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2005
AI
Multi-particle entanglement presents unique properties distinct from bipartite entanglement, allowing for states comprised of multiple qubits that can exhibit tri-partite entanglement without any bi-partite entanglement. This chapter aims to outline the differences in the multi-partite setting, focusing on pure and mixed states, and introduces concepts such as stabilizer and graph states, reflecting on their theoretical implications and experimental applications in quantum information processing and metrology.
2001
Entanglement, according to Erwin Schrödinger the essence of quantum mechanics, is at the heart of the Einstein-Podolsky-Rosen paradox and of the so called quantum-nonlocality -the fact that a local realistic explanation of quantum mechanics is not possible as quantitatively expressed by violation of Bell's inequalities. Even as entanglement gains increasing importance in most quantum information processing protocols, its conceptual foundation is still widely debated. Among the open questions are: What is the conceptual meaning of quantum entanglement? What are the most general constraints imposed by local realism? Which general quantum states violate these constraints? Developing Schrödinger's ideas in an information-theoretic context we suggest that a natural understanding of quantum entanglement results when one accepts (1) that the amount of information per elementary system is finite and (2) that the information in a composite system resides more in the correlations than in properties of individuals. The quantitative formulation of these ideas leads to a rather natural criterion of quantum entanglement. Independently, extending Bell's original ideas, we obtain a single general Bell inequality that summarizes all possible constraints imposed by local realism on the correlations for a multi-particle system. Violation of the general Bell inequality results in an independent general criterion for quantum entanglement. Most importantly, the two criteria agree in essence, though the two approaches are conceptually very different. This concurrence strongly supports the information-theoretic interpretation of quantum entanglement and of quantum physics in general.
Foundations of Science, 2021
and the United States, to animate an interdisciplinary dialogue about fundamental issues of science and society. 'Entanglement' is a genuine quantum phenomenon, in the sense that it has no counterpart in classical physics. It was originally identified in quantum physics experiments by considering composite entities made up of two (or more) sub-entities which have interacted in the past but are now sufficiently distant from each other. If joint measurements are performed on the sub-entities when the composite entity is in an 'entangled state', then the sub-entities exhibit, despite their spatial separation, statistical correlations (expressed by the violation of 'Bell inequalities') which cannot be represented in the formalism of classical physics.
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.
All our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory. But the essence of quantum formalism -entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger -waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including "canonical" ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form -bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized. quantum computing with quantum data structure 37 IX. Classical algorithms detecting entanglement 37 X. Quantum entanglement and geometry 38 XI. The paradigm of local operations and classical communication (LOCC) 39 A. Quantum channel -the main notion 39 B. LOCC operations 39 XII. Distillation and bound entanglement 41 A. One-way hashing distillation protocol 41 B. Two-way recurrence distillation protocol 42 93 C. Byzantine agreement -useful entanglement for quantum and classical distributed computation 94 ACKNOWLEDGMENTS 94
2006
We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of the sets of separable and maximally entangled states. We treat in detail the two-qubit system and emphasise in what respect this case is a special one.
International Journal of Modern Physics B, 2013
The aspects of many particle systems as far as their entanglement is concerned is highlighted. To this end we briefly review the bipartite measures of entanglement and the entanglement of pairs both for systems of distinguishable and indistinguishable particles. The analysis of these quantities in macroscopic systems shows that close to quantum phase transitions, the entanglement of many particles typically dominates that of pairs. This leads to an analysis of a method to construct many-body entanglement measures. SL-invariant measures are a generalization to quantities as the concurrence, and can be obtained with a formalism containing two (actually three) orthogonal antilinear operators. The main drawback of this antilinear framework, namely to measure these quantities in the experiment, is resolved by a formula linking the antilinear formalism to an equivalent linear framework.
Foundations of Physics
A classical analogy of quantum mechanical entanglement is presented, using classical light beams. The analogy can be pushed a long way, only to reach its limits when we try to represent multiparticle, or nonlocal, entanglement. This demonstrates that the latter is of exclusive quantum nature. On the other hand, the entanglement of different degrees of freedom of the same particle might be considered classical. The classical analog cannot replace Einstein± Podolsky± Rosen type experiments, nor can it be used to build a quantum computer. Nevertheless, it does provide a reliable guide to the intuition and a tool for visualizing abstract concepts in low-dimensional Hilbert spaces.
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.
Journal of statistical physics, 2002
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of the paper deals with composite systems in pure states. After a detailed discussion and a precise formal analysis of the case of systems of distinguishable particles, the problems of entanglement and the one of the properties of subsystems of systems of identical particles are thoroughly discussed. This part is the most interesting and new and it focuses in all details various subtle questions which have never been adequately discussed in the literature. Some inappropriate assertions which appeared in recent papers are analyzed. The relations of the main subject of the paper with the nonlocal aspects of quantum mechanics, as well as with the possibility of deriving Bell's inequality are also considered.
2013
In [M. Piani et al., arXiv:1103.4032 (2011)] an activation protocol was introduced which maps the general non-classical (multipartite) correlations between given systems into bipartite entanglement between the systems and local ancillae by means of a potentially highly entangling interaction. Here, we study how this activation protocol can be used to entangle the starting systems themselves via entanglement swapping through a measurement on the ancillae. Furthermore, we bound the relative entropy of quantumness (a naturally arising measure of non-classicality in the scheme of Piani et al. above) for a special class of separable states, the so-called classical-quantum states. In particular, we fully characterize the classical-quantum two-qubit states that are maximally non-classical.
arXiv: Quantum Physics, 2015
We explore the question of entanglement as a universal resource for implementing quantum measurements by local operations and classical communication (LOCC). We show that for most multipartite systems (consisting of three or more subsystems), there is no entangled state from the same space that can enable all measurements by LOCC. This is in direct contrast to the bipartite case, where a maximally entangled state is an universal resource. Our results are obtained by considering the problem of local state discrimination using entanglement as a resource; and a key ingredient in our proofs is showing an equivalence between the problem of local state discrimination and that of unambiguous local state transformation. We also present partial characterization of universal resource states in multipartite systems.
(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.
But in this work which used the new method of decomposing the structure, such weakly entangled states violated the local bound and were confirmed to be genuine multipartite entanglement. [39]
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.
We present a notion of generalized entanglement which goes beyond the conventional definition based on quantum subsystems. This is accomplished by directly defining entanglement as a property of quantum states relative to a distinguished set of observables singled out by Physics. While recovering standard entanglement as a special case, our notion allows for substantially broader generality and flexibility, being applicable, in particular, to situations where existing tools are not directly useful.
We introduce a generalization of entanglement based on the idea that entanglement is relative to a distinguished subspace of observables rather than a distinguished subsystem decomposition. A pure quantum state is entangled relative to such a subspace if its expectations are a proper mixture of those of other states. Many information-theoretic aspects of entanglement can be extended to the general setting, suggesting new ways of measuring and classifying entanglement in multipartite systems. By going beyond the distinguishable-subsystem framework, generalized entanglement also provides novel tools for probing quantum correlations in interacting many-body systems.
Physics Letters A, 2015
The familiar Greenberger-Horne-Zeilinger (GHZ) states can be rewritten by entangling the Bell states for two qubits with a state of the third qubit, which is dubbed entangled entanglement. We show that in this way we obtain all 8 independent GHZ states that form the simplex of entangled entanglement, the magic simplex. The construction procedure allows a generalization to higher dimensions both, in the degrees of freedom (considering qudits) as well as in the number of particles (considering n-partite states). Such bases of GHZ-type states exhibit a certain geometry that is relevant for experimental and quantum information theoretic applications. Furthermore, we study the geometry of these particular state spaces, the inherent symmetries, the cyclicity of the phase operations, and the regions of (genuine multi-partite) entanglement and the several classes of separability. We find non-trivial geometrical properties and a conceptually clear procedure to compare state spaces of different dimensions and number of particles.
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