arXiv subjects

Eliahu Cohen

Publications and source records attributed to Eliahu Cohen.

At least 91 records · Page 5Linked to original sources

arXiv2019

Why physical understanding should precede the mathematical formalism - conditional quantum probabilities as a case-study

Conditional probabilities in quantum systems which have both initial and final boundary conditions are commonly evaluated using the Aharonov-Bergmann-Lebowitz rule. In this short note we present a seemingly disturbing paradox that appears when applying the rule to systems with slightly broken degeneracies. In these cases we encounter a singular limit - the probability "jumps" when going from perfect degeneracy to negligibly broken one. We trace the origin of the paradox and solve it from both traditional and modern perspectives in order to highlight the physics behind it: the necessity to take into account the finite resolution of the measuring device. As a practical example, we study the application of the rule to the Zeeman effect. The analysis presented here may stress the general need to first consider the governing physical principles before heading to the mathematical formalism, in particular when exploring puzzling quantum phenomena.

quant-ph↗

arXiv2019

A Hydrodynamic Interpretation of Quantum Mechanics via Turbulence

A stochastic Euler equation is proposed, describing the motion of a particle density, forced by the random action of virtual photons in vacuum. After time averaging, the Euler equation is reduced to the Reynolds equation, well studied in turbulent hydrodynamics. It is shown that the average pressure is nonlocal and the magnitude of the turbulent flow obeys the Fick law. Using the Madelung transformation, the Schrodinger equation is derived without any other assumptions.

quant-ph↗

arXiv2019

Multiplicative Bell Inequalities

Bell inequalities are important tools in contrasting classical and quantum behaviors. To date, most Bell inequalities are linear combinations of statistical correlations between remote parties. Nevertheless, finding the classical and quantum mechanical (Tsirelson) bounds for a given Bell inequality in a general scenario is a difficult task which rarely leads to closed-form solutions. Here we introduce a new class of Bell inequalities based on products of correlators that alleviate these issues. Each such Bell inequality is associated with a unique coordination game. In the simplest case, Alice and Bob, each having two random variables, attempt to maximize the area of a rectangle and the rectangle's area is represented by a certain parameter. This parameter, which is a function of the correlations between their random variables, is shown to be a Bell parameter, i.e. the achievable bound using only classical correlations is strictly smaller than the achievable bound using non-local quantum correlations We continue by generalizing to the case in which Alice and Bob, each having now n random variables, wish to maximize a certain volume in n-dimensional space. We term this parameter a multiplicative Bell parameter and prove its Tsirelson bound. Finally, we investigate the case of local hidden variables and show that for any deterministic strategy of one of the players the Bell parameter is a harmonic function whose maximum approaches the Tsirelson bound as the number of measurement devices increases. Some theoretical and experimental implications of these results are discussed.

quant-ph↗

arXiv2019

Relativistic independence bounds nonlocality

If Nature allowed nonlocal correlations other than those predicted by quantum mechanics, would that contradict some physical principle? Various approaches have been put forward in the past two decades in an attempt to single out quantum nonlocality. However, none of them can explain the set of quantum correlations arising in the simplest scenarios. Here it is shown that generalized uncertainty relations, as well as a specific notion of locality give rise to both familiar and new characterizations of quantum correlations. In particular, we identify a condition, relativistic independence, which states that uncertainty relations are local in the sense that they cannot be influenced by other experimenters' choices of measuring instruments. We prove that theories with nonlocal correlations stronger than the quantum ones do not satisfy this notion of locality and therefore they either violate the underlying generalized uncertainty relations or allow experimenters to nonlocally tamper with the uncertainty relations of their peers.

quant-ph↗

arXiv2018

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.

quant-ph↗

arXiv2018

Determination of weak values of quantum operators using only strong measurements

Weak values have been shown to be helpful especially when considering them as the outcomes of weak measurements. In this paper we show that in principle, the real and imaginary parts of the weak value of any operator may be elucidated from expectation values of suitably defined density, flux and hermitian commutator operators. Expectation values are the outcomes of strong (projective) measurements implying that weak values are general properties of operators in association with pre- and post-selection and they need not be preferentially associated with weak measurements. They should be considered as an important measurable property which provides added information as compared with the "standard" diagonal expectation value of an operator. As a first specific example we consider the determination of the real and imaginary parts of the weak value of the momentum operator employing projective time of flight experiments. Then the results are analyzed from the point of view of Bohmian mechanics. Finally we consider recent neutron interferometry experiments used to determine the weak values of the neutron spin.

quant-ph↗

arXiv2018

Structured Quantum Projectiles

Matter wave interferometry is becoming an increasingly important technique in quantum metrology. However, unlike its photonic counterpart, this technique relies on the interference of particles possessing a non-zero rest mass and an electric charge. Matter waves, thus, can experience alterations in their wave-like features while propagating through uniform fields to which a linear potential can be attributed. Here, we derive analytical expressions for structured matter waves subjected to linear potentials. We show that the center of mass of corresponding to these wavefunctions follows the classical parabolic trajectory attributed to this potential and also provide the additional phase profile acquired by the wave upon propagation. Furthermore, we find that these features are identical for any structured wave, thus significantly simplifying the action of quantum effects pertaining to this potential in applications relying on structured quantum waves.

quant-ph↗

arXiv2018

Entangled Histories vs. the Two-State-Vector Formalism - Towards a Better Understanding of Quantum Temporal Correlations

The Two-State-Vector formalism and the Entangled Histories formalism are attempts to better understand quantum correlations in time. The main objective of this paper is to show that, with appropriately defined scalar products, both formalisms can be made isomorphic. We show that they treat operators and states on equal footing leading to the same statistics for all measurements. In particular, we discuss the topic of quantum correlations in time and show how they can be generated and analyzed in a consistent way in these formalisms. Furthermore, we elaborate on a novel behavior of quantum histories of evolving multipartite systems which do not exhibit global non-local correlations in time but nevertheless can lead to entangled reduced histories characterizing evolution of an arbitrarily chosen sub-system.

quant-ph↗

arXiv2018

On the Significance of the Quantum Mechanical Covariance Matrix

The characterization of quantum correlations, being stronger than classical, yet weaker than those appearing in non-signaling models, still poses many riddles. In this work we show that the extent of binary correlations in a general class of nonlocal theories can be characterized by the~existence of a certain covariance matrix. The set of quantum realizable two-point correlators in the~bipartite case then arises from a subtle restriction on the structure of this general covariance matrix. We also identify a class of theories whose covariance does not have neither a quantum nor an "almost quantum" origin, but which nevertheless produce the accessible two-point quantum mechanical correlators. Our approach leads to richer Bell-type inequalities in which the extent of nonlocality is intimately related to a non-additive entropic measure. In particular, it suggests that the Tsallis entropy with parameter q=1/2 is a natural operational measure of non-classicality. Moreover, when~generalizing this covariance matrix we find novel characterizations of the quantum mechanical set of correlators in multipartite scenarios. All these predictions might be experimentally validated when adding weak measurements to the conventional Bell test (without adding postselection).

quant-ph↗

arXiv2018

Interaction-Free Ghost-Imaging of Structured Objects

Quantum - or classically correlated - light can be employed in various ways to improve resolution and measurement sensitivity. In an "interaction-free" measurement, a single photon can be used to reveal the presence of an object placed within one arm of an interferometer without being absorbed by it. This method has previously been applied to imaging. With a technique known as "ghost imaging", entangled photon pairs are used for detecting an opaque object with significantly improved signal-to-noise ratio while preventing over-illumination. Here, we integrate these two methods to obtain a new imaging technique which we term "interaction-free ghost-imaging" that possesses the benefits of both techniques. While maintaining the image quality of conventional ghost-imaging, this new technique is also sensitive to phase and polarisation changes in the photons introduced by a structured object. Furthermore, thanks to the "interaction-free" nature of this new technique, it is possible to reduce the number of photons required to produce a clear image of the object (which could be otherwise damaged by the photons) making this technique superior for probing light-sensitive materials and biological tissues.

quant-ph↗

arXiv2018

Anomalous Weak Values Emerging from Strong Interactions between Light and Matter

Some predictions regarding pre- and post-selected states are far-reaching, thereby requiring validation with standard quantum measurements in addition to the customary weak measurements used so far, as well as other advanced techniques. We go further pursuing this goal, proposing two thought experiments which incorporate novel yet feasible validation methods of unconventional light-matter interactions. An excited atom traverses a Mach-Zehnder interferometer (MZI) under a special combination of pre- and post-selection. In the first experiment, photons emitted by the superposed atom, after being hit by two laser beams, are individually counted. Despite the interaction having definitely taken place, the numbers of photons emitted from each arm of the MZI are predicted, at the ensemble level, to be different from those expected with standard stimulated emission. In the second experiment, the atom spontaneously emits a photon while still in the MZI. This photon later serves as a strong measurement of the atom's energy upon hitting a photographic plate. The experiment is repeated to enable an interference effect of the emitted photons. Interestingly, the latter gives the appearance that the photons have been emitted by the atom from a position much farther from the two MZI arms L and R, as if in a "phantom arm" R'. These experiments also emphasize the key role of anomalous weak values in determining light-matter interactions. In fact, they present a straightforward realization of an entity we term counter-particles, namely pre- and post-selected states acting as if they have negative physical variables such as mass and energy. The novel verification methods we suggest for testing these predictions resemble weak measurements in some aspects, yet result from definite atomic transitions verified by the detected photons.

quant-ph↗

arXiv2018

Nonlocal Position Changes of a Photon Revealed by Quantum Routers

Since its publication, Aharonov and Vaidman's three-box paradox has undergone three major advances: i). A non-counterfactual scheme by the same authors in 2003 with strong rather than weak measurements for verifying the particle's subtle presence in two boxes. ii) A realization of the latter by Okamoto and Takeuchi in 2016. iii) A dynamic version by Aharonov et al. in 2017, with disappearance and reappearance of the particle. We now combine these advances together. Using photonic quantum routers the particle acts like a quantum "shutter." It is initially split between Boxes A, B and C, the latter located far away from the former two. The shutter particle's whereabouts can then be followed by a probe photon, split in both space and time and reflected by the shutter in its varying locations. Measuring the former is expected to reveal the following time-evolution: The shutter particle was, with certainty, in boxes A+C at t1, then only in C at t2, and finally in B+C at t3. Another branch of the split probe photon can show that boxes A+B were empty at t2. A Bell-like theorem applied to this experiment challenges any alternative interpretation that avoids disappearance-reappearance in favor of local hidden variables.

quant-ph↗

arXiv2018

Is the Quilted Multiverse Consistent with a Thermodynamic Arrow of Time?

Theoretical achievements, as well as much controversy, surround multiverse theory. Various types of multiverses, with an increasing amount of complexity, were suggested and thoroughly discussed in literature by now. While these types are very different, they all share the same basic idea: our physical reality consists of more than just one universe. Each universe within a possibly huge multiverse might be slightly or even very different from the others. The quilted multiverse is one of these types, whose uniqueness arises from the postulate that every possible event will occur infinitely many times in infinitely many universes. In this paper we show that the quilted multiverse is not self-consistent due to the instability of entropy decrease under small perturbations. We therefore propose a modified version of the quilted multiverse which might overcome this shortcoming. It includes only those universes where the minimal entropy occurs at the same instant of (cosmological) time. Only these universes whose initial conditions are fine-tuned within a small phase-space region would evolve consistently to form their "close" states at present. A final boundary condition on the multiverse may further lower the amount of possible, consistent universes. Finally, some related observations regarding the many-worlds interpretation of quantum mechanics and the emergence of classicality are discussed.

gr-qc↗

arXiv2018

Comment on "Measurements without probabilities in the final state proposal"

The final state proposal [G.T. Horowitz and J.M. Maldacena, J. High Energy Phys. 2004(2), 8 (2004)] is an attempt to relax the apparent tension between string theory and semiclassical arguments regarding the unitarity of black hole evaporation. The authors of [R. Bousso and D. Stanford, Phys. Rev. D 89, 044038 (2014)] analyze thought experiments where an infalling observer first verifies the entanglement between early and late Hawking modes and then verifies the interior purification of the same Hawking particle. They claim that "probabilities for outcomes of these measurements are not defined" and therefore suggest that "the final state proposal does not offer a consistent alternative to the firewall hypothesis." We show, in contrast, that one may define all the relevant probabilities based on the so-called ABL rule [Y. Aharonov, P.G. Bergmann, and J.L. Lebowitz, Phys. Rev. 134, 1410 (1964)], which is better suited for this task than the decoherence functional. We thus assert that the analysis of Bousso and Stanford cannot yet rule out the final state proposal.

quant-ph↗

arXiv2017

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.

quant-ph↗

arXiv2017

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.

quant-ph↗

arXiv2017

A 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 the following paper we answer these questions on the negative for a specific class of systems and measurements. We begin with simple two-particle example, where strong correlations arise between two apparently empty boxes. This leads to new surprising effects within atomic and electromagnetic systems. A general construction based on pre- and post-selected ensembles is then suggested, where the N-body correlation can be genuinely perceived as a global property, as long as one is limited to preforming a small set of measurements which we term "strictly local". We conclude that within time-symmetric quantum mechanics and under certain boundary conditions, high-order correlations can determine low-order ones, but not vice versa. Moreover, the latter seem to provide no information at all regarding the former. This supports a top-down structure in many-body quantum mechanics.

quant-ph↗

arXiv2017

Unveiling the curtain of superposition: Recent gedanken and laboratory experiments

What is the true meaning of quantum superposition? Can a particle genuinely reside in several places simultaneously? These questions lie at the heart of this paper which presents an updated survey of some important stages in the evolution of the three-boxes paradox, as well as novel conclusions drawn from it. We begin with the original thought experiment of Aharonov and Vaidman, and proceed to its non-counterfactual version. The latter was recently realized by Okamoto and Takeuchi using a quantum router. We then outline a dynamic version of this experiment, where a particle is shown to "disappear" and "re-appear" during the time evolution of the system. This surprising prediction based on self-cancellation of weak values is directly related to our notion of Quantum Oblivion. Finally, we present the non-counterfactual version of this disappearing-reappearing experiment. Within the near future, this last version of the experiment is likely to be realized in the lab, proving the existence of exotic hitherto unknown forms of superposition. With the aid of Bell's theorem, we prove the inherent nonlocality and nontemporality underlying such pre- and post-selected systems, rendering anomalous weak values ontologically real.

quant-ph↗