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Revista Mexicana de Física E

Anomaly of non-locality and entanglement in teaching quantum information

Josep Amengual i Batle, M.M. Abutalib, S. Abdalla

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

"Non-locality and quantum entanglement constitute two special features of quantum systems of enormous relevance in quantum information theory (QIT). Historically regarded as identical or equivalent for many years, they constitute different concepts. We want to stress in the present contribution such difference which actually may guide the instructor to cover the most essential topics of QIT in any section of some introductory course. We shall address the simplest possible case of that of two qubits. The material may be of interest to instructors teaching high-undergraduate quantum mechanics, as well as students."

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Nonlocality and quantum entanglement constitute two special features of quantum systems of paramount importance in quantum-information theory (QIT). Essentially regarded as identical or equivalent for many years, they constitute different concepts. Describing nonlocality by means of the maximal violation of two Bell inequalities, we study both entanglement and nonlocality for two and three spins in the $\mathit{XY}$ model. Our results shed light on the description of nonlocality and the possible information-theoretic task limitations of entanglement in an infinite quantum system.

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The surprising aspects of quantum information are due to two distinctly non-classical features of the quantum world: first, different quantum states need not be orthogonal and, second, quantum states may be entangled. Non-orthogonality leads to the blurring of classical distinctions. On the other hand, entanglement leads via non-locality to teleportation and other ``entanglement-assisted'' forms of communication that go beyond what is classically possible. In this article we attempt to understand these new possibilities via an analysis of the significance of entanglement for the basic physical concepts of a ``particle'' and a ``localized physical system''. Classical particles can be individuated on the basis of qualitative differences in their sets of properties. But in entangled states the ``particle labels'' of the quantum formalism usually do not pick out such sets of individuating particle properties. It is sometimes nevertheless possible to think in terms of individual particles, which may be localized; but we argue that in general the structure of quantum mechanics is at odds with such a particle interpretation. This finally leads us to the conclusion that quantum mechanics is best seen as not belonging to the category of space-time theories, in which physical quantities are functions on space-time points. The resulting picture of the quantum world is relevant for our understanding of the way in which quantum theory is non-local, and it sheds light on the novel aspects of quantum information.

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We argue, from epistemological point of view, the relationship between quantum entanglement and non-locality in quantum mechanics. The questions of how to quantify entanglement and non-locality and the need to clarify the relationship between them are important not only conceptually, but also practically, insofar as entanglement and non-locality seem to be different resources for the performance of quantum information processing tasks. Quantum information science is in the process of transforming our understanding of both QM and information theory.

Prespacetime journal•Nov 23, 2017•0 citations
"Non-locality and quantum entanglement constitute two special features of quantum systems of enormous relevance in quantum information theory (QIT). Historically regarded as identical or equivalent for many years, they constitute different concepts. We want to stress in the present contribution such difference which actually may guide the instructor to cover the most essential topics of QIT in any section of some introductory course. We shall address the simplest possible case of that of two qubits. The material may be of interest to instructors teaching high-undergraduate quantum mechanics, as well as students."
Nonlocality and quantum entanglement constitute two special features of quantum systems of paramount importance in quantum-information theory (QIT). Essentially regarded as identical or equivalent for many years, they constitute different concepts. Describing nonlocality by means of the maximal violation of two Bell inequalities, we study both entanglement and nonlocality for two and three spins in the XY\mathit{XY}XY model. Our results shed light on the description of nonlocality and the possible information-theoretic task limitations of entanglement in an infinite quantum system.
The surprising aspects of quantum information are due to two distinctly non-classical features of the quantum world: first, different quantum states need not be orthogonal and, second, quantum states may be entangled. Non-orthogonality leads to the blurring of classical distinctions. On the other hand, entanglement leads via non-locality to teleportation and other ``entanglement-assisted'' forms of communication that go beyond what is classically possible. In this article we attempt to understand these new possibilities via an analysis of the significance of entanglement for the basic physical concepts of a ``particle'' and a ``localized physical system''. Classical particles can be individuated on the basis of qualitative differences in their sets of properties. But in entangled states the ``particle labels'' of the quantum formalism usually do not pick out such sets of individuating particle properties. It is sometimes nevertheless possible to think in terms of individual particles, which may be localized; but we argue that in general the structure of quantum mechanics is at odds with such a particle interpretation. This finally leads us to the conclusion that quantum mechanics is best seen as not belonging to the category of space-time theories, in which physical quantities are functions on space-time points. The resulting picture of the quantum world is relevant for our understanding of the way in which quantum theory is non-local, and it sheds light on the novel aspects of quantum information.
Abstract: The exact nature of non-locality and entanglement is still a matter of an ongoing controversy. Especially, the concept of non-locality as postulated by the orthodox Copenhagen quantum mechanics is claiming to reflect any non-locality in the quantum realm. Attention should be called to the obvious but very disconcerting fact that the concept of non-locality cannot contradict the theory of special relativity, as long as the same is not refuted theoretically or by experiments. Another way of expressing the peculiar situation is, under conditions of the special theory of relativity it remains rather discomforting to alter the properties of a distant system instantaneously (i. e. no light signal can travel) by acting on a local system. The purpose of this publication is to solve the problem of non-locality and entanglement from the standpoint of the special theory of relativity.
This helpful and pedagogical book offers problems and solutions in quantum mechanics from areas of current research, rarely addressed in introductory courses or textbooks. It is based on the authors' own experience of teaching undergraduate and graduate courses in quantum mechanics, and adapts problems from contemporary research publications to be accessible to students. Each section introduces key quantum mechanical concepts, which are followed by exercises that grow progressively more challenging throughout the chapter. The step-by-step solutions provide detailed mathematical derivations, and explore their application to wider research topics. This is an indispensable resource for undergraduate and graduate students alike, expanding the range of topics usually covered in the classroom, as well as for instructors and early-career researchers in quantum mechanics, quantum computation and communication, and quantum information.
Just as expert physicists vary in their personal stances on interpretation in quantum mechanics, instructors vary on whether and how to teach interpretations of quantum phenomena in introductory modern physics courses. In this paper, we document variations in instructional approaches with respect to interpretation in two similar modern physics courses recently taught at the University of Colorado, and examine associated impacts on student perspectives regarding quantum physics. We find students are more likely to prefer realist interpretations of quantum-mechanical systems when instructors are less explicit in addressing student ontologies. We also observe contextual variations in student beliefs about quantum systems, indicating that instructors who choose to address questions of ontology in quantum mechanics should do so explicitly across a range of topics.
We argue, from epistemological point of view, the relationship between quantum entanglement and non-locality in quantum mechanics. The questions of how to quantify entanglement and non-locality and the need to clarify the relationship between them are important not only conceptually, but also practically, insofar as entanglement and non-locality seem to be different resources for the performance of quantum information processing tasks. Quantum information science is in the process of transforming our understanding of both QM and information theory.