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Journal of Shaanxi Normal University

New theory of quantum entanglement

Zha Xin

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

By properties of independence state vector in quantum mechanics, a theory to produce entanglement is put forward for the first time and the definition of entangled state and the basic forms of entangledment for multiparticle system are given. Finally the definition is given of entangled degree for basic form entangled state and the formula is derived of entangled degree for two and three_particles system. Furthermore, the criterion of disentangled state for three particles system is described.

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By properties of independence state vector in quantum mechanics, a theory to produce entanglement is put forward for the first time and the definition of entangled state and the basic forms of entangledment for multiparticle system are given. Finally the definition is given of entangled degree for basic form entangled state and the formula is derived of entangled degree for two and three_particles system. Furthermore, the criterion of disentangled state for three particles system is described.
Abstract This review is about single‐particle entanglement. Entanglement occurs when the state of a quantum system with at least two degrees of freedom has a particular non‐separable form. In the case of single‐particle entanglement, this quantum correlation is shared by the same particle being it a photon, a neutron, an ion, or an atom. Here, the basics of quantum entanglement are discussed focusing on the case it is related to the degrees of freedom of a single particle. It is discussed how the violation of peculiar inequalities in this context rules out any realistic non‐contextual hidden variable theory alternative to quantum mechanics. Moreover, experiments that demonstrate single‐particle entanglement for photons, neutrons, and atoms are discussed. Finally, the applications of single‐particle entanglement as a resource for quantum information are discussed and specifically quantum key distribution is detailed, where the use of single‐particle entangled photons allows to improve the security of the BB84 protocol.
Entanglement finds wide application in the development of quantum information theory. After reviewing states in classical mechanics, this chapter discusses the fundamental aspects of characterization of quantum entanglement like the definition, the detection, the classification and quantification of entanglement. The density operator is used to describe the state of a quantum system in a more general way than provided by the state vector of the Hilbert space. Multipartite entanglement theory is much complex compared to the bipartite case. One cannot generalize the results of bipartite entanglement to multipartite entanglement. The Peres criterion known as positive partial transpose criterion is an important criterion to find the separability of mixed states at least for low-dimensional systems. B.W. Terhal introduced the term entanglement witnesses for operators detecting quantum entanglement states. It is found that any entangled state can be detected by some entanglement witnesses.
We present an alternative definition of quantum entanglement for bipartite system based on Bell inequality and operators' noncommutativity. A state is said to be entangled, if the maximum of CHSH expectation value Fmax⁡F_{\max}Fmax​ is obtain by noncommutative measures on each particle of the bipartite system; otherwise, the state is a disentangled state. A uniform measure quantifying the degree of entanglement for any state of the bipartite system is also proposed.
Waves and particles are alternative modes of being for the elements of atomic dimensions. This feature appears to be evident at the experimental level but remains a conundrum at the theoretical level. The squared wavefunction |Ψ|2 yields the probability of finding a particle at a particular position and time, namely, the wave is conceived as a derivation or a physical condition of the particle and not a condition of the quantum. What the wavefunction represents, whether it really exists, whether it is a purely formal representation and if the observer influences the wavefunction are the major arguments of quantum mechanics (QM). The double nature of electrons, photons, and so on has been clearly recognized, and the two natures should be established by precise formulations. This work adheres totally to this methodological criterion and puts forward two formal definitions. The measurement process and wave collapse problems are also discussed. Finally, we verify the theoretical conclusions using the double slit experiment and the photoelectric effect. Probability plays a crucial role in the quantum literature, and the definitions of the wave and the particle should be illustrated by exploiting the probability theory; however, the various probability theories are not univocal and propose irreconcilable views. Therefore, in a preliminary stage, we unify the ontological and epistemic interpretations of probability using four theorems that have been already published. In summary, this work is developed on the basis of two methodological criteria, which seek to improve the probability theory and fix the definitional formulas of QM.