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Optics and Spectroscopy

On entanglement of quantum states of noninteracting subsystems

Ashat M. Basharov, Edward A. Manykin

Published Jan 1, 2004• 3 citations
Publisher

Abstract

Simple models for measuring the characteristics of a system of two atoms that do not interact with each other are used to show that the nonselectivity of measurement, related to the indistinguishability of the quantum subsystems with respect to some general parameter, leads to entanglement of the atomic states of the subsystem selected in such a way. This entanglement is in no way related to some collective process and is only due to the effective measurement in an entangled basis. An analogy between the preparation of entangled states of a system of subsystems that do not interact with each other by a quantum reduction (a measurement) and a quantum evolution is found.

DOI
10.1134/1.1643990

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Simple models for measuring the characteristics of a system of two atoms that do not interact with each other are used to show that the nonselectivity of measurement, related to the indistinguishability of the quantum subsystems with respect to some general parameter, leads to entanglement of the atomic states of the subsystem selected in such a way. This entanglement is in no way related to some collective process and is only due to the effective measurement in an entangled basis. An analogy between the preparation of entangled states of a system of subsystems that do not interact with each other by a quantum reduction (a measurement) and a quantum evolution is found.
Entanglement of quantum systems refers to the situation where two or more systems interact and the state of the whole system cannot be seen as a superposition of states of the single systems. This chapter is devoted to the definition of entanglement both for pure states and mixed states. It also discusses methods to detect entanglement. The chapter is devoted to the study of the dynamics of entanglement. It is also devoted to the problem of local equivalence between states, i.e., how to determine when, given two states, it is possible to evolve from one to the other by transformations which act on systems separately.
Quantum correlation is an important resource in quantum information, quantum computation, and quantum metrology. Quantum entanglement, Einstein-Podolsky-Rosen (EPR) quantum steering and Bell nonlocality are the major quantum correlations. For quantum entanglement and Bell nonlocality, two subsystems play the same significant roles. EPR quantum steering is stronger than entanglement and weaker than Bell nonlocality. It represents the ability of one subsystem to nonlocally affect another subsystem's states through local measurements. In this paper, the dynamic quantum correlation between the modes in the two-site Bose-Hubbard model is investigated. According to Hillery-Zubairy entanglement criterion and based on maximum mean quantum Fisher information, the influences of initial states on the quantum entanglement evolutions are explored. If the coupling between the modes is much greater than that of the particles at the same site, and the initial states are symmetric or anti-symmetric SU(2) coherent states, the quantum correlations show simple periodic evolutions. The oscillation amplitudes of the evolutions increase with the interaction between the particles at the same site. The oscillation period decreases with the coupling strength between the modes. The dependence of the period on the interaction of the particles at the same site is related to the initial states. In other words, the time evolutions of quantum correlation are closely related to the symmetry of the initial states. In the case of symmetric (anti-symmetric) SU(2) coherent state and repulsive (attractive) interaction of the particles at the same site, the system presents two-way quantum steering. When the subsystem exchange symmetry of the initial states is broken, the collapse and revival of quantum correlation appear, moreover one-way quantum steering emerges in the infancy. One-way quantum steering is asymmetric for two subsystems. So exchange asymmetry of the initial state is necessary condition of one-way quantum steering when the Hamiltonian of the system is symmetric for two subsystems.
Entanglement of quantum systems refers to the situation where two or more systems interact and the state of the whole system cannot be seen as a superposition of states of the single systems. This feature of quantum dynamics is crucial in many algorithms of quantum communication and quantum information processing and it is a resource for many fascinating applications. Moreover entanglement, as a feature of quantum mechanics, has stimulated in-depth investigation on the value of quantum mechanics itself as a physical theory.
In this paper, the Tavis-Cummings model is generalized to simultaneously consider the atomic motion and the field via intensity dependent coupling. Under the conditions of vacuum field, weakly and strongly coherent field, the entanglement evolution properties of two-atom-field and two-atom-two-atom are investigated using atomic reduced entropy and concurrence, respectively. According to evolution characteristics above, we prepare the W-class states of two-atom-field, two-atom Bell state, fidelity state of Bell-state atoms, single-photon state, two-photon state and stable number-states of field by selecting the interaction time of the two-atom-field, selecting the entanglement factor of the two-atom, regulating the field-mode structure parameter, controlling the probability amplitude of pure state of the system and selective measurement. The manipulation of two-atom Bell state sudden generation and its maintenance in a limited time, the formation of periodic quantum echo of Bell-state atoms and the continuous fidelity of Bell-state atomic information are achieved. The results show that the system has a powerful function of quantum information, and provide the physical carrier and theoretical parameters for experimental implementation of quantum information processing.
Identifying the physiological processes in the central nervous system that underlie our conscious experiences has been at the forefront of cognitive neuroscience. While the principles of classical physics were long found to be unaccommodating for a causally effective consciousness, the inherent indeterminism of quantum physics, together with its characteristic dichotomy between quantum states and quantum observables, provides a fertile ground for the physical modeling of consciousness. Here, we utilize the Schrödinger equation, together with the Planck–Einstein relation between energy and frequency, in order to determine the appropriate quantum dynamical timescale of conscious processes. Furthermore, with the help of a simple two-qubit toy model we illustrate the importance of non-zero interaction Hamiltonian for the generation of quantum entanglement and manifestation of observable correlations between different measurement outcomes. Employing a quantitative measure of entanglement based on Schmidt decomposition, we show that quantum evolution governed only by internal Hamiltonians for the individual quantum subsystems preserves quantum coherence of separable initial quantum states, but eliminates the possibility of any interaction and quantum entanglement. The presence of non-zero interaction Hamiltonian, however, allows for decoherence of the individual quantum subsystems along with their mutual interaction and quantum entanglement. The presented results show that quantum coherence of individual subsystems cannot be used for cognitive binding because it is a physical mechanism that leads to separability and non-interaction. In contrast, quantum interactions with their associated decoherence of individual subsystems are instrumental for dynamical changes in the quantum entanglement of the composite quantum state vector and manifested correlations of different observable outcomes. Thus, fast decoherence timescales could assist cognitive binding through quantum entanglement across extensive neural networks in the brain cortex.