arXiv subjects

Eliahu Cohen

Publications and source records attributed to Eliahu Cohen.

At least 73 records · Page 4Linked to original sources

arXiv2020

Correlation Minor Norms, Entanglement Detection and Discord

In this paper we develop an approach for detecting entanglement, which is based on measuring quantum correlations and constructing a correlation matrix. The correlation matrix is then used for defining a family of parameters, named Correlation Minor Norms, which allow one to detect entanglement. This approach generalizes the computable cross-norm or realignment (CCNR) criterion, and moreover requires measuring a state-independent set of operators. Furthermore, we illustrate a scheme which yields for each Correlation Minor Norm a separable state that maximizes it. The proposed entanglement detection scheme is believed to be advantageous in comparison to other methods because correlations have a simple, intuitive meaning and in addition they can be directly measured in experiment. Moreover, it is demonstrated to be stronger than the CCNR criterion. We also illustrate the relation between the Correlation Minor Norm and entanglement entropy for pure states. Finally, we discuss the relation between the Correlation Minor Norm and quantum discord. We demonstrate that the CMN may be used to define a new measure for quantum discord.

quant-ph↗

arXiv2020

Realism and Causality II: Retrocausality in Energetic Causal Sets

We describe a new form of retrocausality, which is found in the behaviour of a class of causal set theories, called energetic causal sets (ECS). These are discrete sets of events, connected by causal relations. They have three orders: (1) a birth order, which is the order in which events are generated; this is a total order which is the true causal order, (2) a dynamical partial order, which prescribes the flows of energy and momentum amongst events, (3) an emergent causal order, which is defined by the geometry of an emergent Minkowski spacetime, in which the events of the causal sets are embedded. However, the embedding of the events in the emergent Minkowski spacetime may preserve neither the true causal order in (1), nor correspond completely with the microscopic partial order in (2). We call this disordered causality, and we here demonstrate its occurrence in specific ECS models. This is the second in a series of papers centered around the question: Should we accept violations of causality as a lesser price to pay in order to keep realist formulations of quantum theory? We begin to address this in the first paper [1] and continue here by giving an explicit example of an ECS model in the classical regime, in which causality is disordered.

gr-qc↗

arXiv2020

Weak-to-strong transition of quantum measurement in a trapped-ion system

Quantum measurement remains a puzzle through its stormy history from the birth of quantum mechanics to state-of-the-art quantum technologies. Two complementary measurement schemes have been widely investigated in a variety of quantum systems: von Neumann's projective 'strong' measurement and Aharonov's weak measurement. Here, we report the observation of a weak-to-strong measurement transition in a single trapped $40Ca^+$ ion system. The transition is realized by tuning the interaction strength between the ion's internal electronic state and its vibrational motion, which play the roles of the measured system and the measuring pointer, respectively. By pre- and post-selecting the internal state, a pointer state composed of two of the ion's motional wavepackets is obtained, and its central-position shift, which corresponds to the measurement outcome, demonstrates the transition from the weak-value asymptotes to the expected-value asymptotes. Quantitatively, the weak-to-strong measurement transition is characterized by a universal transition factor $e^{-Γ^2}$, where $Γ$ is a dimensionless parameter related to the system-apparatus coupling. This transition, which continuously connects weak measurements and strong measurements, may open new experimental possibilities to test quantum foundations and prompt us to re-examine and improve the measurement schemes of related quantum technologies.

quant-ph↗

arXiv2020

Experimental tests of Multiplicative Bell Inequalities

Bell inequalities are mathematical constructs that demarcate the boundary between quantum and classical physics. A new class of multiplicative Bell inequalities originating from a volume maximization game (based on products of correlators within bipartite systems) has been recently proposed. For these new Bell parameters, it is relatively easy to find the classical and quantum, i.e. Tsirelson, limits. Here, we experimentally test the Tsirelson bounds of these inequalities using polarisation-entangled photons for different number of measurements ($n$), each party can perform. For $n=2, 3, 4$, we report the experimental violation of local hidden variable theories. In addition, we experimentally compare the results with the parameters obtained from a fully deterministic strategy, and observe the conjectured nature of the ratio. Finally, utilizing the principle of "relativistic independence" encapsulating the locality of uncertainty relations, we theoretically derive and experimentally test new richer bounds for both the multiplicative and the additive Bell parameters for $n=2$. Our findings strengthen the correspondence between local and nonlocal correlations, and may pave the way for empirical tests of quantum mechanical bounds with inefficient detection systems.

quant-ph↗

arXiv2020

Computational capacity of pyramidal neurons in the cerebral cortex

The electric activities of cortical pyramidal neurons are supported by structurally stable, morphologically complex axo-dendritic trees. Anatomical differences between axons and dendrites in regard to their length or caliber reflect the underlying functional specializations, for input or output of neural information, respectively. For a proper assessment of the computational capacity of pyramidal neurons, we have analyzed an extensive dataset of three-dimensional digital reconstructions from the NeuroMorpho.Org database, and quantified basic dendritic or axonal morphometric measures in different regions and layers of the mouse, rat or human cerebral cortex. Physical estimates of the total number and type of ions involved in neuronal electric spiking based on the obtained morphometric data, combined with energetics of neurotransmitter release and signaling fueled by glucose consumed by the active brain, support highly efficient cerebral computation performed at the thermodynamically allowed Landauer limit for implementation of irreversible logical operations. Individual proton tunneling events in voltage-sensing S4 protein $α$-helices of Na$^{+}$, K$^{+}$ or Ca$^{2+}$ ion channels are ideally suited to serve as single Landauer elementary logical operations that are then amplified by selective ionic currents traversing the open channel pores. This miniaturization of computational gating allows the execution of over 1.2 zetta logical operations per second in the human cerebral cortex without combusting the brain by the released heat.

q-bio.NC↗

arXiv2020

Realism and causality I: Pilot wave and retrocausal models as possible facilitators

Of all basic principles of classical physics, realism should arguably be the last to be given up when seeking a better interpretation of quantum mechanics. We examine the de Broglie-Bohm pilot wave theory as a well developed example of a realistic theory. We present three challenges to a naive reading of pilot-wave theory, each based on a system of several entangled particles. With the help of a coarse graining of pilot wave theory into a discrete system, we show how these challenges can be answered. However this comes with a cost. In the description of individual systems, particles appear to scatter off empty branches of the wave function as if they were particles, and conversely travel through particles as if they were waves. More generally, the "particles" of pilot wave theory are led by the guidance equation to move in ways no classical particle would, involving apparent violations of the principles of inertia and momentum conservation.We next argue that the aforementioned cost can be avoided within a retrocausal model. In the proposed version of the pilot wave theory, the particle is guided by a combination of advanced and retarded waves. The resulting account for quantum physics seems to have greater heuristic power, it demands less damage to intuition, and moreover provides some general hints regarding spacetime and causality. This is the first of two papers. In the second [1] we show that, in the context of an explicit model, retrocausality, with respect to an effective, emergent spacetime metric, can coexist with a strict irreversibility of causal processes.

quant-ph↗

arXiv2020

Probing finite coarse-grained virtual Feynman histories with sequential weak values

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multi-time projection operators for a complete set of orthogonal quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse-graining in time and establish the incompatibility of weak values for non-orthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories.

quant-ph↗

arXiv2020

Analysis of single-particle nonlocality through the prism of weak measurements

Although regarded today as an important resource in quantum information, nonlocality has yielded over the years many conceptual conundrums. Among the latter are nonlocal aspects of single particles which have been of major interest. In this paper, the nonlocality of single quanta is studied in a square nested Mach-Zehnder interferometer with spatially separated detectors using a delayed choice modification of quantum measurement outcomes that depend on the complex-valued weak values. We show that if spacelike separated Bob and Alice are allowed to freely control their quantum devices, the geometry of the setup constrains the local hidden variables models. In particular, hidden signaling and a list of contextual instructions are required to split a quantum state characterized by a positive Wigner function into two quantum states with non-positive Wigner functions. This implies that local hidden variables models could rely neither on only two hidden variables for position and momentum, nor on simultaneous factorizability of both the hidden probability densities and weights of splitting to reproduce the correct quantum distributions. While our analysis does not fully exclude the existence of nonfactorizable local hidden variables models, it demonstrates that the recently proposed weak values of quantum histories necessitate contextual splitting of prior commitments to measurement outcomes, due to functional dependence on the total Feynman sum that yields the complex-valued quantum probability amplitude for the studied quantum transition. This analysis also highlights the quantum nature of weak measurements.

quant-ph↗

arXiv2020

Double Slit with an Einstein-Podolsky-Rosen Pair

In this somewhat pedagogical paper we revisit complementarity relations in bipartite quantum systems. Focusing on continuous variable systems, we examine the influential class of EPR-like states through a generalization to Gaussian states and present some new quantitative relations between entanglement and local interference within symmetric and asymmetric double-double-slit scenarios. This approach is then related to ancilla-based quantum measurements, and weak measurements in particular. Finally, we tie up the notions of distinguishability, predictability, coherence and visibility while drawing some specific connections between them.

quant-ph↗

arXiv2019

Geometric phase from Aharonov-Bohm to Pancharatnam-Berry and beyond

Whenever a quantum system undergoes a cycle governed by a slow change of parameters, it acquires a phase factor: the geometric phase. Its most common formulations are known as the Aharonov-Bohm, Pancharatnam and Berry phases, but both prior and later manifestations exist. Though traditionally attributed to the foundations of quantum mechanics, the geometric phase has been generalized and became increasingly influential in many areas from condensed-matter physics and optics to high energy and particle physics and from fluid mechanics to gravity and cosmology. Interestingly, the geometric phase also offers unique opportunities for quantum information and computation. In this Review we first introduce the Aharonov-Bohm effect as an important realization of the geometric phase. Then we discuss in detail the broader meaning, consequences and realizations of the geometric phase emphasizing the most important mathematical methods and experimental techniques used in the study of geometric phase, in particular those related to recent works in optics and condensed-matter physics.

quant-ph↗

arXiv2019

Entanglement: Quantum or Classical?

From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedankenexperiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced by Erwin Schrödinger nearly a century ago, entanglement has remained one of the most fascinating ideas that came out of quantum mechanics. Here, we attempt to explain what makes entanglement fundamentally different from any classical phenomenon. To this end, we start with a historical overview of entanglement and discuss several hidden variables models that were conceived to provide a classical explanation and demystify quantum entanglement. We discuss some inequalities and bounds that are violated by quantum states thereby falsifying the existence of some of the classical hidden variables theories. We also discuss some exciting manifestations of entanglement, such as N00N states and the non-separable single particle states. We conclude by discussing some contemporary results regarding quantum correlations and present a future outlook for the research of quantum entanglement.

quant-ph↗

arXiv2019

Photonic realization of erasure-based nonlocal measurements

Relativity theory severely restricts the ability to perform nonlocal measurements in quantum mechanics. Studying such nonlocal schemes may thus reveal insights regarding the relations between these two fundamental theories. Therefore, for the last several decades, nonlocal measurements have stimulated considerable interest. However, the experimental implementation of nonlocal measurements imposes profound restrictions due to the fact that the interaction Hamiltonian cannot contain, in general, nonlocal observables such as the product of local observables belonging to different particles at spacelike-separated regions. In this work, we experimentally realize a scheme for nonlocal measurements with the aid of probabilistic quantum erasure. We apply this scheme to the tasks of performing high accuracy nonlocal measurements of the parity, as well as measurements in the Bell basis, which do not necessitate classical communication between the parties. Unlike other techniques, the nonlocal measurement outcomes are available locally (upon successful postselection). The state reconstructed via performing quantum tomography on the system after the nonlocal measurement indicates the success of the scheme in retrieving nonlocal information while erasing any local data previously acquired by the parties. This measurement scheme allows realizing any controlled-controlled-gate with any coupling strength. Hence our results are expected to have conceptual and practical applications to quantum communication and quantum computation.

quant-ph↗

arXiv2019

A relational time-symmetric framework for analyzing the quantum computational speedup

The usual representation of quantum algorithms is limited to the process of solving the problem. We extend it to the process of setting the problem. Bob, the problem setter, selects a problem-setting by the initial measurement. Alice, the problem solver, unitarily computes the corresponding solution and reads it by the final measurement. This simple extension creates a new perspective from which to see the quantum algorithm. First, it highlights the relevance of time-symmetric quantum mechanics to quantum computation: the problem-setting and problem solution, in their quantum version, constitute pre- and post-selection, hence the process as a whole is bound to be affected by both boundary conditions. Second, it forces us to enter into relational quantum mechanics. There must be a representation of the quantum algorithm with respect to Bob, and another one with respect to Alice, from whom the outcome of the initial measurement, specifying the setting and thus the solution of the problem, must be concealed. Time-symmetrizing the quantum algorithm to take into account both boundary conditions leaves the representation to Bob unaltered. It shows that the representation to Alice is a sum over histories in each of which she remains shielded from the information coming to her from the initial measurement, not from that coming to her backwards in time from the final measurement. In retrospect, all is as if she knew in advance, before performing her problem-solving action, half of the information that specifies the solution of the problem she will read in the future and could use this information to reach the solution with fewer computation steps (oracle queries). This elucidates the quantum computational speedup in all the quantum algorithms examined.

quant-ph↗

arXiv2019

Spin-Spacetime Censorship

Quantum entanglement and relativistic causality are key concepts in theoretical works seeking to unify quantum mechanics and gravity. In this article, we show that the interplay between relativity theory and quantum entanglement has intriguing consequences for the spacetime surrounding elementary particles with spin. Classical and quantum gravity theories predict that a spin-generated magnetic dipole field causes a (slight) bending to the spacetime around particles, breaking its spherical symmetry. Motivated by the apparent break of spherical symmetry, we propose a very general gedanken experiment that does not rely on any specific theory of classical or quantum gravity, and analyze this gedanken experiment in the context of quantum information. We show that any spin-related deviation from spherical symmetry would violate relativistic causality. To avoid the violation of causality, the measurable spacetime around the particle's rest frame must remain spherically symmetric, potentially as a back-action by the act of measurement. This way, our gedanken experiment proves that there must be a censorship mechanism preventing the possibility of spacetime-based spin detection, which sheds new light on the interface between quantum mechanics and gravity. We emphasize that our proposed gedanken experiment is independent of any theory and by allowing spacetime to be quantized its purpose is to be used for testing present and future candidate theories of quantum gravity.

gr-qc↗

arXiv2019

Accelerated-Cherenkov radiation and signatures of radiation reaction

In this manuscript we examine an accelerated charged particle moving through an optical medium, and explore the emission of accelerated-Cherenkov radiation. The particle's reaction to acceleration creates a low-frequency spectral cutoff in the Cherenkov emission that has a sharp resonance at the superluminal threshold. Moreover, the effect of recoil on the radiation is incorporated kinematically through the use of an Unruh-DeWitt detector by setting an energy gap, i.e., the change in electron energy, to the recoil energy of the emitted photon. The simultaneous presence of recoil and acceleration conspire to produce a localized resonance peak in the emission. These theoretical considerations could be used to construct high precision tests of radiation reaction using Cherenkov emission under acceleration.

hep-ph↗

arXiv2019

Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes

Bell's theorem renders quantum correlations distinct from those of any local-realistic model. Although being stronger than classical correlations, quantum correlations are limited by the Tsirelson bound. This bound, however, applies for Hermitian, commutative operators corresponding to non-signaling observables in Alice's and Bob's spacelike-separated labs. As an attempt to explore theories beyond quantum mechanics and analyze the uniqueness of the latter, we examine in this work the extent of non-local correlations when relaxing these fundamental assumptions, which allows for theories with non-local signaling. We prove that, somewhat surprisingly, the Tsirelson bound in the Bell-Clauser-Horne-Shimony-Holt scenario, and similarly other related bounds on non-local correlations, remain effective as long as we maintain the Hilbert space structure of the theory. Furthermore, in the case of Hermitian observables we find novel relations between non-locality, local correlations, and signaling. We demonstrate that such non-local signaling theories are naturally simulated by quantum systems of parafermionic zero modes. We numerically study the derived bounds in parafermionic systems, confirming the bounds' validity yet finding a drastic difference between correlations of 'signaling' and 'non-signaling' sets of observables. We also propose an experimental procedure for measuring the relevant correlations.

quant-ph↗

arXiv2019

Nonlocal Quantum Erasure of Phase Objects

The Franson interference is a fourth order interference effect, which unlike the better known Hong-Ou-Mandel interference, does not require the entangled photon pairs to be present at the same space-time location for interference to occur - it is nonlocal. Here, we use a modified Franson interferometer to experimentally demonstrate the nonlocal erasure and correction of an image of a phase-object taken through coincidence imaging. This non-local quantum erasure technique can have several potential applications such as phase corrections in quantum imaging and microscopy and also user authentication of two foreign distant parties.

quant-ph↗

arXiv2019

Knowledge of Quantum Hidden Variables Enables Backwards-In-Time Signaling

Bell's theorem implies that any completion of quantum mechanics which uses hidden variables (that is, preexisting values of all observables) must be nonlocal in the Einstein sense. This customarily indicates that knowledge of the hidden variables would permit superluminal communication. Such superluminal signaling, akin to the existence of a preferred reference frame, is to be expected. However, here we provide a protocol that allows an observer with knowledge of the hidden variables to communicate with her own causal past, without superluminal signaling. That is, such knowledge would contradict causality, irrespectively of the validity of relativity theory. Among the ways we propose for bypassing the paradox there is the possibility of hidden variables that change their values even when the state does not, and that means that signaling backwards in time is prohibited in Bohmian mechanics.

quant-ph↗