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Fortschritte der Physik

Quantum entanglement and the uncertainty relations

Yanhua H. Shih

Published Oct 11, 2004• 0 citations
Publisher

Abstract

Abstract Entangled EPR two‐particle system is characterized by Δ(p1+p2) = 0 and Δ (x1‐ x2) = 0, simultaneous. Even the momentum and position of each individual particle are completely undefined: Δ pj ∼ ∞, Δ xj ∼∞. This remarkable feature does not violate the uncertainty principle of quantum theory. It is the result of the surprising two‐particle quantum coherent superposition. Although questions regarding fundamental issues of quantum theory still exist, quantum entanglement has brought about a novel concept in nonlocal timing and positioning measurements with ultra‐high accuracy, even beyond the classical limit.

DOI
10.1002/prop.200410179

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Abstract Entangled EPR two‐particle system is characterized by Δ(p1+p2) = 0 and Δ (x1‐ x2) = 0, simultaneous. Even the momentum and position of each individual particle are completely undefined: Δ pj ∼ ∞, Δ xj ∼∞. This remarkable feature does not violate the uncertainty principle of quantum theory. It is the result of the surprising two‐particle quantum coherent superposition. Although questions regarding fundamental issues of quantum theory still exist, quantum entanglement has brought about a novel concept in nonlocal timing and positioning measurements with ultra‐high accuracy, even beyond the classical limit.
An entangled EPR two-particle system is characterized by Δ(p 1 + p 2) = 0 and Δ(x 1 - x 2) = 0, simultaneously, with the momentum and position of each individual particle completely undefined. Statistically, however, the uncertainty of the correlation measurements on the two individual particles must obey Δ(p1 + p 2) > Δp 1,2 and Δ(x 1 - x 2) > Δx 1,2. While one sees the measurements of p 1 + p 2 and x 1 - x 2 of the two individual particles satisfying the EPR δ-function, and believes the classical statistical inequality, one might easily be trapped into concluding either there is a violation of the uncertainty principle or there exists action-at-a-distance. Through the analysis of three typical EPR experiments, we show that the measurement of p 1 + p 2 and x 1 - x 2 for an entangled system can indeed violate the classical statistical inequality. Based on the experimental results, we emphasize, again, the surprising physics of quantum coherent two-particle superposition. Although questions regarding fundamental issues of quantum theory still exist, quantum entanglement has brought us a novel concept in non-local timing and positioning measurements with ultra-high accuracy, even beyond the classical limit.
EPR paper contains an error. Its correction leads to a conclusion that position and momentum of a particle can be defined precisely simultaneously, EPR paradox does not exist and uncertainty relations have nothing to do with quantum mechanics. Logic of the EPR paper shows that entangled states of separated particles do not exist and therefore there are no nonlocality in quantum mechanics. Bell's inequalities are never violated, and results of experiments, proving their violation, are shown to be false. Experiments to prove absence of nonlocality are proposed where Bell's inequalities are replaced by precise prediction. Interpretation of quantum mechanics in terms of classical field theory is suggested. Censorship against this paper is demonstrated.
Abstract One of the most surprising consequences of quantum mechanics is the entanglement of two or more distance particles. The “ghost” interference and the “ghost” image experiments demonstrated the astonishing nonlocal behavior of an entangled photon pair. Even though we still have questions in regard to fundamental issues of the entangled quantum systems, quantum entanglement has started to play important roles in quantum information and quantum computation. Quantum teleportation is one of the hot topics. We have demonstrated a quantum teleportation experiment recently. The experimental results proved the working principle of irreversibly teleporting an unknown arbitrary quantum state from one system to another distant system by disassembling into and then later reconstructing from purely classical information and nonclassical EPR correlations. The distinct feature of this experiment is that the complete set of Bell states can be distinguished in the Bell state measurement. Teleportation of a quantum state can thus occur with certainty in principle.
Abstract: One of the most surprising consequences of quantum mechanics is the entanglement of two or more distant particles. In an entangled EPR two-particle system, the value of the momentum (position) for neither single subsystem is determined. However, if one of the subsystems is measured to have a certain momentum (position), the other subsystem is determined to have a unique corresponding value, despite the distance between them. This peculiar behavior of an entangled quantum system has surprisingly been observed experimentally in two-photon temporal and spatial correlation measurements, such as “ghost ” interference and “ghost ” imaging. This article addresses the fundamental concerns behind these experimental observations and to explore the nonclassical nature of two-photon superposition by emphasizing the physics of 2 ̸ = 1 + 1. 1
The EPR paradox appears when measurement results of some properties of two distantly entangled particles are correlated in a way that cannot be explained classically, and apparently violate locality. The resolution of the paradox depends on one’s interpretation of quantum mechanics. Explanations from quantum mechanics remain commonplace today, but they fail to explain the EPR (Einstein, Podolsky and Rosen) paradox totally in a way than can be accepted by the whole community. Here, we present a simple resolution to this paradox in which the uncertainty in the energy of the two-particle system is reduced by its lack of interaction during the journey so that the uncertainty in time becomes greater than the time they have been separating. Consequently, the present and past become indistinguishable because when we measure an observable in the system its value is the same as if the two particle were still together or very close. It is also argued that the destruction of information as the present and past become identical should release heat by Landauer’s principle, and this might make this proposal testable.