Quantum averages of weak values
TLDR
In this article, the authors re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability.Abstract:
We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability We show that the weak value can be regarded as a definite mechanical effect on a measuring probe specifically designed to minimize the back reaction on the measured system We then present an interesting framework for general measurement conditions (where the back reaction on the system may not be negligible) in which the measurement outcomes can still be interpreted as quantum averages of weak values We show that in the classical limit, there is a direct correspondence between quantum averages of weak values and posterior expectation values of classical dynamical properties according to the classical inference frameworkread more
Citations
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Journal ArticleDOI
Nonperturbative theory of weak pre- and post-selected measurements
TL;DR: In this paper, a nonperturbative theory of weak PPS measurements of an arbitrary system with an arbitrary meter, for arbitrary initial states of the system and the meter, is presented.
Book ChapterDOI
The Two-State Vector Formalism: An Updated Review
TL;DR: The two-state vector formalism of quantum mechanics is a time-symmetrized approach to standard quantum theory particularly helpful for the analysis of experiments performed on preand post-selected ensembles as mentioned in this paper.
Journal ArticleDOI
Weak values and the Leggett-Garg inequality in solid-state qubits
TL;DR: It is demonstrated that a weak value can be nonclassical if and only if a Leggett-Garg inequality can also be violated, and generalized weak values are described in which post-selection occurs on a range of weak measurement results.
Journal ArticleDOI
Weak values as interference phenomena
TL;DR: Weak values arise experimentally as conditioned averages of weak (noisy) observable measurements that minimally disturb an initial quantum state, and also as dynamical variables for reduced quantum state evolution even in the absence of measurement as discussed by the authors.
References
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Book
Mathematical Methods of Classical Mechanics
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Book
Mathematical Foundations of Quantum Mechanics
TL;DR: The Mathematical Foundations of Quantum Mechanics as discussed by the authors is a seminal work in theoretical physics that introduced the theory of Hermitean operators and Hilbert spaces and provided a mathematical framework for quantum mechanics.
Mathematical Foundations of Quantum Mechanics
TL;DR: The Mathematical Foundations of Quantum Mechanics as discussed by the authors is a seminal work in theoretical physics that introduced the theory of Hermitean operators and Hilbert spaces and provided a mathematical framework for quantum mechanics.
Journal ArticleDOI
How the result of a measurement of a component of the spin of a spin- 1/2 particle can turn out to be 100
TL;DR: It is found that the usual measuring procedure for preselected and postselected ensembles of quantum systems gives unusual results and under some natural conditions of weakness of the measurement, its result consistently defines a new kind of value for a quantum variable, which is called the weak value.
Journal ArticleDOI
Properties of a quantum system during the time interval between two measurements.
TL;DR: A description of quantum systems at the time interval between two successive measurements is presented, and how this approach leads to a new concept: a weak value of an observable.