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The Physics of 2 = 1 + 1

Yanhua Shih

Published Dec 4, 2012• 0 citations
OpenAlex

Abstract

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

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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
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 is not 1 + 1.
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.
One of the most surprising consequences of quantum mechanics is the nonlocal behavior of a multi-particle system. Although questions regarding fundamental issues of quantum theory still exist, nonclassical surprises have started to play important roles in practical applications. Ghost imaging is one of these exciting areas. Two types of ghost imaging have been experimentally demonstrated since 1995. Type-one ghost imaging uses entangled photon pairs and type-two ghost imaging uses chaotic light. The unique point-to-point image-forming correlation between the object and image planes in ghost imaging is the result of a constructive-destructive interference which involves the nonlocal superposition of two-photon amplitudes, a nonclassical entity corresponding to different yet indistinguishable alternative ways of triggering a joint-detection event. This talk will explore and analyze the quantum nature of ghost imaging. It is true that classical challenges have never stopped. Quantum? Classical? A hot debate is currently focused on ghost imaging. This talk will defend the quantum mechanical point of view.
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.
We report a quantum interference and imaging experiment which allows identifying the entanglement in momentum and position variables of a two-photon system. The measurements show indeed that the uncertainties in the sum of momenta and in the difference of positions of the entangled two-photon satisfy both EPR inequalities $\ensuremath{\Delta}({k}_{1}+{k}_{2})<\mathrm{min}(\ensuremath{\Delta}{k}_{1},\ensuremath{\Delta}{k}_{2})$ and $\ensuremath{\Delta}({x}_{1}\ensuremath{-}{x}_{2})<\mathrm{min}(\ensuremath{\Delta}{x}_{1},\ensuremath{\Delta}{x}_{2})$. These two inequalities, together, represent a nonclassicality condition. Our measurements provide a direct way to distinguish between quantum entanglement and classical correlation in continuous variables for systems of pairs of photons.
One of the most intriguing concepts of quantum mechanics is quantum entanglement. Two physical systems are said to be entangled with respect to a certain variable, if their individual outcomes of the variable are undetermined before measurement, but strictly correlated. Measurement of the variable for only one system immediately determines the outcome for the other system, irrespective of the distance between the two systems. It is this strong correlation that provides a basis for perspective, powerful applications like quantum cryptography and quantum computation. The most studied entangled systems, often called EPR systems (after the pioneers Einstein, Podolsky and Rosen), are pairs of light particles or photon pairs. These photon pairs, usually generated via the optical process of a spontaneous parametric down-conversion, are, in principal, simultaneously entangled in three variables, being polarization (polarization entanglement), energy or time (time entanglement), and momentum or transverse space (spatial entanglement). The contents of this thesis cover new insights in the polarization and spatial entanglement of photons. We have investigated both the entanglement quality and the yield of entangled photons for different experimental geometries that are associated with the production and detection of the photons.