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Physica Scripta

Interpreting concurrence in terms of covariances in spin systems

F Palumbo, Anna Napoli, ANTONINO MESSINA

Published Mar 14, 2008• 1 citation
Publisher

Abstract

A conceptual and quantitative link between the concurrence function and measurable quantities is brought to light in a system composed of M pairwise coupled spins . As a consequence, a physical interpretation for the concurrence itself as well as a way to measure it is provided. We illustrate our theory exactly investigating a generalized spin star system, showing that the spin?spin entanglement evolution is traceable back to the covariance time behavior of appropriate commuting observables of the two spins.

DOI
10.1088/0031-8949/77/4/045003

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A conceptual and quantitative link between the concurrence function and measurable quantities is brought to light in a system composed of M pairwise coupled spins . As a consequence, a physical interpretation for the concurrence itself as well as a way to measure it is provided. We illustrate our theory exactly investigating a generalized spin star system, showing that the spin?spin entanglement evolution is traceable back to the covariance time behavior of appropriate commuting observables of the two spins.
The quantum dynamics of M pairwise coupled spin 1/2 is analyzed and the time evolution of the entanglement get established within a prefixed couple of spins is studied. A conceptual and quantitative link between the concurrence function and measurable quantities is brought to light providing a physical interpretation for the concurrence itself as well as a way to measure it. A generalized spin star system is exactly investigated showing that the entanglement accompanying its rich dynamics is traceable back to the covariance of appropriate commuting observables of the two spins.
The problem of detecting quantum signatures in the correlations formed in dynamical evolution of quantum bipartite systems receives a lot of attention in current literature. Generally speaking, the occurrence of correlations between two observables of a system does not necessarily reflect nonclassical behaviour. In this paper, the exact dynamics of a pair of uncoupled spins 1/2 interacting with a common spin 1/2 bath is investigated. Starting from a separable initial condition, the ability of the system to develop purely quantum correlations is brought to light. Physical interpretation of the concurrence function as well as a suggestion on how to measure it are given.
A general scheme to seek for the relations between entanglement and bservables is proposed in principle. In two-qubit systems with enough general Hamiltonian, we find the entanglement to be the functions of observables for six kinds of chosen state sets and verify how these functions be invariant with time evolution. Moreover, we demonstrate and illustrate the cases with entanglement versus a set of commutable observables under eight kinds of given initial states. Our conclusions show how entanglement become observable even measurable by experiment, and they are helpful for understanding of the nature of entanglement in physics.
For an electron spin in coupling with an interacting spin chain via hyperfine-type interaction, we investigate the dynamical evolutions of the pairwise entanglement of the spin chain, and a correlation function joined the electron spin with a pair of chain spins in correspondence to the electron-spin coherence evolution. Both quantities manifest a periodic and a decaying evolution. The entanglement of the spin bath is significant in distinguishing the zero-coherence status exhibited in periodic and decoherence evolutions of the electron spin. The periodical concurrence evolution of the spin bath characterizes the whole system in a coherence-preserving phase, particularly for the case that the associated periodic coherence evolution is predominated by zero value in the infinite chain-length limit, which was often regarded as the realization of decoherence.