Entanglement and quantum interference

2000

A fundamental entity in quantum mechanics is the quantum mechanical state. The only connection between the theory of quantum mechanics and our observable world is provided by state measurements, and in this interference between quantum states plays a key role. Recent interference experiments probing the world of quantum mechanics have started to resolve paradoxes and give new insights. While the classical concepts of phase and polarization are well established, the understanding of their quantum mechanical counterparts is not complete. While examining those concepts the increased understanding of quantum interference give r i s e t o n e w applications: In quantum cryptography, secure (protected by the laws of physics) secret quantum key distribution has been setup between places tens of kilometers apart. Quantum computers can be viewed as complex quantum interferometers. This emerging technique anticipates the construction of a new class of computers that can process data (superposition states) in parallel. Certain algorithms exist that can solve problems that groves exponentially for classical computers on a much faster polynomial growing time using quantum computers. The thesis is focused on the generation and detection of some non-classical few-photon states, and in particular on entangled states. A common aspect between the experiments of the thesis is the use of quantum interference. In paper A, the complementary wave-particle duality of light is examined. Paper B, C and D implements relative phase and polarization rotation experiments based on analogous theories. Using two photons, three orthogonal states of the relative phase operator and the polarization rotation operator can be generated. The techniques give a linear increase of the sensitivity of relative phase shifts and polarization rotations with the number of available photons. The sensitivity of classical measurement techniques are limited to the square of the number of available photons. Paper E uses the complementary wave-particle duality o f light i n a n i n terference experiment. The technique called interaction free measurements enables (at least in principle) the perfect detection of an absorbing object without the object absorbing any photon. Our method is based on the principle that a Fabry Perot interferometer tuned to resonance transmits an impinging photon. In contrast, when placing an object between the mirrors of the Fabry Perot Interferometer, the impinging photon will be re ected from the rst mirror. This technique using quantum objects could be used to produce entangled multi-photon states that can be used to improve the schemes of papers A, B, C, and D by going to an higher manifold (using a higher number of photons). v vi First of all I would like to thank my main supervisor Prof. Gunnar Bj ork for accepting me as a graduate student 1 in his group and for always being available whenever I needed guidance. I w ould like to express my deep and sincere gratitude to my (rst) experimental and (later) industrial supervisor Dr. Edgard Goobar for introducing me to the fascinating world of experimental optics. I would like to thank Prof. Anders Karlsson for giving me the opportunity t o p a rticipate in the quantum cryptography project. It has been a pleasure to cooperate with Mohamed Bourennane, Per Jonsson, Fredrik Gibson, Daniel Ljunggren and Dr. Andy Hening in that project. Likewise I have enjoyed searching for single photons with Val ery Zwiller and Hans G. Blom, even though I still regret that we d i d n ' t i n vestigate all the experimental facilities at Karolinska Institutet. It has also been a great experience to work with Dr. Alexei Trifonov's and Jonas S oderholm in the parametric down conversion experiments. Thanks to Prof. John Rarity at the Defense Research Agency in England for introducing me to their experimental setup in the beginning of my graduate studies. I w ould like to thank Prof. Alexander Sergienko, Prof. Bahaa E. A. Saleh, Prof. Malvin C. Teich and their Graduate Students for welcoming me with great hospitality to the Quantum Imaging Laboratory at Boston University (BU) 2. I am grateful to Mete Atature for providing me with assistance with the experimental setup at BU. A big and special thanks to my mother Wudase Goitom and my late father Tsegaye T errefe 3 for their never ending support and great con dence in me. My brother Tomas Tsegaye h a ve been the great pillar of our family and I owe h i m a big thank for taking care of our mother especially while I was in Boston and when I returned to write this thesis. I w ould also like to thank all my f r i e n d s 4 from KTH, BU and elsewhere that have in uenced me deeply. 1 Financial support has been provided from KTH (excellenstj anst), Ericsson (ISS'90), SSF and NFR is gratefully acknowledged 2 The trip was made possible by a grant from Jan och Karin Engbloms Stipendiefond 3 To whom this thesis is dedicated

1976

Continuamos con nuestro intento de demostrar la razones de nuestra inconformidad con la interpretacione de Mecanica Cwintica sobre los fen6menos de interferencia y difracci6n dadas pOl' las E cuelas de "Copenhagen" y .. tatistical". En e te articulo proponemo que el principio de uperposici6n e acepte como una realidad fi ica, no como una construcci6n matematica proyectada para obtener re u ILados y se debe e cudriiiar hasta el illtimo para averiguar us limites en el reino Cuantico.

Unpublished, 2019

The historical development of Quantum Mechanics is analysed and an alternative theory is proposed for the photo-electric effect. Einstein's photons are found to be unnecessary which brings into question the concept of Wave-Particle duality. An explanation of why particles behave as waves is given which uncovers the true 'wave function' and the reality of what happens during 'wave function collapse. These ideas lead in turn to an explanation of the phenomenon of Entanglement.

Journal of Physics A: Mathematical and General, 2002

An addition rule of impure density operators, which provides a pure state density operator, is formulated. Quantum interference including visibility property is discussed in the context of the density operator formalism. A measure of entanglement is then introduced as the norm of the matrix equal to the difference between a bipartite density matrix and the tensor product of partial traces. Entanglement for arbitrary quantum observables for multipartite systems is discussed. Star-product kernels are used to map the formulation of the addition rule of density operators onto the addition rule of symbols of the operators. Entanglement and nonlocalization of the pure state projector and allied operators are discussed. Tomographic and Weyl symbols (tomograms and Wigner functions) are considered as examples. The squeezed-states and some spin-states (two qubits) are studied to illustrate the formalism.

(Typo Corrections and minor revisions 5-10-23) The conventional analysis of both quantum product states and quantum entanglement is shown to be consistent with a local, hidden variable (LHV) model, where two spatially separated observers make independent local measurements on local wave functions that share a common random hidden source variable. A conventional quantum mechanical LHV derivation also suggests that four quanta are required to truly measure a "zero spin" singlet state, with two quanta detected by each observer. In contrast, Bell local hidden variable (BLHV) models and inequalities assume one quantum detection by each observer, which does accurately model product states, but NOT entangled states. It is also shown that quantum entanglement can be viewed as an interference phenomenon, and can be factored into a "disentangled" product of local wave functions at the two spatially separated observers. Experimental measurements of quantum entanglement appear to be measuring Bell product states, and yet see quantum entanglement; which may suggest a non-local hidden variable (NLHV) process, where a detection by one observer instantaneously modifies the wave function in transit to the other observer. However, this proposed non-local process has serious potential flaws. Alternatively, it is shown that "coincidence of clicks" measurements on local, hidden variable (LHV) entangled or product states can approximate the experimentally reported entangled behavior. Additional experiments could potentially discriminate between these interpretations of the experimental data.

2000

Many experiments have shown that quantum entanglement is physically real. In this paper, we will discuss its ontological origin, implications and applications by thinking outside the standard interpretations of quantum mechanics. We argue that quantum entanglement originates from the primordial spin processes in non-spatial and non-temporal pre-spacetime, implies genuine interconnectedness and inseparableness of once interacting quantum entities, plays vital roles

2019

Quantum entanglement, a term coined by Erwin Schrodinger in 1935, is a mechanical phenomenon at the quantum level wherein the quantum states of two (or more) particles have to be described with reference to each other though these particles may be spatially separated. This phenomenon leads to paradox and has puzzled us for a long time. The behaviour of entangled particles is apparently inexplicable, incomprehensible and like magic at work. Locality has been a reliable and fruitful principle which has guided us to the triumphs of twentieth century physics. But the consequences of the local laws in quantum theory could seem "spooky" and nonlocal, with some theorists questioning locality itself. Could two subatomic particles on opposite sides of the universe be really instantaneously connected? Is any theory which predicts such a connection essentially flawed or incomplete? Are the results of experiments which demonstrate such a connection being misinterpreted? These questions challenge our most basic concepts of spatial distance and time. Modern physics is in the process of dismantling the space all around us and the universe will never be the same. Quantum entanglement involves the utilisation of cutting edge technology and will bring great benefits to society. This paper traces the development of quantum entanglement and presents some possible explanations for the strange behaviour of entangled particles. This paper is published in an international journal.

The Schrödinger's wave function can naturally be realized as an 'instantaneous resonant spatial mode' in which quantum particle moves and hence the Born's rule is derived after identifying its origin. This realization facilitates the visualization of 'what's really going on?' in the Young's double-slit experiment which is known to be the central mystery of quantum mechanics. Also, an actual mechanism underlying the 'spooky-action-at-a-distance', another mystery regarding the entangled quantum particles, is revealed. Wheeler's delayed choice experiments, delayed choice quantum eraser experiment and delayed choice entanglement swapping experiments are unambiguously and naturally explained at a single quantum level without violating the causality. The reality of Nature represented by the quantum mechanical formalism is conceptually intuitive and is independent of the measurement problem. Quantum mechanics is an extremely successful theoretical description of Nature, especially in the sub-atomic world where the classical mechanistic concepts seem to fail completely. Nevertheless, for more than ninety years, there is no consensus about what kind of physical reality is being revealed by the quantum formalism irrespective of its ability to predict accurately the exact outcomes of various experiments. According to Prof. Feynman, the central mystery of quantum mechanics is contained in the Young's double-slit experiment which is about the wave-particle duality of a single quantum [1]. Twenty years later, he once again declared that the entanglement of two or more particles is one more deep mystery in the quantum world [2]. It is not only important but also unavoidably necessary to conceptually visualize the true picture of reality described by the quantum formalism not only for solving the above mentioned mysteries, but also for further progress in fundamental physics like quantum gravity, unification of fundamental forces, quantum cosmology e.t.c. In Young's double-slit experiment, a monochromatic source emits coherent light which passes through a double-slit assembly to a detector screen where an interference pattern reminiscent of wave nature is formed. On the other hand, photoelectric effect, Compton effect, Raman effect, e.t.c., strongly suggests the existence of particle nature of light. The usual intuition about particle is that it is a localized entity present at some definite position in space, whereas the wave is a delocalized one and hence they are incompatible with each other. But, light seems to possess both natures simultaneously; however, only one nature seems to be observable at a given moment. These mutually exclusive natures of light's behavior is generally known as wave-particle duality. Not only light, but all material particles like electrons, protons, atoms, molecules e.t.c., are known to exhibit the wave-particle duality [3–7]. The quantum formalism itself never imposes any limitations on its validity only to microscopic objects and it can, in principle, be applied to materials of any scale. See the Fig. 1 below representing the Youngs's double-slit experiment. Consider the single particles to be photons. In this case, each photon is fired at the double-slit one-at-a-time such that the time interval between consecutively fired photons may be greater than the time of arrival of any one photon from the source to the screen. This assures that, each and every photon is really independent and they don't know each other. As a large number of photons are being collected on the screen, an interference pattern gradually emerges. If slit-1 (slit-2) is blocked, then a clump pattern corresponding to single slit diffraction of slit-2 (slit-1), supposed to be of particle nature, appears on the screen. This suggests that every individual photon is aware of whether one or both slits are open. The interference pattern suggests to infer that a single particle-like photon 'somehow' passes through both the slits simultaneously. A surprise occurs when a detector observes through which slit a photon is really passing through. It always appears as going through slit-1 or slit-2 like a particle but never through both the slits simultaneously like a wave. However, now the interference pattern disappears and two clump patterns appear which look like a proof for the observed particle behavior at the respective slits. This is generally known as quantum enigma i.e., when photons are watched, they appear to go through only one slit like particles. But, when they are not watched, then they seem to go through both the slits simultaneously like a wave. Now, consider the Wheeler's delayed-choice situation [8]. The screen is removed quickly exposing the twin telescopes, after a photon has already passed through the double slits. The interference pattern which would have occurred on * Electronic address: [email protected]

Scientific God Journal, 2011

Knowing the mutual interconnection of everything with everything, it is no problem to interpret the interactions between the measuring and quantum systems as any other interactions between two or more systems consisting of elementary quantum dipoles. So, all relations between the measuring apparatus and measured quantum objects are only parts of the universal cosmic network of elementary quantum interactions creating the objective physical reality, independent of a human consciousness. But the observer, as a conscious subject, plays an active and creative role in his communication with the micro-world.