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arXiv:0708.0180 · Nature Physics

Evolution equation for quantum entanglement

Thomas Konrad, Fernando de Melo, Markus Tiersch, Christian Kasztelan, Adriano Aragão, Andreas Buchleitner

Published Dec 23, 2007• 163 citations
arXivHTMLPDF
DOI
10.1038/nphys885

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We investigate the time evolution of the entanglement of assistance when one subsystem undergoes the action of local noisy channels. A general factorization law is presented for the evolution equation of entanglement of assistance. Our results demonstrate that the dynamics of the entanglement of assistance is determined by the action of a noisy channel on the pure maximally entangled state, in which the entanglement reduction turns out to be universal for all quantum states entering the channel. This single quantity will make it easy to characterize the entanglement dynamics of entanglement of assistance under unknown channels in the experimental process of producing entangled states by assisted entanglement.
This paper proposes a quantum mechanical state equation for describing evolution of projects of financial investment, while the parameters of this equation well simulate the fundamental elements of financial market, including investment (input), assets loss (assets decrease), assets increase and income (output), the quantum mechanics operators involved in this equation also can reflect the dynamic process and characteristics of the project, so the equation can be taken as the evolution model of a kind of financial investment projects in the market. The entangled state representation is introduced to solve this equation and its solution is obtained in an infinite operator-sum form, which exhibits the link between the initial state and final state, i.e., the dynamic process of the financial investment project. As an example, we derive the evolution law of a pure investment project in financial market, which conforms with the evolution trend of the market. In solving the equation we also find a new state which we name it as the binomial-negative binomial entangled state. Throughout the discussions we make full use of Dirac's symbolic method and the technique of integration within an ordered product (IWOP) of operators.