Weak measurements and quantum-to-classical transitions in free electron-photon interactions.

How does the quantum-to-classical transition of measurement occur? This question is vital for both foundations and applications of quantum mechanics. Here, we develop a new measurement-based framework for characterizing the classical and quantum free electron-photon interactions and then experimentally test it. We first analyze the transition from projective to weak measurement in generic light-matter interactions and show that any classical electron-laser-beam interaction can be represented as an outcome of weak measurement. In particular, the appearance of classical point-particle acceleration is an example of an amplified weak value resulting from weak measurement. A universal factor, [Formula: see text], quantifies the measurement regimes and their transition from quantum to classical, where [Formula: see text] corresponds to the ratio between the electron wavepacket size and the optical wavelength. This measurement-based formulation is experimentally verified in both limits of photon-induced near-field electron microscopy and the classical acceleration regime using a DLA. Our results shed new light on the transition from quantum to classical electrodynamics, enabling us to employ the essence of the wave-particle duality of both light and electrons in quantum measurement for exploring and applying many quantum and classical light-matter interactions.

Conservation laws and the foundations of quantum mechanics.

In a recent paper, [Y. Aharonov, S. Popescu, D. Rohrlich, Proc. Natl. Acad. Sci. U.S.A.118 e1921529118 (2021)], it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature and it can and must be revisited to address the issue of conservation/nonconservation in individual cases. Specifically, in the above paper, an experiment was presented in which it can be proven that in some individual cases, energy is not conserved, despite being conserved statistically. It was felt however that this is worrisome and that something must be wrong if there are individual instances in which conservation does not hold, even though this is not required by the standard conservation law. Here, we revisit that experiment and show that although its results are correct, there is a way to circumvent them and ensure individual case conservation in that situation. The solution is however quite unusual, challenging one of the basic assumptions of quantum mechanics, namely that any quantum state can be prepared, and it involves a time-holistic, double nonconservation effect. Our results bring light on the role of the preparation stage of the initial state of a particle and on the interplay of conservation laws and frames of reference. We also conjecture that when such a full analysis of any conservation experiment is performed, conservation is obeyed in every individual case.

Quantum reality with negative-mass particles.

Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric formulation to assign eigenvalues to unmeasured observables of a system, which results in logical paradoxes, and no clear physical picture. A top-down ontological model is introduced that treats the weak values of observables as physically real during the time between pre- and post-selection (PPS), which avoids these paradoxes. The generally delocalized rank-1 projectors of a quantum system describe its fundamental ontological elements, and the highest-rank projectors corresponding to individual localized objects describe an emergent particle model, with unusual particles, whose masses and energies may be negative or imaginary. This retrocausal top-down model leads to an intuitive particle-based ontological picture, wherein weak measurements directly probe the properties of these exotic particles, which exist whether or not they are actually measured.

A unified approach to Schrödinger evolution of superoscillations and supershifts.

Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time-dependent Schrödinger equation is an important and challenging problem in quantum mechanics and mathematical analysis. The concept that encodes the persistence of superoscillations during the evolution is the (more general) supershift property of the solution. In this paper, we give a unified approach to determine the supershift property for the solution of the time-dependent one-dimensional Schrödinger equation. The main advantage and novelty of our results is that they only require suitable estimates and regularity assumptions on the Green's function, but not its explicit form. With this efficient general technique, we are able to treat various potentials.

A dynamical quantum Cheshire Cat effect and implications for counterfactual communication.

Here we report a type of dynamic effect that is at the core of the so called "counterfactual computation" and especially "counterfactual communication" quantum effects that have generated a lot of interest recently. The basic feature of these counterfactual setups is the fact that particles seem to be affected by actions that take place in locations where they never (more precisely, only with infinitesimally small probability) enter. Specifically, the communication/computation takes place without the quantum particles that are supposed to be the information carriers travelling through the communication channel or entering the logic gates of the computer. Here we show that something far more subtle is taking place: It is not necessary for the particle to enter the region where the controlling action takes place; it is enough for the controlled property of the particle, (i.e., the property that is being controlled by actions in the control region), to enter that region. The presence of the controlled property, without the particle itself, is possible via a quantum Cheshire Cat type effect in which a property can be disembodied from the particle that possesses it. At the same time, we generalize the quantum Cheshire Cat effect to dynamical settings, in which the property that is "disembodied" from the particle possessing it propagates in space, and leads to a flux of "disembodied" conserved quantities.

On conservation laws in quantum mechanics.

We raise fundamental questions about the very meaning of conservation laws in quantum mechanics, and we argue that the standard way of defining conservation laws, while perfectly valid as far as it goes, misses essential features of nature and has to be revisited and extended.

What Is Nonlocal in Counterfactual Quantum Communication?

We revisit the "counterfactual quantum communication" of Salih et al. [1], who claim that an observer "Bob" can send one bit of information to a second observer "Alice" without any physical particle traveling between them. We show that a locally conserved, massless current-specifically, a current of modular angular momentum, L_{z} mod 2ℏ-carries the one bit of information. We integrate the flux of L_{z} mod 2ℏ from Bob to Alice and show that it equals one of the two eigenvalues of L_{z} mod 2ℏ, either 0 or ℏ, thus precisely accounting for the one bit of information he sends her. We previously [2] obtained this result using weak values of L_{z} mod ℏ; here we do not use weak values.

Completely top-down hierarchical structure in quantum mechanics.

Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest "atoms"? In this paper we answer these questions in the negative for a specific class of systems and measurements. After a general introduction of the topic, we present the main idea with a simple two-particle example, where strong correlations arise between two apparently empty boxes. This leads to surprising effects within atomic and electromagnetic systems. A general construction based on pre- and postselected ensembles is then suggested, wherein the N-body correlation can be genuinely perceived as a global property, as long as one is limited to performing measurements which we term "strictly local." We conclude that under certain boundary conditions, higher-order correlations within quantum mechanical systems can determine lower-order ones, but not vice versa. Surprisingly, the lower-order correlations provide no information whatsoever regarding the higher-order correlations. This supports a top-down structure in many-body quantum mechanics.

The Weak Reality That Makes Quantum Phenomena More Natural: Novel Insights and Experiments.

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.

Interaction-Free Effects Between Distant Atoms.

A Gedanken experiment is presented where an excited and a ground-state atom are positioned such that, within the former's half-life time, they exchange a photon with 50% probability. A measurement of their energy state will therefore indicate in 50% of the cases that no photon was exchanged. Yet other measurements would reveal that, by the mere possibility of exchange, the two atoms have become entangled. Consequently, the "no exchange" result, apparently precluding entanglement, is non-locally established between the atoms by this very entanglement. This quantum-mechanical version of the ancient Liar Paradox can be realized with already existing transmission schemes, with the addition of Bell's theorem applied to the no-exchange cases. Under appropriate probabilities, the initially-excited atom, still excited, can be entangled with additional atoms time and again, or alternatively, exert multipartite nonlocal correlations in an interaction free manner. When densely repeated several times, this result also gives rise to the Quantum Zeno effect, again exerted between distant atoms without photon exchange. We discuss these experiments as variants of interaction-free-measurement, now generalized for both spatial and temporal uncertainties. We next employ weak measurements for elucidating the paradox. Interpretational issues are discussed in the conclusion, and a resolution is offered within the Two-State Vector Formalism and its new Heisenberg framework.

Finally making sense of the double-slit experiment.

Feynman stated that the double-slit experiment "…has in it the heart of quantum mechanics. In reality, it contains the only mystery" and that "nobody can give you a deeper explanation of this phenomenon than I have given; that is, a description of it" [Feynman R, Leighton R, Sands M (1965) The Feynman Lectures on Physics]. We rise to the challenge with an alternative to the wave function-centered interpretations: instead of a quantum wave passing through both slits, we have a localized particle with nonlocal interactions with the other slit. Key to this explanation is dynamical nonlocality, which naturally appears in the Heisenberg picture as nonlocal equations of motion. This insight led us to develop an approach to quantum mechanics which relies on pre- and postselection, weak measurements, deterministic, and modular variables. We consider those properties of a single particle that are deterministic to be primal. The Heisenberg picture allows us to specify the most complete enumeration of such deterministic properties in contrast to the Schrödinger wave function, which remains an ensemble property. We exercise this approach by analyzing a version of the double-slit experiment augmented with postselection, showing that only it and not the wave function approach can be accommodated within a time-symmetric interpretation, where interference appears even when the particle is localized. Although the Heisenberg and Schrödinger pictures are equivalent formulations, nevertheless, the framework presented here has led to insights, intuitions, and experiments that were missed from the old perspective.

The Case of the Disappearing (and Re-Appearing) Particle.

A novel prediction is derived by the Two-State-Vector-Formalism (TSVF) for a particle superposed over three boxes. Under appropriate pre- and post-selections, and with tunneling enabled between two of the boxes, it is possible to derive not only one, but three predictions for three different times within the intermediate interval. These predictions are moreover contradictory. The particle (when looked for using a projective measurement) seems to disappear from the first box where it would have been previously found with certainty, appearing instead within the third box, to which no tunneling is possible, and later re-appearing within the second. It turns out that local measurement (i.e. opening one of the boxes) fails to indicate the particle's presence, but subtler measurements performed on the two boxes together reveal the particle's nonlocal modular momentum spatially separated from its mass. Another advance of this setting is that, unlike other predictions of the TSVF that rely on weak and/or counterfactual measurements, the present one uses actual projective measurements. This outcome is then corroborated by adding weak measurements and the Aharonov-Bohm effect. The results strengthen the recently suggested time-symmetric Heisenberg ontology based on nonlocal deterministic operators. They can be also tested using the newly developed quantum router.

Quantum violation of the pigeonhole principle and the nature of quantum correlations.

The pigeonhole principle: "If you put three pigeons in two pigeonholes, at least two of the pigeons end up in the same hole," is an obvious yet fundamental principle of nature as it captures the very essence of counting. Here however we show that in quantum mechanics this is not true! We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box. Furthermore, we show that the above "quantum pigeonhole principle" is only one of a host of related quantum effects, and points to a very interesting structure of quantum mechanics that was hitherto unnoticed. Our results shed new light on the very notions of separability and correlations in quantum mechanics and on the nature of interactions. It also presents a new role for entanglement, complementary to the usual one. Finally, interferometric experiments that illustrate our effects are proposed.

Time and the quantum: erasing the past and impacting the future.

The quantum eraser effect of Scully and Drühl dramatically underscores the difference between our classical conceptions of time and how quantum processes can unfold in time. Such eyebrow-raising features of time in quantum mechanics have been labeled "the fallacy of delayed choice and quantum eraser" on the one hand and described "as one of the most intriguing effects in quantum mechanics" on the other. In the present paper, we discuss how the availability or erasure of information generated in the past can affect how we interpret data in the present. The quantum eraser concept has been studied and extended in many different experiments and scenarios, for example, the entanglement quantum eraser, the kaon quantum eraser, and the use of quantum eraser entanglement to improve microscopic resolution.

Classical analog to topological nonlocal quantum interference effects.

The two main features of the Aharonov-Bohm effect are the topological dependence of accumulated phase on the winding number around the magnetic fluxon, and nonlocality-local observations at any intermediate point along the trajectories are not affected by the fluxon. The latter property is usually regarded as exclusive to quantum mechanics. Here we show that both the topological and nonlocal features of the Aharonov-Bohm effect can be manifested in a classical model that incorporates random noise. The model also suggests new types of multiparticle topological nonlocal effects which have no quantum analog.