Quantum entanglement, one of the most intriguing features of multi-particle quantum systems, has become a fundamental building block in both quantum information processing and quantum computation. [10] The microscopic world is governed by the rules of quantum mechanics, where the properties of a particle can be completely undetermined and yet strongly correlated with those of other particles. Physicists from the University of Basel have observed these so-called Bell correlations for the first time between hundreds of atoms. [9] For the past 100 years, physicists have been studying the weird features of quantum physics, and now they're trying to put these features to good use. One prominent example is that quantum superposition (also known as quantum coherence)—which is the property that allows an object to be in two states at the same time—has been identified as a useful resource for quantum communication technologies. [8] Quantum entanglement—which occurs when two or more particles are correlated in such a way that they can influence each other even across large distances—is not an all-or-nothing phenomenon, but occurs in various degrees. The more a quantum state is entangled with its partner, the better the states will perform in quantum information applications. Unfortunately, quantifying entanglement is a difficult process involving complex optimization problems that give even physicists headaches. [7] A trio of physicists in Europe has come up with an idea that they believe would allow a person to actually witness entanglement. Valentina Caprara Vivoli, with the University of Geneva, Pavel Sekatski, with the University of Innsbruck and Nicolas Sangouard, with the University of Basel, have together written a paper describing a scenario where a human subject would be able to witness an instance of entanglement—they have uploaded it to the arXiv server for review by others. [6] The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron’s spin also, building the Bridge between the Classical and Quantum Theories. The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry. The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the relativistic quantum theory.
Quantum entanglement, one of the most intriguing features of multi-particle quantum systems, has become a fundamental building block in both quantum information processing and quantum computation. [10] The microscopic world is governed by the rules of quantum mechanics, where the properties of a particle can be completely undetermined and yet strongly correlated with those of other particles. Physicists from the University of Basel have observed these so-called Bell correlations for the first time between hundreds of atoms. [9] For the past 100 years, physicists have been studying the weird features of quantum physics, and now they're trying to put these features to good use. One prominent example is that quantum superposition (also known as quantum coherence)—which is the property that allows an object to be in two states at the same time—has been identified as a useful resource for quantum communication technologies. [8] Quantum entanglement—which occurs when two or more particles are correlated in such a way that they can influence each other even across large distances—is not an all-or-nothing phenomenon, but occurs in various degrees. The more a quantum state is entangled with its partner, the better the states will perform in quantum information applications. Unfortunately, quantifying entanglement is a difficult process involving complex optimization problems that give even physicists headaches. [7] A trio of physicists in Europe has come up with an idea that they believe would allow a person to actually witness entanglement. Valentina Caprara Vivoli, with the University of Geneva, Pavel Sekatski, with the University of Innsbruck and Nicolas Sangouard, with the University of Basel, have together written a paper describing a scenario where a human subject would be able to witness an instance of entanglement—they have uploaded it to the arXiv server for review by others. [6] The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron’s spin also, building the Bridge between the Classical and Quantum Theories. The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry. The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the relativistic quantum theory.
A team of quantum physicists from Harvard University measured a property called entanglement entropy, which quantifies the apparent randomness that comes with observing just a portion of an entangled whole. Markus Greiner and colleagues used lasers to create an optical cage with four compartments, each of which held a rubidium atom chilled to nearly absolute zero. The researchers could tweak the laser settings to adjust the height of the walls between compartments. If the walls were low enough, atoms could exploit their strange quantum ability to occupy multiple compartments at once. As the four atoms jumped around, they interacted and established a state of entanglement. [11] Physicists in the US and Serbia have created an entangled quantum state of nearly 3000 ultracold atoms using just one photon. This is the largest number of atoms ever to be entangled in the lab, and the researchers say that the technique could be used to boost the precision of atomic clocks. [10] The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron’s spin also, building the Bridge between the Classical and Quantum Theories. The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry. The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the relativistic quantum theory. The asymmetric sides are creating different frequencies of electromagnetic radiations being in the same intensity level and compensating each other. One of these compensating ratios is the electron – proton mass ratio. The lower energy side has no compensating intensity level, it is the dark energy and the corresponding matter is the dark matter.
Non-locality, Einstein's ''spooky action at a distance, has been observed between quantum objects separated by more than one kilometer. [29] Physicists at Saarland University in Saarbrucken, Germany, have succeeded in entangling a single atom with a single photon in the telecom wavelength range. [28] A team of physicists from ICTP-Trieste and IQOQI-Innsbruck has come up with a surprisingly simple idea to investigate quantum entanglement of many particles. [27] For the first time, physicists have experimentally demonstrated ternary—rather than binary—quantum correlations between entangled objects. [26] The physicists, Sally Shrapnel, Fabio Costa, and Gerard Milburn, at The University of Queensland in Australia, have published a paper on the new quantum probability rule in the New Journal of Physics. [25] Researchers have studied how a 'drumstick' made of light could make a microscopic 'drum' vibrate and stand still at the same time. [24] A University of Oklahoma physicist, Alberto M. Marino, is developing quantum-enhanced sensors that could find their way into applications ranging from biomedical to chemical detection. [23] A team of researchers from Shanghai Jiao Tong University and the University of Science and Technology of China has developed a chip that allows for two-dimensional quantum walks of single photons on a physical device. [22] The physicists, Sally Shrapnel, Fabio Costa, and Gerard Milburn, at The University of Queensland in Australia, have published a paper on the new quantum probability rule in the New Journal of Physics. [21] Probabilistic computing will allow future systems to comprehend and compute with uncertainties inherent in natural data, which will enable us to build computers capable of understanding, predicting and decision-making. [20] For years, the people developing artificial intelligence drew inspiration from what was known about the human brain, and it has enjoyed a lot of success as a result. Now, AI is starting to return the favor. [19]
While physicists are continually looking for ways to unify the theory of relativity, which describes large-scale phenomena, with quantum theory, which describes small-scale phenomena, computer scientists are searching for technologies to build the quantum computer using Quantum Information. In August 2013, the achievement of fully deterministic quantum teleportation, using a hybrid technique, was reported. On 29 May 2014, scientists announced a reliable way of transferring data by quantum teleportation. Quantum teleportation of data had been done before but with highly unreliable methods. The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron’s spin also, building the Bridge between the Classical and Quantum Theories. The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry. The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the Relativistic Quantum Theory and making possible to build the Quantum Computer with the help of Quantum Information.
A quantum entangled state is a quantum superposition state. The principle of quantum superposition, and therefore the existence of quantum entanglement, is contingent upon the validity of quantum theory. Thus, the generation of quantum entanglement requires that interactions occur between small-mass particles localized in a confined spatial region, resulting in each particle’s quantum state being a bound state. In other words, the prerequisite for the validity of quantum theory must be satisfied. At the same time, conserved quantities must exist between quantum superposition states, as only quantum states with conserved quantities can undergo superposition, allowing the particle system to generate quantum entangled states. Quantum entangled states can occur between electrons within an atom, between atoms, between molecules, or between atoms and molecules. Within the atomic nucleus, quantum entanglement can exist among protons, neutrons, and the quarks. In superconductivity, superfluidity, and Bose-Einstein condensation, they manifest as macroscopic quantum entanglement, which respectively come from the statistical results of a large amount of microscopic quantum entanglement between electrons, atoms or molecules. For massive macroscopic objects, they exhibit classical properties that cannot be described by quantum theory, and the principle of quantum superposition does not hold. Therefore, no entangled state is generated. It should be particularly emphasized that even for microscopic particle systems, if they exist in a large spatial region, they cannot be described by quantum theory. In such cases, the quantum superposition principle does not hold, and quantum entanglement phenomena do not exist. Therefore, within a large spatial region, multi-electron, multi-photon, and other microscopic systems do not have quantum entangled states; under certain conditions, quantum correlated states can be generated. Consequently, in a large spatial region, the mainstream viewpoints about non-locality—such as the so-called instantaneous collapse of entangled particles during measurement, infinite propagation speed, and the “spooky action at a distance”—are all incorrect. In experiments related to quantum communication and the verification of Bell’s inequality, the quantum states used are quantum correlated states rather than quantum entangled states. Regardless of whether the systems are microscopic or macroscopic, phenomena occurring in a large spatial region must adhere to the principles of causality, realism, and locality. In other words, Einstein’s viewpoint is correct.
In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible quantities are not allowed by classical mechanics, a feature that is called as "quantum nonlocality". An experimental observation of those correlations, in other words, a violation of the limits imposed by classical physics, implies the correctness of quantum description and invalidates the classical, local realistic models. The first Bell experiments were proposed by Clauser, Horne, Shimony, and Holt, who invented the most famous Bell's inequality [13]. Later, the Aspect experiments were satisfactory enough for the physics community to be conclusive about the validation of quantum mechanics [1][3][4][2]. Ekert's work on applications of quantum nonlocality to communication resulted in the new field of quantum communication and cryptography, and turned the research program into a practical one [20]. Pitowsky showed a method to find all expressions of limitations due to local realism, all Bell's inequalities, for a given physical scenario. He also proved that the problem is, unfortunately, NP-complete and hence as the scenarios get more complex, they also become computationally intractable [33][34]. Therefore, different methods for the solution of special cases of the problem are necessary. Inequalities found for those special cases can be called classes of Bell's inequalities. For example, Werner and Wolf [41] and Collins, Gisin, Linden, Massar, and Popescu [16] found classes that cover a wide range of scenarios. Our work is a similar kind of effort to produce and study new types of Bell's inequalities.
Introduction We will now turn to quantum entanglements and their contemporary, possibly practical, interest. Entanglements, first discussed in the E.P.R. paradox (Einstein, Podolsky, Rosen, 1935) are a perplexing nonlocal feature of quantum mechanics. This was immediately and succinctly discussed by Schrödinger (1935). The long history of this apparent paradox is outlined in the wonderful book of Jammer (1974). We will not focus on the central issue of “hidden variables” and their resolution by the Bell inequalities (Bell, 1964) and the test, nor the failure, of these in experiment (see Fry, 1998). The distinctive quantum nature of entanglements has led to two quantum effects which we will discuss: quantum information teleportation (Zeilenger, 1998) and quantum computation by means of entangled states. A nice, recent, elementary introduction to the latter is in the Los Alamos reports of James and Kwiat (2002). The quantum correlations or entanglements are sensitive to environmental destruction. This was pointed out early by Zurek, who termed this “decoherence.” The loss of coherence may occur on a short time scale. Recent discussions have been given by Zurek (2002, 2003). We have already given a theoretical example early in Chapter 2. It is pertinent to discuss this here, since it is a property of opensystem quantum master equations that is a central part of our study in this book. In a sense, the decoherence of correlations has turned out to be a “practical” application of these theoretical notions. Are there remedies for unwanted decoherence? Quantum error correction is a possibility. This will be mentioned also. Entanglements: foundations Following the reading of the E.P.R. paper, Schrödinger (1935b) quickly repeated the argument from quantum theory, but more generally. He introduced the term “entanglement” to describe what he seemed to agree was a curious, if not unacceptable, property. Let us follow his point of view. Given a state ψ ( x, y ) of a composite system of particles x and y formed in their mutual interaction. ψ ( x , y ) is not a product state.