What weak measurements and weak values really mean - Reply to Kastner

Despite their important applications in metrology and in spite of numerous experimental demonstrations, weak measurements are still confusing for part of the community. This sometimes leads to unjustified criticism. Recent papers have experimentally clarified the meaning and practical significance of weak measurements, yet in [R.E. Kastner, Found. Phys. 47, 697-707 (2017)], Kastner seems to take us many years backwards in the debate, casting doubt on the very term "weak value" and the meaning of weak measurements. Kastner appears to ignore both the basics and frontiers of weak measurements and misinterprets the weak measurement process and its outcomes. In addition, she accuses the authors of [Y. Aharonov et al., Ann. Phys. 355, 258-268 (2015)] in statements completely opposite to the ones they have actually made. There are many points of disagreement between Kastner and us, but in this short reply I will leave aside the ontology (which is indeed interpretational and far more complex than that described by Kastner) and focus mainly on the injustice in her criticism. I shall add some general comments regarding the broader theory of weak measurements and the Two-State-Vector Formalism (TSVF), as well as supporting experimental results. Finally, I will point out some recent promising results, which can be proven by (strong) projective measurements, without the need of employing weak measurements.Comment: Reply to arXiv:1702.04021 which criticizes our [Ann. Phys. 355, 258-268 (2015)]. Slightly revised version, Found. Phys. (2017

Quantum to Classical Transitions via Weak Measurements and Post-Selection

This work will incorporate a few related tools for addressing the conceptual difficulties arising from sewing together classical and quantum mechanics: deterministic operators, weak measurements and post-selection. Weak Measurement, based on a very weak von Neumann coupling, is a unique kind of quantum measurement with numerous theoretical and practical applications. In contrast to other measurement techniques, it allows to gather a small amount of information regarding the quantum system, with only a negligible probability of collapsing it. A single weak measurement yields an almost random outcome, but when performed repeatedly over a large ensemble, the averaged outcome becomes increasingly robust and accurate. Importantly, a long sequence of weak measurements can be thought of as a single projective measurement. I claim in this work that classical variables appearing in the macro-world, such as centre of mass, moment of inertia, pressure and average forces, result from a multitude of quantum weak measurements performed in the micro-world. Here again, the quantum outcomes are highly uncertain, but the law of large numbers obliges their convergence to the definite quantities we know from our everyday lives. By augmenting this description with a final boundary condition and employing the notion of "classical robustness under time-reversal" I will draw a quantitative borderline between the classical and quantum regimes. I will conclude by analyzing the role of macroscopic systems in amplifying and recording quantum outcomes.Comment: To be published as a book chapter in "Quantum Structural Studies: Classical Emergence from the Quantum Level", R.E. Kastner, J. Jeknic-Dugic, G. Jaroszkiewicz (Eds.), World Scientific Publishing Co. arXiv admin note: substantial text overlap with arXiv:1406.638

Past of a particle in an entangled state

Vaidman has proposed a controversial criterion for determining the past of a single quantum particle based on the "weak trace" it leaves. We here consider more general examples of entangled systems and analyze the past of single, as well as pairs of entangled pre- and postselected particles. Systems with non-trivial time evolution are also analyzed. We argue that in these cases, examining only the single-particle weak trace provides information which is insufficient for understanding the system as a whole. We therefore suggest to examine, alongside with the past of single particles, also the past of pairs, triplets and eventually the entire system, including higher-order, multipartite traces in the analysis. This resonates with a recently proposed top-down approach by Aharonov, Cohen and Tollaksen for understanding the structure of correlations in pre- and postselected systems.Comment: Added one reference and corrected a typo. Accepted to Int. J. Quantum In