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Eshan Mehrotra - One of the best experts on this subject based on the ideXlab platform.
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Topological aspects of Quantum Entanglement
Quantum Information Processing, 2019Co-Authors: Louis H Kauffman, Eshan MehrotraAbstract:Kauffman and Lomonaco (New J Phys 4:73.1–73.18, 2002. arXiv:quant-ph/0401090, New J Phys 6:134.1–134.40, 2004) explored the idea of understanding Quantum Entanglement (the non-local correlation of certain properties of particles) topologically by viewing unitary entangling operators as braiding operators. In Alagic et al. (Yang–Baxter operators need Quantum Entanglement to distinguish knots, 2015. arXiv:1507.05979v1), it is shown that Entanglement is a necessary condition for forming non-trivial invariants of knots from braid closures via solutions to the Yang–Baxter equation. We show that the arguments used by Alagic et al. (2015) generalize to essentially the same results for Quantum invariant state summation models of knots. In one case (the unoriented swap case) we give an example of a Yang–Baxter operator, and associated Quantum invariant, that can detect the Hopf link. Again this is analogous to the results of Alagic et al. (2015). We also give a class of R matrices that are entangling and are weak invariants of classical knots and links yet strong invariants of virtual knots and links. We also give an example of an SU(2) representation of the three-strand braid group that models the Jones polynomial for closures of three-strand braids. This invariant is a Quantum model for the Jones polynomial restricted to three-strand braids, and it does not involve Quantum Entanglement. These relationships between topological braiding and Quantum Entanglement can be used as a framework for future work in understanding the properties of entangling gates in topological Quantum computing. The paper ends with a discussion of the Aravind hypothesis about the direct relationship of knots and Quantum Entanglement and the \(ER = EPR\) hypothesis about the relationship of Quantum Entanglement with the connectivity of space. We describe how, given a background space and a Quantum tensor network, to construct a new topological space that welds the network and the background space together. This construction embodies the principle that Quantum Entanglement and topological connectivity are intimately related.
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Topological aspects of Quantum Entanglement
Quantum Information Processing, 2019Co-Authors: Louis H Kauffman, Eshan MehrotraAbstract:Kauffman and Lomonaco (New J Phys 4:73.1–73.18, 2002 . arXiv:quant-ph/0401090 , New J Phys 6:134.1–134.40, 2004 ) explored the idea of understanding Quantum Entanglement (the non-local correlation of certain properties of particles) topologically by viewing unitary entangling operators as braiding operators. In Alagic et al. (Yang–Baxter operators need Quantum Entanglement to distinguish knots, 2015 . arXiv:1507.05979v1 ), it is shown that Entanglement is a necessary condition for forming non-trivial invariants of knots from braid closures via solutions to the Yang–Baxter equation. We show that the arguments used by Alagic et al. ( 2015 ) generalize to essentially the same results for Quantum invariant state summation models of knots. In one case (the unoriented swap case) we give an example of a Yang–Baxter operator, and associated Quantum invariant, that can detect the Hopf link. Again this is analogous to the results of Alagic et al. ( 2015 ). We also give a class of R matrices that are entangling and are weak invariants of classical knots and links yet strong invariants of virtual knots and links. We also give an example of an SU (2) representation of the three-strand braid group that models the Jones polynomial for closures of three-strand braids. This invariant is a Quantum model for the Jones polynomial restricted to three-strand braids, and it does not involve Quantum Entanglement. These relationships between topological braiding and Quantum Entanglement can be used as a framework for future work in understanding the properties of entangling gates in topological Quantum computing. The paper ends with a discussion of the Aravind hypothesis about the direct relationship of knots and Quantum Entanglement and the $$ER = EPR$$ E R = E P R hypothesis about the relationship of Quantum Entanglement with the connectivity of space. We describe how, given a background space and a Quantum tensor network, to construct a new topological space that welds the network and the background space together. This construction embodies the principle that Quantum Entanglement and topological connectivity are intimately related.
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Topological aspects of Quantum Entanglement
Quantum Information Processing, 2019Co-Authors: Louis H Kauffman, Eshan MehrotraAbstract:Kauffman and Lomonaco explored the idea of understanding Quantum Entanglement (the non-local correlation of certain properties of particles) topologically by viewing unitary entangling operators as braiding operators. In the work of G. Alagic, M. Jarret, and S. Jordan it is shown that Entanglement is a necessary condition for forming invariants of knots from braid closures via solutions to the Yang-Baxter Equation. We show that the arguments used by these authors generalize to essentially the same results for Quantum invariant state summation models of knots. We also given an example of an SU(2) representation of the three-strand braid group that models the Jones polynomial for closures of three-strand braids. This invariant is a Quantum model for the Jones polynomial restricted to three strand braids, and it does not involve Quantum Entanglement. These relationships between topological braiding and Quantum Entanglement can be used as a framework for future work in understanding the properties of entangling gates in topological Quantum computing.The paper ends with a discussion of the Aravind hypothesis about the direct relationship of knots and Quantum Entanglement, and the ER = EPR hypothesis about the relationship of Quantum Entanglement with the connectivity of space. We describe how, given a background space and a Quantum tensor network, to construct a new topological space, that welds the network and the background space together. This construction embodies the principle that Quantum Entanglement and topological connectivity are intimately related.
Louis H Kauffman - One of the best experts on this subject based on the ideXlab platform.
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Topological aspects of Quantum Entanglement
Quantum Information Processing, 2019Co-Authors: Louis H Kauffman, Eshan MehrotraAbstract:Kauffman and Lomonaco (New J Phys 4:73.1–73.18, 2002 . arXiv:quant-ph/0401090 , New J Phys 6:134.1–134.40, 2004 ) explored the idea of understanding Quantum Entanglement (the non-local correlation of certain properties of particles) topologically by viewing unitary entangling operators as braiding operators. In Alagic et al. (Yang–Baxter operators need Quantum Entanglement to distinguish knots, 2015 . arXiv:1507.05979v1 ), it is shown that Entanglement is a necessary condition for forming non-trivial invariants of knots from braid closures via solutions to the Yang–Baxter equation. We show that the arguments used by Alagic et al. ( 2015 ) generalize to essentially the same results for Quantum invariant state summation models of knots. In one case (the unoriented swap case) we give an example of a Yang–Baxter operator, and associated Quantum invariant, that can detect the Hopf link. Again this is analogous to the results of Alagic et al. ( 2015 ). We also give a class of R matrices that are entangling and are weak invariants of classical knots and links yet strong invariants of virtual knots and links. We also give an example of an SU (2) representation of the three-strand braid group that models the Jones polynomial for closures of three-strand braids. This invariant is a Quantum model for the Jones polynomial restricted to three-strand braids, and it does not involve Quantum Entanglement. These relationships between topological braiding and Quantum Entanglement can be used as a framework for future work in understanding the properties of entangling gates in topological Quantum computing. The paper ends with a discussion of the Aravind hypothesis about the direct relationship of knots and Quantum Entanglement and the $$ER = EPR$$ E R = E P R hypothesis about the relationship of Quantum Entanglement with the connectivity of space. We describe how, given a background space and a Quantum tensor network, to construct a new topological space that welds the network and the background space together. This construction embodies the principle that Quantum Entanglement and topological connectivity are intimately related.
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Topological aspects of Quantum Entanglement
Quantum Information Processing, 2019Co-Authors: Louis H Kauffman, Eshan MehrotraAbstract:Kauffman and Lomonaco (New J Phys 4:73.1–73.18, 2002. arXiv:quant-ph/0401090, New J Phys 6:134.1–134.40, 2004) explored the idea of understanding Quantum Entanglement (the non-local correlation of certain properties of particles) topologically by viewing unitary entangling operators as braiding operators. In Alagic et al. (Yang–Baxter operators need Quantum Entanglement to distinguish knots, 2015. arXiv:1507.05979v1), it is shown that Entanglement is a necessary condition for forming non-trivial invariants of knots from braid closures via solutions to the Yang–Baxter equation. We show that the arguments used by Alagic et al. (2015) generalize to essentially the same results for Quantum invariant state summation models of knots. In one case (the unoriented swap case) we give an example of a Yang–Baxter operator, and associated Quantum invariant, that can detect the Hopf link. Again this is analogous to the results of Alagic et al. (2015). We also give a class of R matrices that are entangling and are weak invariants of classical knots and links yet strong invariants of virtual knots and links. We also give an example of an SU(2) representation of the three-strand braid group that models the Jones polynomial for closures of three-strand braids. This invariant is a Quantum model for the Jones polynomial restricted to three-strand braids, and it does not involve Quantum Entanglement. These relationships between topological braiding and Quantum Entanglement can be used as a framework for future work in understanding the properties of entangling gates in topological Quantum computing. The paper ends with a discussion of the Aravind hypothesis about the direct relationship of knots and Quantum Entanglement and the \(ER = EPR\) hypothesis about the relationship of Quantum Entanglement with the connectivity of space. We describe how, given a background space and a Quantum tensor network, to construct a new topological space that welds the network and the background space together. This construction embodies the principle that Quantum Entanglement and topological connectivity are intimately related.
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Topological aspects of Quantum Entanglement
Quantum Information Processing, 2019Co-Authors: Louis H Kauffman, Eshan MehrotraAbstract:Kauffman and Lomonaco explored the idea of understanding Quantum Entanglement (the non-local correlation of certain properties of particles) topologically by viewing unitary entangling operators as braiding operators. In the work of G. Alagic, M. Jarret, and S. Jordan it is shown that Entanglement is a necessary condition for forming invariants of knots from braid closures via solutions to the Yang-Baxter Equation. We show that the arguments used by these authors generalize to essentially the same results for Quantum invariant state summation models of knots. We also given an example of an SU(2) representation of the three-strand braid group that models the Jones polynomial for closures of three-strand braids. This invariant is a Quantum model for the Jones polynomial restricted to three strand braids, and it does not involve Quantum Entanglement. These relationships between topological braiding and Quantum Entanglement can be used as a framework for future work in understanding the properties of entangling gates in topological Quantum computing.The paper ends with a discussion of the Aravind hypothesis about the direct relationship of knots and Quantum Entanglement, and the ER = EPR hypothesis about the relationship of Quantum Entanglement with the connectivity of space. We describe how, given a background space and a Quantum tensor network, to construct a new topological space, that welds the network and the background space together. This construction embodies the principle that Quantum Entanglement and topological connectivity are intimately related.
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Quantum Entanglement and topological Entanglement
New Journal of Physics, 2002Co-Authors: Louis H Kauffman, Samuel J. LomonacoAbstract:This paper discusses relationships between topological Entanglement and Quantum Entanglement. Specifically, we propose that it is more fundamental to view topological Entanglements such as braids as Entanglement operators and to associate with them unitary operators that are capable of creating Quantum Entanglement.
D. N. Makarov - One of the best experts on this subject based on the ideXlab platform.
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Quantum Entanglement of a harmonic oscillator with an electromagnetic field
Scientific reports, 2018Co-Authors: D. N. MakarovAbstract:At present, there are many methods for obtaining Quantum Entanglement of particles with an electromagnetic field. Most methods have a low probability of Quantum Entanglement and not an exact theoretical apparatus based on an approximate solution of the Schrodinger equation. There is a need for new methods for obtaining Quantum-entangled particles and mathematically accurate studies of such methods. In this paper, a Quantum harmonic oscillator (for example, an electron in a magnetic field) interacting with a quantized electromagnetic field is considered. Based on the exact solution of the Schrodinger equation for this system, it is shown that for certain parameters there can be a large Quantum Entanglement between the electron and the electromagnetic field. Quantum Entanglement is analyzed on the basis of a mathematically exact expression for the Schmidt modes and the Von Neumann entropy.
M. Suhail Zubairy - One of the best experts on this subject based on the ideXlab platform.
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Protecting Quantum Entanglement from amplitude damping
Journal of Physics B: Atomic Molecular and Optical Physics, 2013Co-Authors: Zeyang Liao, Mohammad Al-amri, M. Suhail ZubairyAbstract:Quantum Entanglement is a critical resource for Quantum information and Quantum computation. However, Entanglement of a Quantum system is subjected to change due to the interaction with the environment. One typical result of the interaction is the amplitude damping that usually results in the reduction of the Entanglement. Here we propose a protocol to protect Quantum Entanglement from the amplitude damping by applying Hadamard and CNOT gates. As opposed to some recently studied methods, the scheme presented here does not require weak measurement in the reversal process, leading to a faster recovery of Entanglement. We propose a possible experimental implementation based on linear optical system.
Tadashi Takayanagi - One of the best experts on this subject based on the ideXlab platform.
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Quantum Entanglement of local operators in conformal field theories
Physical Review Letters, 2014Co-Authors: Masahiro Nozaki, Tokiro Numasawa, Tadashi TakayanagiAbstract:We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of Quantum Entanglement. It is defined by the increased amount of (Renyi) Entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the Entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of Quantum Entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles.
