables A and B. However, the additional constraint in the form of separated reproducibility of the B − A − B type makes this coexistence impossible. The problem under consideration was motivated by attempts to apply the quantum formalism outside of physics, especially, in cognitive psychology and psychophysics. However, it is also important for foundations of quantum physics as a part of the problem about the structure of sequential quantum measurements.

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On the quantum theory of sequential measurements

Cited by 44 publications

References 9 publications

Tunneling time in attosecond experiments and the time-energy uncertainty relation

Tunneling time in attosecond experiments and the time-energy uncertainty relation

How to understand the tunneling in attosecond experiment?

On the Possibility to Combine the Order Effect with Sequential Reproducibility for Quantum Measurements

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