Quantum entanglement for the uninitiated

AIP Conference Proceedings, 2009

A) Bell's theorem rests on a conjunction of three assumptions: realism, locality and "free will". A discussion of these assumptions will be presented. It will be also shown that, if one adds to the assumptions the principle or rotational symmetry of physical laws, a stronger version of the theorem emerges. (B) A link between Bell's theorem and communication complexity problems will be presented. This also includes experimental realizations, which surprisingly do not involve entanglement. (C) A new sufficient and necessary criterion for entanglement of general (mixed) states will be presented. It is derived using the same geometric starting point as the inclusion of the symmetry in (A). The set of entanglement identifiers (EI's) emerging via this method contains entanglement witnesses (EW's), but they form only a subset of all EI's. Thus the method is more powerful than the one based on EW's.

SSRN Electronic Journal, 2021

In this article give a very simple presentation of Bell's inequality by comparing it to a "quantum game show", followed by a simple description of Aspect's 1985 experiment involving entangled photons which confirms the inequality. The entire article is non-technical and requires no mathematical background other than high school mathematics and an understanding of basic concepts in probability. The physics involved in Aspect's experiment is also explained.

Handbook of Natural Computing, 2012

For individual events quantum mechanics makes only probabilistic predictions. Can one go beyond quantum mechanics in this respect? This question has been a subject of debate and research since the early days of the theory. Efforts to construct deeper, realistic, level of physical description, in which individual systems have, like in classical physics, preexisting properties revealed by measurements are known as hidden-variable programs. Demonstrations that a hiddenvariable program necessarily requires outcomes of certain experiments to disagree with the predictions of quantum theory are called "no-go theorems". The Bell theorem excludes local hidden variable theories. The Kochen-Specker theorem excludes noncontextual hidden variable theories. In local hidden-variable theories faster-thatlight-influences are forbidden, thus the results for a given measurement (actual, or just potentially possible) are independent of the settings of other measurement devices which are at space-like separation. In noncontextual hidden-variable theories the predetermined results of a (degenerate) observable are independent of any other observables that are measured jointly with it. It is a fundamental doctrine of quantum information science that quantum communication and quantum computation outperforms their classical counterparts. If this is to be true, some fundamental quantum characteristics must be behind betterthan-classical performance of information processing tasks. This chapter aims at establishing connections between certain quantum information protocols and foundational issues in quantum theory. After a brief discusion of the most common misinterpretations of Bell's theorem and a discussion of what its real me aning is, iť

viXra, 2017

Elementary particles such as electrons and photons can be entangled in pairs, meaning that while they appear to have separate lives they share a quantum-level interaction that defies a straightforward physical interpretation. In the case of electrons, this entanglement can manifest itself in spin states describing two particles that may be separated by enormous distances, yet somehow remain together in the same state. Consequently, a measurement performed on one electron’s spin appears to instantaneously determine the spin of its partner, even if it’s on the other side of the universe. This strange phenomenon, which has been verified many times in carefully conducted laboratory experiments, appears to violate the notions of objective reality and locality—the classical belief that nothing can travel faster than the speed of light.

Physica Scripta, 1998

The quantum physics of light is a most fascinating field. Here I present a very personal viewpoint, focusing on my own path to quantum entanglement and then on to applications. I have been fascinated by quantum physics ever since I heard about it for the first time in school. The theory struck me immediately for two reasons: (1) its immense mathematical beauty, and (2) the unparalleled precision to which its predictions have been verified again and again. Particularly fascinating for me were the predictions of quantum mechanics for individual particles, individual quantum systems. Surprisingly, the experimental realization of many of these fundamental phenomena has led to novel ideas for applications. Starting from my early experiments with neutrons, I later became interested in quantum entanglement, initially focusing on multi-particle entanglement like GHZ states. This work opened the experimental possibility to do quantum teleportation and quantum hyper-dense coding. The latter became the first entanglement-based quantum experiment breaking a classical limitation. One of the most fascinating phenomena is entanglement swapping, the teleportation of an entangled state. This phenomenon is fundamentally interesting because it can entangle two pairs of particles which do not share any common past. Surprisingly, it also became an important ingredient in a number of applications, including quantum repeaters which will connect future quantum computers with each other. Another application is entanglement-based quantum cryptography where I present some recent long-distance experiments. Entanglement swapping has also been applied in very recent so-called loophole-free tests of Bell's theorem. Within the physics community such loophole-free experiments are perceived as providing nearly definitive proof that local realism is untenable. While, out of principle, local realism can never be excluded entirely, the 2015 achievements narrow down the remaining possibilities for local realistic explanations of the quantum phenomenon of entanglement in a significant way. These experiments may go down in the history books of science. Future experiments will address particularly the freedom-of-choice loophole using cosmic sources of randomness. Such experiments confirm that unconditionally secure quantum cryptography is possible, since quantum cryptography based on Bell's theorem can provide unconditional security. The fact that the experiments were loophole-free proves that an eavesdropper cannot avoid detection in an experiment that correctly follows the protocol. I finally discuss some recent experiments with single-and entangled-photon states in higher dimensions. Such experiments realized quantum entanglement between two photons, each with quantum numbers beyond 10 000 and also simultaneous entanglement of two photons where each carries more than 100 dimensions. Thus they offer the possibility of quantum communication with more than one bit or qubit per photon. The paper concludes discussing Einstein's contributions and viewpoints of quantum mechanics. Even if some of his positions are not supported by recent experiments, he has to be given credit for the fact that his analysis of fundamental issues gave rise to developments which led to a new information technology. Finally, I reflect on some of the lessons learned by the fact that Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

2019

This work is a collection of papers on quantum entanglement. It is intended as a glimpse for the younger colleagues of the author at Ericsson Hungary. Our intention was to introduce as many features as possible, within a readable extent. Our selection criteria are very wide, the work spans the gap from university lecture through research paper to magazine article. Our goal is to illustrate that the topic is very interesting and it covers several unsolved problems. It can be a good basis for research.

2000

The paper is intended to be a survey of all the important aspects and results that have shaped the field of quantum computation and quantum information. The reader is first familiarized with those features and principles of quantum mechanics providing a more efficient and secure information processing. Their applications to the general theory of information, cryptography, algorithms, computational complexity and error-correction are then discussed. Prospects for building a practical quantum computer are also analyzed.

Mathematical Aspects of Quantum Computing 2007, 2008

Elements of quantum computing and quantum infromation processing are introduced for mathematics students. Subjects inclulde quantum physics, qubits, quantum gates, quantum algorithms, decoherece, quantum error correcting codes and physical realizations. My lectures should serve as introduction to other lectures. i λ i |λ i λ i |, where A|λ i = λ i |λ i. Then the expectation value A of a after measurements with respect to many copies of |ψ is A = ψ|A|ψ. (2) Let us expand |ψ in terms of |λ i as |ψ = i c i |λ i. According to A 2, the probability of observing λ i upon measurement of a is |c i | 2 and therefore the expectation value after many measurements is i λ i |c i | 2. If, conversely, Eq. (2) is employed, we will obtain the same result since ψ|A|ψ = i,j c * j c i λ j |A|λ i = i,j λ i c * j c i δ ij = i λ i |c i | 2. This measurement is called the projective measurement. Any particular outcome λ i will be found with the probability |c i | 2 = ψ|P i |ψ , where P i = |λ i λ i | is the projection operator and the state immediately after the measurement is |λ i or equivalently P i |ψ / ψ|P i |ψ .

Nature, 2000

This Chapter deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, and concludes by considering whether a perspective in terms of quantum information sheds new light on the conceptual problems of quantum mechanics.

2010