16 Multi-Photon Entanglement and Quantum Non-Locality
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Arxiv:2002.00255V3 [Quant-Ph] 13 Feb 2021 Lem (BVP)
A Path Integral approach to Quantum Fluid Dynamics Sagnik Ghosh Indian Institute of Science Education and Research, Pune-411008, India Swapan K Ghosh UM-DAE Centre for Excellence in Basic Sciences, University of Mumbai, Kalina, Santacruz, Mumbai-400098, India ∗ (Dated: February 16, 2021) In this work we develop an alternative approach for solution of Quantum Trajectories using the Path Integral method. The state-of-the-art technique in the field is to solve a set of non-linear, coupled partial differential equations (PDEs) simultaneously. We opt for a fundamentally different route. We first derive a general closed form expression for the Path Integral propagator valid for any general potential as a functional of the corresponding classical path. The method is exact and is applicable in many dimensions as well as multi-particle cases. This, then, is used to compute the Quantum Potential (QP), which, in turn, can generate the Quantum Trajectories. For cases, where closed form solution is not possible, the problem is formally boiled down to solving the classical path as a boundary value problem. The work formally bridges the Path Integral approach with Quantum Fluid Dynamics. As a model application to illustrate the method, we work out a toy model viz. the double-well potential, where the boundary value problem for the classical path has been computed perturbatively, but the Quantum part is left exact. Using this we delve into seeking insight in one of the long standing debates with regard to Quantum Tunneling. Keywords: Path Integral, Quantum Fluid Dynamics, Analytical Solution, Quantum Potential, Quantum Tunneling, Quantum Trajectories Submitted to: J. -
Simulation of the Bell Inequality Violation Based on Quantum Steering Concept Mohsen Ruzbehani
www.nature.com/scientificreports OPEN Simulation of the Bell inequality violation based on quantum steering concept Mohsen Ruzbehani Violation of Bell’s inequality in experiments shows that predictions of local realistic models disagree with those of quantum mechanics. However, despite the quantum mechanics formalism, there are debates on how does it happen in nature. In this paper by use of a model of polarizers that obeys the Malus’ law and quantum steering concept, i.e. superluminal infuence of the states of entangled pairs to each other, simulation of phenomena is presented. The given model, as it is intended to be, is extremely simple without using mathematical formalism of quantum mechanics. However, the result completely agrees with prediction of quantum mechanics. Although it may seem trivial, this model can be applied to simulate the behavior of other not easy to analytically evaluate efects, such as defciency of detectors and polarizers, diferent value of photons in each run and so on. For example, it is demonstrated, when detector efciency is 83% the S factor of CHSH inequality will be 2, which completely agrees with famous detector efciency limit calculated analytically. Also, it is shown in one-channel polarizers the polarization of absorbed photons, should change to the perpendicular of polarizer angle, at very end, to have perfect violation of the Bell inequality (2 √2 ) otherwise maximum violation will be limited to (1.5 √2). More than a half-century afer celebrated Bell inequality 1, nonlocality is almost totally accepted concept which has been proved by numerous experiments. Although there is no doubt about validity of the mathematical model proposed by Bell to examine the principle of the locality, it is comprehended that Bell’s inequality in its original form is not testable. -
Violation of Bell Inequalities: Mapping the Conceptual Implications
International Journal of Quantum Foundations 7 (2021) 47-78 Original Paper Violation of Bell Inequalities: Mapping the Conceptual Implications Brian Drummond Edinburgh, Scotland. E-mail: [email protected] Received: 10 April 2021 / Accepted: 14 June 2021 / Published: 30 June 2021 Abstract: This short article concentrates on the conceptual aspects of the violation of Bell inequalities, and acts as a map to the 265 cited references. The article outlines (a) relevant characteristics of quantum mechanics, such as statistical balance and entanglement, (b) the thinking that led to the derivation of the original Bell inequality, and (c) the range of claimed implications, including realism, locality and others which attract less attention. The main conclusion is that violation of Bell inequalities appears to have some implications for the nature of physical reality, but that none of these are definite. The violations constrain possible prequantum (underlying) theories, but do not rule out the possibility that such theories might reconcile at least one understanding of locality and realism to quantum mechanical predictions. Violation might reflect, at least partly, failure to acknowledge the contextuality of quantum mechanics, or that data from different probability spaces have been inappropriately combined. Many claims that there are definite implications reflect one or more of (i) imprecise non-mathematical language, (ii) assumptions inappropriate in quantum mechanics, (iii) inadequate treatment of measurement statistics and (iv) underlying philosophical assumptions. Keywords: Bell inequalities; statistical balance; entanglement; realism; locality; prequantum theories; contextuality; probability space; conceptual; philosophical International Journal of Quantum Foundations 7 (2021) 48 1. Introduction and Overview (Area Mapped and Mapping Methods) Concepts are an important part of physics [1, § 2][2][3, § 1.2][4, § 1][5, p. -
Quantum Nonlocality Explained
Quantum Nonlocality Explained Ulrich Mohrhoff Sri Aurobindo International Centre of Education Pondicherry 605002 India [email protected] Abstract Quantum theory's violation of remote outcome independence is as- sessed in the context of a novel interpretation of the theory, in which the unavoidable distinction between the classical and quantum domains is understood as a distinction between the manifested world and its manifestation. 1 Preliminaries There are at least nine formulations of quantum mechanics [1], among them Heisenberg's matrix formulation, Schr¨odinger'swave-function formu- lation, Feynman's path-integral formulation, Wigner's phase-space formula- tion, and the density-matrix formulation. The idiosyncracies of these forma- tions have much in common with the inertial reference frames of relativistic physics: anything that is not invariant under Lorentz transformations is a feature of whichever language we use to describe the physical world rather than an objective feature of the physical world. By the same token, any- thing that depends on the particular formulation of quantum mechanics is a feature of whichever mathematical tool we use to calculate the values of observables or the probabilities of measurement outcomes rather than an objective feature of the physical world. That said, when it comes to addressing specific questions, some formu- lations are obviously more suitable than others. As Styer et al. [1] wrote, The ever-popular wavefunction formulation is standard for prob- lem solving, but leaves the conceptual misimpression that [the] wavefunction is a physical entity rather than a mathematical tool. The path integral formulation is physically appealing and 1 generalizes readily beyond the domain of nonrelativistic quan- tum mechanics, but is laborious in most standard applications. -
Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars
PHYSICAL REVIEW LETTERS 121, 080403 (2018) Editors' Suggestion Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars Dominik Rauch,1,2,* Johannes Handsteiner,1,2 Armin Hochrainer,1,2 Jason Gallicchio,3 Andrew S. Friedman,4 Calvin Leung,1,2,3,5 Bo Liu,6 Lukas Bulla,1,2 Sebastian Ecker,1,2 Fabian Steinlechner,1,2 Rupert Ursin,1,2 Beili Hu,3 David Leon,4 Chris Benn,7 Adriano Ghedina,8 Massimo Cecconi,8 Alan H. Guth,5 † ‡ David I. Kaiser,5, Thomas Scheidl,1,2 and Anton Zeilinger1,2, 1Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria 2Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria 3Department of Physics, Harvey Mudd College, Claremont, California 91711, USA 4Center for Astrophysics and Space Sciences, University of California, San Diego, La Jolla, California 92093, USA 5Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 6School of Computer, NUDT, 410073 Changsha, China 7Isaac Newton Group, Apartado 321, 38700 Santa Cruz de La Palma, Spain 8Fundación Galileo Galilei—INAF, 38712 Breña Baja, Spain (Received 5 April 2018; revised manuscript received 14 June 2018; published 20 August 2018) In this Letter, we present a cosmic Bell experiment with polarization-entangled photons, in which measurement settings were determined based on real-time measurements of the wavelength of photons from high-redshift quasars, whose light was emitted billions of years ago; the experiment simultaneously ensures locality. Assuming fair sampling for all detected photons and that the wavelength of the quasar photons had not been selectively altered or previewed between emission and detection, we observe statistically significant violation of Bell’s inequality by 9.3 standard deviations, corresponding to an estimated p value of ≲7.4 × 10−21. -
Quantum Nonlocality As an Axiom
Foundations of Physics, Vol. 24, No. 3, 1994 Quantum Nonlocality as an Axiom Sandu Popescu t and Daniel Rohrlich 2 Received July 2, 1993: revised July 19, 1993 In the conventional approach to quantum mechanics, &determinism is an axiom and nonlocality is a theorem. We consider inverting the logical order, mak#1g nonlocality an axiom and indeterminism a theorem. Nonlocal "superquantum" correlations, preserving relativistic causality, can violate the CHSH inequality more strongly than any quantum correlations. What is the quantum principle? J. Wheeler named it the "Merlin principle" after the legendary magician who, when pursued, could change his form again and again. The more we pursue the quantum principle, the more it changes: from discreteness, to indeterminism, to sums over paths, to many worlds, and so on. By comparison, the relativity principle is easy to grasp. Relativity theory and quantum theory underlie all of physics, but we do not always know how to reconcile them. Here, we take nonlocality as the quantum principle, and we ask what nonlocality and relativistic causality together imply. It is a pleasure to dedicate this paper to Professor Fritz Rohrlich, who has contributed much to the juncture of quantum theory and relativity theory, including its most spectacular success, quantum electrodynamics, and who has written both on quantum paradoxes tll and the logical structure of physical theory, t2~ Bell t31 proved that some predictions of quantum mechanics cannot be reproduced by any theory of local physical variables. Although Bell worked within nonrelativistic quantum theory, the definition of local variable is relativistic: a local variable can be influenced only by events in its back- ward light cone, not by events outside, and can influence events in its i Universit6 Libre de Bruxelles, Campus Plaine, C.P. -
Quantum Nonlocality Does Not Exist
Quantum nonlocality does not exist Frank J. Tipler1 Department of Mathematics, Tulane University, New Orleans, LA 70118 Edited* by John P. Perdew, Temple University, Philadelphia, PA, and approved June 2, 2014 (received for review December 30, 2013) Quantum nonlocality is shown to be an artifact of the Copenhagen instantaneously the spin of particle 2 would be fixed in the op- interpretation, in which each observed quantity has exactly one posite direction to that of particle 1—if we assume that [2] col- value at any instant. In reality, all physical systems obey quantum lapses at the instant we measure the spin of particle 1. The mechanics, which obeys no such rule. Locality is restored if observed purported mystery of quantum nonlocality lies in trying to un- and observer are both assumed to obey quantum mechanics, as in derstand how particle 2 changes—instantaneously—in re- the many-worlds interpretation (MWI). Using the MWI, I show that sponse to what has happened in the location of particle 1. the quantum side of Bell’s inequality, generally believed nonlocal, There is no mystery. There is no quantum nonlocality. Particle is really due to a series of three measurements (not two as in the 2 does not know what has happened to particle 1 when its spin is standard, oversimplified analysis), all three of which have only measured. State transitions are entirely local in quantum me- local effects. Thus, experiments confirming “nonlocality” are actu- chanics. All these statements are true because quantum me- ally confirming the MWI. The mistaken interpretation of nonlocal- chanics tells us that the wave function does not collapse when ity experiments depends crucially on a question-begging version the state of a system is measured. -
The Mathematical Structure of Non-Locality & Contextuality
The Mathematical Structure of Non-locality & Contextuality Shane Mansfield Wolfson College University of Oxford A thesis submitted for the degree of Doctor of Philosophy Trinity Term 2013 To my family. Acknowledgements I would like to thank my supervisors Samson Abramsky and Bob Coecke for taking me under their wing, and for their encouragement and guidance throughout this project; my collaborators Samson Abramsky, Tobias Fritz and Rui Soares Barbosa, who have contributed to some of the work contained here; and all of the members of the Quantum Group, past and present, for providing such a stimulating and colourful environment to work in. I gratefully acknowledge financial support from the National University of Ireland Travelling Studentship programme. I'm fortunate to have many wonderful friends, who have played a huge part in making this such an enjoyable experience and who have been a great support to me. A few people deserve a special mention: Rui Soares Barbosa, who caused me to and kept me from `banging two empty halves of coconut together' at various times, and who very generously proof-read this dissertation; Daniel `The Font of all Knowledge' Corbett; Tahir Mansoori, who looked after me when I was laid up with a knee injury; mo chara dh´ılis,fear m´orna Gaeilge, Daith´ı O´ R´ıog´ain;Johan Paulsson, my companion since Part III; all of my friends at Wolfson College, you know who you are; Alina, Michael, Jon & Pernilla, Matteo; Bowsh, Matt, Lewis; Ant´on,Henry, Vincent, Joe, Ruth, the Croatians; Jerry & Joe at the lodge; the Radish, Ray; my flatmates; again, the entire Quantum Group, past and present; the Cambridge crew, Raph, Emma & Marion; Colm, Dave, Goold, Samantha, Steve, Tony and the rest of the UCC gang; the veteran Hardy Bucks, Rossi, Diarmuid & John, and the Abbeyside lads; Brendan, Cormac, and the organisers and participants of the PSM. -
1 Photon Statistics at Beam Splitters: an Essential Tool in Quantum Information and Teleportation
1 Photon statistics at beam splitters: an essential tool in quantum information and teleportation GREGOR WEIHS and ANTON ZEILINGER Institut f¨ur Experimentalphysik, Universit¨at Wien Boltzmanngasse 5, 1090 Wien, Austria 1.1 INTRODUCTION The statistical behaviour of photons at beam splitters elucidates some of the most fundamental quantum phenomena, such as quantum superposition and randomness. The use of beam splitters was crucial in the development of such early interferometers as the Michelson-Morley interferometer, the Mach- Zehnder interferometer and others for light. The most generally discussed beam splitter is the so-called half-silvered mirror. It was apparently originally considered to be a mirror in which the reflecting metallic layer is so thin that only half of the incident light is reflected, the other half being transmitted, splitting an incident beam into two equal parts. Today beam splitters are no longer constructed in this way, so it might be more appropriate to call them semi-reflecting beam splitters. Unless otherwise noted, we always consider in this paper a beam splitter to be semi-reflecting. While from the point of view of classical physics a beam splitter is a rather simple device and its physical understanding is obvious, its operation becomes highly non-trivial when we consider quantum behaviour. Therefore the questions we ask and discuss in this paper are very simply as follows: What happens to an individual particle incident on a semi-reflecting beam splitter? What will be the behaviour of two particle incidents simultaneously on a beam splitter? How can the behaviour of one- or two-particle systems in a series of beam splitters like a Mach-Zehnder interferometer be understood? i ii Rather unexpectedly it has turned out that, in particular, the behaviour of two-particle systems at beam splitters has become the essential element in a number of recent quantum optics experiments, including quantum dense coding, entanglement swapping and quantum teleportation. -
Do We Really Understand Quantum Mechanics? Franck Laloë
Do we really understand quantum mechanics? Franck Laloë To cite this version: Franck Laloë. Do we really understand quantum mechanics?. American Journal of Physics, American Association of Physics Teachers, 2001, 69, pp.655 - 701. hal-00000001v2 HAL Id: hal-00000001 https://hal.archives-ouvertes.fr/hal-00000001v2 Submitted on 14 Nov 2004 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Do we really understand quantum mechanics? Strange correlations, paradoxes and theorems. F. Lalo¨e Laboratoire de Physique de l’ENS, LKB, 24 rue Lhomond, F-75005 Paris, France February 4, 2011 Abstract This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general arguments based on realism and local causality. In fact, these correlations are completely impossible in any circumstance, except the very special situations designed by physicists especially to observe these purely quantum effects. Another general point that is emphasized is the necessity for the theory to predict the emergence of a single result in a single realization of an experiment. -
Experimental Quantum Teleportation
Experimental quantum teleportation Dirk Bouwmeester, Jian‐Wei Pan, Klaus Mattle, Manfred Eibl, Harald Weinfurter & Anton Zeilinger NATURE | VOL 390 | 11 DECEMBER 1997 Overview • Motivation • General theory behind teleportation • Experimental setup • Applications of teleportation • New research from this study Relaying quantum information is difficult Sending directly can take a lot of time Coherence can be lost in the transfer We can’t just measure a particle’s state and then reconstruct, because‐‐ Each state is a superposition of many states. Once we measure the particle, it will collapse into only one state, and all the other information is lost For example, a photon can be polarized or in a superposition of polarized states. Beam Splitter: horizontally polarized photons are reflected, vertically polarized photons are transmitted The measurement projects the photon onto one polarization or the other, and we lose information about the original state So, if we want to replicate the state, we can’t just measure and reconstruct… But we can use entanglement to replicate the state by quantum teleportation. We have Alice, with a particle in state <ψ1|. She wants to transfer it to Bob. Bob and Alice also have particles 2 and 3, which are entangled. …if Alice can entangle particle 1 and particle 2, …then particle 3 should be in the same state as the original particle 1. But how can we do this experimentally? Experimental verification of teleportation theory ‐1993: Bennett et al. suggest it is possible to transfer the state of one particle to another using entanglement Meanwhile: Quantum computing and cryptography develop ‐1995: Kwiat et al. -
Aspects of Quantum Non-Locality
2 Aspects of Quantum Non-locality. David Roberts. H. H. Wills Physics Laboratory, University of Bristol. A thesis submitted to the University of Bristol in accordance with the requirements of the degree of Doctor of Philosophy in the Faculty of Science. June 2004. i Abstract. In this thesis I will present work in three main areas, all related to quantum non-locality. The ¯rst is multipartite Bell inequalities. It is well known that quan- tum mechanics can not be described by any local hidden variable model, and so is considered to be a non-local theory. However for a system of several particles it is conceivable that this non-locality takes the form of non-local correlations within subsets of the particles, but only local correlations between the subsets themselves. This was ¯rst considered by Svetlichny [1] who produced a Bell type inequality to distinguish genuine three party non-locality from weaker forms involving only sub- sets of two particles. In chapter 3 I show that recent experiments to produce three particle entangled states can not yet con¯rm this three particle non-locality. In chapter 4 I give the generalization of Svetlichny's inequality for n particle systems. The second main area of research is presented in chapter 5. Entangled quan- tum systems produce correlations that are non-local, in the sense that they violate Bell inequalities. It is possible to abstract away from the physical source of these correlations and consider sets of correlations that are more non-local than quantum mechanics allows. The only constraint I make is that the joint probabilities can not allow signalling.