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arXiv:1207.0655 · Physical Review A

Foundations and applications of weak quantum measurements

Yakir Aharonov, Eliahu Cohen, Avshalom C. Elitzur

Published May 8, 2014• 85 citations
arXivHTMLPDF

Abstract

Weak quantum measurement (WM) is unique in measuring noncommuting operators and other peculiar, otherwise-undetectable phenomena predicted by the two-state-vector-formalism (TSVF). The aim of this article is threefold: (i) introducing the foundations of WM and TSVF, (ii) studying temporal peculiarities predicted by TSVF and manifested by WM, and (iii) presenting applications of WM to single particles.

DOI
10.1103/physreva.89.052105

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Weak quantum measurement (WM) is unique in measuring noncommuting operators and other peculiar, otherwise-undetectable phenomena predicted by the two-state-vector-formalism (TSVF). The aim of this article is threefold: (i) introducing the foundations of WM and TSVF, (ii) studying temporal peculiarities predicted by TSVF and manifested by WM, and (iii) presenting applications of WM to single particles.
The novel physical quantity known as the weak value has attracted much attention for two reasons.First, from the perspective of applications, since the weak value can take arbitrarily large values, it is expected to be useful for detecting very small physical signals.Indeed, following an initial successful demonstration, numerous reports have supported the utility of this method, in which small signals are amplified through large weak values.Second, from the perspective of the foundations of quantum mechanics, the weak value is expected to shed light on certain quantum paradoxes.Its proponents argue that the weak value reveals the behavior of a quantum system prior to measurement.In this dissertation, we analyze the Two-State Vector Formalism (TSVF), which is the theoretical origin of the discovery of the weak value.The TSVF describes a quantum system that is conditioned by both pre-and post-selection.Therefore, the term "weak" does not necessarily imply that the formalism itself requires weak interactions.Rather, it refers to the fact that the measurement performed to detect the weak value is weak, typically characterized by a small coupling constant.While the weak value has attracted much attention, most studies have focused on the weak coupling regime, and the strong or intermediate coupling regions remain relatively unexplored.In this work, we numerically analyze systems described by the TSVF beyond the weak limit.Our findings suggest that the amount of information obtainable from the post-selected system has an upper bound.This observation motivates an information-theoretic analysis, through which we identify peculiar behavior in the information content associated with the quantum state in weak regime.
In this thesis, the article “Can a Future Choice Affect a Past Measurement’s\nOutcome?” is used as a starting point to explore the peculiar\ncorrelations between subsequent weak (i.e. non-projective) and\nstrong measurements in a variation of the EPR-Bell experiment. Bell’s\ntheorem states that particles may not possess predetermined values.\nHowever, as the outcomes of the subsequent weak and strong measurements\ndo statistically agree, an apparent contridiction arises. The\nauthors claim that the correlations between the results are best explained\nusing the time-symmetric two-state vector formalism, stating\nthat the experimenter’s future choice has been encrypted in the weak\nmeasurement’s outcomes.\nAlternative explanations are analyzed and a numerical simulation was\nmade to invigorate the notion of a so called weak-bias. Meaning that\nthe weak measurements sufficiently influence the particles’ states to\naccount for the statistical agreement.
Recently, the notions of Weak Measurement (WM), Weak Value (WV) and Two-State-Vector Formalism (TSVF), firstly introduced by Aharonov and collaborators, have extended the theoretical frame of standard quantum mechanics, thus providing a quantum-theoretical formalism for extracting new information from a system in the limit of small disturbance to its state. Here we provide an application to the case of two-body scattering with one body weakly interacting with its environment — e.g. a neutron being scattered from a H 2 molecule physisorbed in a carbon nanotube. In particular, we make contact with the field of incoherent inelastic neutron scattering from condensed systems. We provide a physically compelling prediction of a new quantum effect — a momentum transfer deficit; or equivalently, an enhanced energy transfer; or an apparent reduction of the mass of the struck particle. E.g., when a neutron collides with a H 2 molecule in a C-nanotube and excites its translational motion along the nanotube, it apparently exchanges energy and momentum with a fictitious particle with mass of 0.64 atomic mass units. Experimental results are shown and discussed in the new theoretical frame. The effect under consideration has no conventional interpretation, thus also supporting the novelty of the quantum theoretical framework of WV and TVSF. Some speculative remarks about possible applications being of technological interest (fuel cells and hydrogen storage; Li + batteries; information and communication technology) are shortly mentioned.
While quantum reality can be probed through measurements, the Two-State Vector Formalism (TSVF) reveals a subtler reality prevailing between measurements. Under special pre- and post-selections, odd physical values emerge. This unusual picture calls for a deeper study. Instead of the common, wave-based picture of quantum mechanics, we suggest a new, particle-based perspective: Each particle possesses a definite location throughout its evolution, while some of its physical variables (characterized by deterministic operators, some of which obey nonlocal equations of motion) are carried by "mirage particles" accounting for its unique behavior. Within the time interval between pre- and post-selection, the particle gives rise to a horde of such mirage particles, of which some can be negative. What appears to be "no-particle", known to give rise to interaction-free measurement, is in fact a self-canceling pair of positive and negative mirage particles, which can be momentarily split and cancel out again. Feasible experiments can give empirical evidence for these fleeting phenomena. In this respect, the Heisenberg ontology is shown to be conceptually advantageous compared to the Schrödinger picture. We review several recent advances, discuss their foundational significance and point out possible directions for future research.
In this paper we present the two-state vector formalism of quantum mechanics. It is a time-symmetrized approach to standard quantum theory particularly helpful for the analysis of experiments performed on pre- and post-selected ensembles. Several peculiar effects which naturally arise in this approach are considered. In particular, the concept of ``weak measurements'' (standard measurements with weakening of the interaction) is discussed in depth revealing a very unusual but consistent picture. Also, a design of a gedanken experiment which implements a kind of quantum ``time machine'' is described. The issue of time-symmetry in the context of the two-state vector formalism is clarified.