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12 - Entanglements

Published online by Cambridge University Press:  05 August 2015

William C. Schieve  and
Lawrence P. Horwitz
William C. Schieve
Affiliation:
University of Texas, Austin
Lawrence P. Horwitz
Affiliation:
Tel-Aviv University
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Summary

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.

Type
Chapter
Information
Quantum Statistical Mechanics , pp. 221 - 239
Publisher: Cambridge University Press
Print publication year: 2009

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