A quantum similarity discussion about Einstein–Podolsky–Rosen (EPR) paradox in Gaussian enfolded spaces

2020 ◽  
Vol 58 (9) ◽  
pp. 1815-1827
Author(s):  
Jing Chang ◽  
Ramon Carbó-Dorca
Keyword(s):  
Quantum Similarity ◽  
Epr Paradox ◽  
Einstein Podolsky Rosen

Einstein-Podolsky-Rosen Paradox and Certain Aspects of Quantum Cryptology with Some Applications

2014 ◽  
pp. 1579-1587
Author(s):  
Narayanankutty Karuppath ◽  
P. Achuthan
Keyword(s):  
Quantum Computing ◽  
Computational Complexity ◽  
Quantum Cryptography ◽  
Scientific Revolution ◽  
Bell’S Inequality ◽  
Epr Paradox ◽  
Bell's Inequality ◽  
Factorization Algorithm ◽  
Einstein Podolsky Rosen ◽  
Modern Context

The developments in quantum computing or any breakthrough in factorization algorithm would have far-reaching consequences in cryptology. For instance, Shor algorithm of factorizing in quantum computing might render the RSA type classical cryptography almost obsolete since it mainly depends on the computational complexity of factorization. Therefore, quantum cryptography is of immense importance and value in the modern context of recent scientific revolution. In this chapter, the authors discuss in brief certain fascinating aspects of Einstein-Podolsky-Rosen (EPR) paradox in the context of quantum cryptology. The EPR protocol and its connections to the famous Bell's inequality are also considered in here.

Über das Einstein-Podolsky-Rosen Paradoxon / On the Einstein-Podolsky-Rosen Paradox

1974 ◽  
Vol 29 (4) ◽  
pp. 539-548 ◽  
Author(s):  
P. Mittelstaedt
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Hidden Variables ◽  
Physical Reality ◽  
Experimental Investigations ◽  
Epr Paradox ◽  
Realistic Interpretation ◽  
Epr Experiment ◽  
Einstein Podolsky Rosen ◽  
Ordinary Quantum

The EPR experiment is analysed in terms of ordinary quantum mechanics and shown to be compatible with the orthodox interpretation of this theory. There is no need to refer to Bohrs resolution of the EPR paradox, nor is it necessary to assume any further unusual properties of the quantum physical reality. In particular, it is shown that the EPR experiment does not contradict the fact that incommensurable properties cannot be objectivized simultaneously in a quantum mechanical system, and that the measuring process can be understood in terms of quantum theory as an interaction of the measuring apparatus and the object system. From these results it follows that there is no reason to search for modifications of the quantum theory which might be more convenient for a realistic interpretation of the EPR experiment. Furthermore, the EPR experiment cannot be used as a motivation for introducing hidden variables into the quantum theory. Experimental investigations which try to test quantum mechanics in respect to the possibility of introducing local hidden variables can therefore not be justified by the EPR paradox.

scholarly journals Orbital angular momentum uncertainty relations of entangled two-photon states

2021 ◽  
Vol 75 (8) ◽  
Author(s):  
Wei Li ◽  
Shengmei Zhao
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Composite System ◽  
Entangled State ◽  
Uncertainty Relations ◽  
Epr Paradox ◽  
Photon State ◽  
Two Photon ◽  
Einstein Podolsky Rosen ◽  
Photon States

Abstract The inseparability of quantum correlation requires that the particles in the composite system be treated as a whole rather than treated separately, a typical example is the Einstein–Podolsky–Rosen (EPR) paradox. In this paper, we provide a theoretical study on the uncertainty relations of two kinds of bipartite observables in two-photon orbital angular momentum (OAM) entanglement, that is, the relative distance and centroid of the two photons at azimuth. We find that the uncertainty relations of the bipartite observables holds in any two-photon state, and they are separable in two-photon OAM entanglement. In addition, the entangled state behaves as a single particle in the bipartite representation. Finally, we find that the uncertainty relations of the bipartite observables can be used to manipulate the degree of the entanglement of an EPR state. Graphic abstract

Einstein-Podolsky-Rosen Paradox and Certain Aspects of Quantum Cryptology with Some Applications

2011 ◽  
pp. 231-239
Author(s):  
Narayanankutty Karuppath ◽  
P. Achuthan
Keyword(s):  
Quantum Computing ◽  
Computational Complexity ◽  
Quantum Cryptography ◽  
Scientific Revolution ◽  
Bell’S Inequality ◽  
Epr Paradox ◽  
Bell's Inequality ◽  
Factorization Algorithm ◽  
Einstein Podolsky Rosen ◽  
Modern Context

The developments in quantum computing or any breakthrough in factorization algorithm would have far-reaching consequences in cryptology. For instance, Shor algorithm of factorizing in quantum computing might render the RSA type classical cryptography almost obsolete since it mainly depends on the computational complexity of factorization. Therefore, quantum cryptography is of immense importance and value in the modern context of recent scientific revolution. In this chapter, the authors discuss in brief certain fascinating aspects of Einstein-Podolsky-Rosen (EPR) paradox in the context of quantum cryptology. The EPR protocol and its connections to the famous Bell’s inequality are also considered in here.

scholarly journals POSITION AND MOMENTUM ENTANGLEMENT OF DIPOLE–DIPOLE INTERACTING ATOMS IN OPTICAL LATTICES: THE EINSTEIN–PODOLSKY–ROSEN PARADOX ON A LATTICE

2004 ◽  
Vol 02 (03) ◽  
pp. 305-321 ◽  
Author(s):  
TOMÁŠ OPATRNÝ ◽  
MICHAL KOLÁŘ ◽  
GERSHON KURIZKI ◽  
BIMALENDU DEB
Keyword(s):  
Optical Lattices ◽  
Epr Paradox ◽  
Dipole Interactions ◽  
Induced Dipole ◽  
Einstein Podolsky Rosen ◽  
Interacting Atoms ◽  
Diffraction Effects ◽  
High Degree

We study a possible realization of the position- and momentum-correlated atomic pairs that are confined to adjacent sites of two mutually shifted optical lattices and are entangled via laser-induced dipole–dipole interactions. The Einstein–Podolsky–Rosen (EPR) "paradox"1 with translational variables is then modified by lattice-diffraction effects. This "paradox" can be verified to a high degree of accuracy in this scheme.

scholarly journals Every Entangled Stuff Has Its Own Avatar

2018 ◽  
Author(s):  
Mario Mastriani
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Physical Reality ◽  
Quantum Communications ◽  
Epr Paradox ◽  
Einstein Podolsky Rosen ◽  
Superluminal Signaling ◽  
Incomplete Theory ◽  
Non Locality

During the last century, entanglement was the bone of contention between the two main pillars of Physics: General Relativity (GR) and Quantum Mechanics (QM). This began in 1935 with the Einstein-Podolsky-Rosen paradox (EPR paradox) which concluded that although Quantum Mechanics is not wrong, it is an incomplete theory to represent physical reality. In this paper it is demonstrated that some byproducts resulting from entanglement and which we will call avatars act as a hinge that link both theories making the completeness of QM clear. Moreover, a thorough analysis of the non-locality of this effect will be carried out. Besides, it is demonstrated that entanglement is an instantaneous phenomenon and that it does not require the use of a superluminal signaling for this purpose. Finally, the avatars will also appear in each wormhole resulting from an entanglement process (WREP) demonstrating that they are traversable with an equivalent path of null length which can be crossed in a null time with all that this implies in Quantum Communications.

scholarly journals Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Benjamin Yadin ◽  
Matteo Fadel ◽  
Manuel Gessner
Keyword(s):  
State Of The Art ◽  
Quantum Fisher Information ◽  
Quantum Metrology ◽  
Epr Paradox ◽  
Apparent Contradiction ◽  
Gaussian States ◽  
Precise Estimation ◽  
Einstein Podolsky Rosen ◽  
Essential Resource ◽  
Non Gaussian

AbstractThe Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our understanding of quantum mechanics, and is associated with the possibility of predicting the results of non-commuting measurements with a precision that seems to violate the uncertainty principle. This apparent contradiction to complementarity is made possible by nonclassical correlations stronger than entanglement, called steering. Quantum information recognises steering as an essential resource for a number of tasks but, contrary to entanglement, its role for metrology has so far remained unclear. Here, we formulate the EPR paradox in the framework of quantum metrology, showing that it enables the precise estimation of a local phase shift and of its generating observable. Employing a stricter formulation of quantum complementarity, we derive a criterion based on the quantum Fisher information that detects steering in a larger class of states than well-known uncertainty-based criteria. Our result identifies useful steering for quantum-enhanced precision measurements and allows one to uncover steering of non-Gaussian states in state-of-the-art experiments.

Randomness and Complexity

2018 ◽  
Author(s):  
Steven E. Vigdor
Keyword(s):  
Quantum Mechanics ◽  
Natural Selection ◽  
Rna World ◽  
Biological Evolution ◽  
Variable Theory ◽  
Cosmological Natural Selection ◽  
Einstein Podolsky Rosen ◽  
World Hypothesis ◽  
Rna World Hypothesis

Chapter 7 describes the fundamental role of randomness in quantum mechanics, in generating the first biomolecules, and in biological evolution. Experiments testing the Einstein–Podolsky–Rosen paradox have demonstrated, via Bell’s inequalities, that no local hidden variable theory can provide a viable alternative to quantum mechanics, with its fundamental randomness built in. Randomness presumably plays an equally important role in the chemical assembly of a wide array of polymer molecules to be sampled for their ability to store genetic information and self-replicate, fueling the sort of abiogenesis assumed in the RNA world hypothesis of life’s beginnings. Evidence for random mutations in biological evolution, microevolution of both bacteria and antibodies and macroevolution of the species, is briefly reviewed. The importance of natural selection in guiding the adaptation of species to changing environments is emphasized. A speculative role of cosmological natural selection for black-hole fecundity in the evolution of universes is discussed.

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