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Kluwer Academic Publishers eBooks

Entanglement of Formation

William K. Wootters

Published Dec 19, 2005• 1 citation
Publisher

Abstract

At least three distinct information-theoretic measures of quantum entanglement have been proposed in recent years. This paper highlights one of them, the entanglement of formation, as well as a related quantity called the tangle. The tangle can be used to express a simple law of entanglement, limiting the extent to which a single qubit may be simultaneously entangled with each of two other qubits. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/0-306-47097-7_9

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At least three distinct information-theoretic measures of quantum entanglement have been proposed in recent years. This paper highlights one of them, the entanglement of formation, as well as a related quantity called the tangle. The tangle can be used to express a simple law of entanglement, limiting the extent to which a single qubit may be simultaneously entangled with each of two other qubits. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The source of inspiration for doing quantum probability lies in the ingenious methods adopted by physicists to compute probabilities of events concerning the subatomic world of elementary particles where the laws of classical mechanics break down and the distinction between a particle and a wave becomes vague. These methods lead to a generalisation of classical probability which may be described as a study of observable quantities concerning any system subject to chance and exhibiting the following basic features: (i) each observable quantity behaves like a classical real valued random variable on a probability space and hence has a probability distribution on the real line; (ii) it may be impossible to measure simultaneously two individually observable quantities in the sense that measurement of one may interfere with and destroy already existing information about the value of the other; (iii) bounded observable quantities constitute a real linear space in which the vectorial sum of two individually observable quantities interfering with each other is different from the arithmetic sum of their actual values. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Quantum information and computation is one of the new fields of physics and information science. Entanglement is one of the most significant resources in quantum information processing. The most basic quantitative measure of entanglement, particularly for mixed states of a bipartite system is the entanglement of formation. This entanglement of formation is used in the concurrence, another measurement of entanglement. Here I have briefly reviewed the entanglement of formation and the concurrence of bipartite systems. I have discussed that for a three qubit pure state, if A, B and C are the three qubits, then sum of the squared concurrence between A and B and the squared concurrence between A and C never exceeds the squared concurrence between A and BC pair. The residual entanglement, obtained from the aforementioned inequality, is also discussed here. Keywords- Quantum information, entanglement, qubit.
In classical physics there is, and always will be, a lack of precision in measurement. We cannot measure any quantity with absolute accuracy so any size, any weight, any velocity, any position, any time must always be stated within certain limits of error. Today we can make such measurements extremely accurately, but not with infinite accuracy. Yet this, though not entirely a practical problem, is practical to the extent that we can always aspire to achieve an accuracy which is sufficient for the purpose in hand. In theory we can go on refining our measurements indefinitely. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The fundamental laws of Nature that govern the physics of atoms, elementary particles, light quanta, and everything else that is small and light, have been found to fit in one grandiose framework called Quantum Mechanics. The internal logic of this framework appears to be counter intuitive and mysterious, while extremely coherent and effective. In this general introduction the author explains why he feels the need for expressing his views on how to understand these facts, even if many known scientists have already given extensive reviews of numerous ideas and approaches. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.