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Introduction to Quantum Information Science$
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Vlatko Vedral

Print publication date: 2006

Print ISBN-13: 9780199215706

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780199215706.001.0001

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Witnessing quantum entanglement

Witnessing quantum entanglement

Introduction to Quantum Information Science

Vlatko Vedral

Oxford University Press

Quantum entanglement is a key resource in quantum information. Teleportation, dense coding, and many other quantum protocols rely on the existence of entanglement, and would not be possible with just classical correlations. Furthermore, using entanglement between qubits that support computation, quantum computers can solve problems faster than classical computers. Bell's inequalities can sometimes help in discriminating between entangled and separable states. However, these inequalities are not always reliable — this is true in the sense that they may fail to detect genuinely entangled states. This question is addressed in the present chapter by focusing on an entanglement witness, a Hermitian operator winch helps us to decide whether a state is entangled or not. The basic idea is that the expectation value of the witness will be different for separable and entangled states. This chapter discusses entanglement witnesses, the Jamiolkowski isomorphism, and the Peres Horodecki criterion. More examples of entanglement witnesses are given.

Keywords:   quantum entanglement, entanglement witnesses, entangled states, Jamiolkowski isomorphism, Peres Horodecki criterion, qubits

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