arXiv subjects
Publications and source records attributed to Eliahu Cohen.
Current methods for measuring magnetic flux are based on performing many measurements over a large ensemble of electrons. We propose a novel method based on wavefunction "revival" for measuring the flux modulo hc/2e using only a single electron. A preliminary analysis of the feasibility of the experiment is provided.
An EPR experiment is studied where each particle within the entangled pair undergoes a few weak measurements (WMs) along some pre-set spin orientations, with the outcomes individually recorded. Then the particle undergoes one strong measurement along an orientation chosen at the last moment. Bell-inequality violation is expected between the two final measurements within each EPR pair. At the same time, statistical agreement is expected between these strong measurements and the earlier weak ones performed on that pair. A contradiction seemingly ensues: (i) Bell's theorem forbids spin values to exist prior to the choice of the orientation measured; (ii) A weak measurement is not supposed to determine the outcome of a successive strong one; and indeed (iii) Almost no disentanglement is inflicted by the WMs; and yet (iv) The outcomes of weak measurements statistically agree with those of the strong ones, suggesting the existence of pre-determined values, in contradiction with (i). Although the conflict can be solved by mere mitigation of the above restrictions, the most reasonable resolution seems to be that of the Two-State-Vector Formalism (TSVF), namely, that the choice of the experimenter has been encrypted within the weak measurement's outcomes, even before the experimenters themselves know what their choice will be.
In this paper we perform a novel analysis of quantum Gaussian channels in the context of weak measurements. Suppose Alice sends classical information to Bob using a quantum channel. Suppose Bob is allowed to use only weak measurements, what would be the channel capacity? We formulate weak measurement theory in these terms and discuss the above question.
We revisit the analogy suggested by Madelung between a non-relativistic time-dependent quantum particle, to a fluid system which is pseudo-barotropic, irrotational and inviscid. We first discuss the hydrodynamical properties of the Madelung description in general, and extract a pressure like term from the Bohm potential. We show that the existence of a pressure gradient force in the fluid description does not violate Ehrenfest's theorem since its expectation value is zero. We also point out that incompressibility of the fluid implies conservation of density along a fluid parcel trajectory and in 1D this immediately results in the non-spreading property of wave packets, as the sum of Bohm potential and an exterior potential must be either constant or linear in space. Next we relate to the hydrodynamic description a thermodynamic counterpart, taking the classical behavior of an adiabatic barotopric flow as a reference. We show that while the Bohm potential is not a positive definite quantity, as is expected from internal energy, its expectation value is proportional to the Fisher information whose integrand is positive definite. Moreover, this integrand is exactly equal to half of the square of the imaginary part of the momentum, as the integrand of the kinetic energy is equal to half of the square of the real part of the momentum. This suggests a relation between the Fisher information and the thermodynamic like internal energy of the Madelung fluid. Furthermore, it provides a physical linkage between the inverse of the Fisher information and the measure of disorder in quantum systems - in spontaneous adiabatic gas expansion the amount of disorder increases while the internal energy decreases.
Among the (in)famous differences between classical and quantum mechanics, quantum counterfactuals seem to be the most intriguing. At the same time, they seem to underlie many quantum oddities. In this article, we propose a simple explanation for counterfactuals, on two levels. Quantum Oblivion (QO) is a fundamental type of quantum interaction that we prove to be the origin of quantum counterfactuals. It also turns out to underlie several well-known quantum effects. This phenomenon is discussed in the first part of the article, yielding some novel predictions. In the second part, a hypothesis is offered regarding the unique spacetime evolution underlying QO, termed Quantum Hesitation (QH). The hypothesis invokes advanced actions and interfering weak values, as derived first by the Two-State-Vector Formalism (TSVF). Here too, weak values are argued to underlie the familiar "strong" quantum values. With these, an event that appears to have never occurred can exert causal effects and then succumb to QO by another time-evolution involving negative weak values that eliminate them. We conclude with briefly discussing the implications of these ideas on the nature of time.
Entanglement and nonlocality are studied in the framework of pre-/post-selected ensembles with the aid of weak measurements and the Two-State-Vector Formalism. In addition to the EPR-Bohm experiment, we revisit the Hardy and Cheshire Cat experiments, whose pre- or post-selected states give rise to curious phenomena. We then turn to even more peculiar phenomenon suggesting "emerging correlations" between independent pre- and post-selected ensembles of particles. This can be viewed as a quantum violation of the classical "pigeonhole principle".
Motivated by successful classical models for noise reduction, we suggest a quantum technique for filtering noise out of quantum states. The purpose of this paper is twofold: presenting a simple construction of quantum cross-correlations between two wave-functions, and presenting a scheme for a quantum noise filtering. We follow a well-known scheme in classical communication theory that attenuates random noise, and show that one can build a quantum analog by using non-trace-preserving operators. By this we introduce a classically motivated signal processing scheme to quantum information theory, which can help reducing quantum noise, and particularly, phase flip noise.
Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the dynamics of a particle change when the particle interacts with its own (self) field. Self-force is a pressing issue and an active research topic in gravitational phenomena, as well as a source of controversies in classical electromagnetism. In this work, we study a hidden geometrical structure manifested by the electromagnetic field-lines that has the potential of eliminating all singularities from classical electrodynamics. We explore preliminary results towards a consistent way of treating both self- and external fields.
We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when and how a set of consecutive weak measurements converges to a strong measurement. Second, we show that for a small set of consecutive weak measurements, long before their convergence, one can separate close states without causing their collapse. We thus demonstrate a tradeoff between the success probability and the bias of the original vector towards collapse. Next we use post-selection within the Two-State-Vector Formalism and present the non-linear expansion of the expectation value of the measurement device's pointer to distinguish between two predetermined close vectors.
The novel concept of quantum logical entropy is presented and analyzed. We prove several basic properties of this entropy with regard to density matrices. We hereby motivate a different approach for the assignment of quantum entropy to density matrices.
A simple quantum interaction is analyzed, where the paths of two superposed particles asymmetrically cross, while a detector set to detect an interaction between them remains silent. Despite this negative result, the particles' states leave no doubt that a peculiar interaction has occurred: One particle's momentum changes while the other's remains unaffected, in apparent violation of momentum conservation. Revisiting the foundations of the quantum measurement process offers the resolution. Prior to the macroscopic recording of no interaction, a brief Critical Interval prevails, during which the particles and the detector's pointer form a subtle entanglement which immediately dissolves. It is this self-cancellation, henceforth "Quantum Oblivion (QO)," that lies at the basis of some well-known intriguing quantum effects. Such is Interaction-Free Measurement (IFM) [1] and its more paradoxical variants, like Hardy's Paradox [2] and the Quantum Liar Paradox [3]. Even the Aharonov-Bohm (AB) effect [4] and weak measurement [5] turn out to belong to this group. We next study interventions within the Critical Interval that produce some other peculiar effects. Finally we discuss some of the conceptual issues involved. Under the time-resolution of the Critical Interval, some nonlocal phenomena turn out to be local. Momentum is conserved due to the quantum uncertainties inflicted by the particle-pointer interaction, which sets the experiment's final boundary condition.
In [1] the authors claim that "weak values are not inherently quantum but rather a purely statistical feature". I argue that their model reproduces only few elements of weak measurements but fails to reproduce all the other intrinsically quantum features.
We briefly review various computational methods for the solution of optimization problems. First, several classical methods such as Metropolis algorithm and simulated annealing are discussed. We continue with a description of quantum methods, namely adiabatic quantum computation and quantum annealing. Next, the new D-Wave computer and the recent progress in the field claimed by the D-Wave group are discussed. We present a set of criteria which could help in testing the quantum features of these computers. We conclude with a list of considerations with regard to future research.
The notion of collapse is discussed and refined within the Two-State-Vector Formalism (TSVF). We show how a definite result of a measurement can be fully determined when considering specific forward and backward-evolving quantum states. Moreover, we show how macroscopic time-reversibility is attained, at the level of a single branch of the wavefunction, when several conditions regarding the final state and dynamics are met, a property for which we coin the term "classical robustness under time-reversal". These entail a renewed perspective on the measurement problem, the Born rule and the many-worlds interpretation.
Classical ergodicity retains its meaning in the quantum realm when the employed measurement is protective. This unique measuring technique is reexamined in the case of post-selection, giving rise to novel insights studied in the Heisenberg representation. Quantum statistical mechanics is then briefly described in terms of two-state density operators.
An experiment is proposed which can distinguish between two approaches to the reality of the electric field, and whether it has mechanical properties such as mass and stress. A charged pendulum swings within the field of a much larger charge. The two fields manifest the familiar apparent curvature of their field-lines, "bent" so as not to cross each other. If this phenomenon is real, the pendulum's center of mass must be proportionately shifted according to its lines' curvature. This prediction has no precise counterpart in the conventional interpretation, where this curvature is a mere superposition of the two fields' crossing lines. This empirical distinction, meriting test in itself, further bears on several unresolved issues in classical, quantum and relativistic electromagnetism.
Weak value is increasingly acknowledged as an important research tool for probing quantum pre- and post-selected ensembles, where some extraordinary phenomena occur. We generalize this concept to the broader notion of "weak potential" which enables predicting the interactions between particles when one of them is pre-/post-selected and the interaction potential is small. A harmonic oscillator is considered, undergoing weak position and momentum measurements between strong position measurement, and shown to possess peculiar physical properties, affecting the momentum rather than the position of another oscillator interacting with it.
Weak measurement is unique in enabling measurements of non-commuting operators as well as otherwise-undetectable peculiar phenomena predicted by the Two-State-Vector-Formalism (TSVF). This article, the first in two parts, explores novel applications of weak measurement. We first revisit the basic principles of quantum measurement with the aid of the Michelson interferometer. Weak measurement is then introduced in a simple visualized manner by a specific choice of the reflecting mirror's position and momentum uncertainties. Having introduced the method, we proceed to its refinement for a single particle. We consider a photon going back and forth inside the interferometer, oscillating between a superposed and a localized state, while subjected to alternating strong and weak measurements. This cyclic process enables directly measuring both the photon's position ("which-path") and momentum (interference), without disturbing either. An alternative explanation of this result, not invoking weak values, is thoroughly considered and shown to be at odds with the experimental data. Finally a practical application of this experiment is demonstrated, where a single photon measures the various transmission coefficients of a multiport beam-splitter yet remains superposed. This method is then generalized to measurement of the wave-function itself, performed again on a single particle.