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Acta Sinica Quantum Optica

The Derivation of Quantum Diffusion Equation and the Evolution of Coherent States in Diffusion Channels

李学超 LI Xue-chao, 范洪义 FAN Hong-yi

Published Jan 1, 2016• 0 citations
Publisher
DOI
10.3788/asqo20162204.0307

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Abstract Using the operator correspondence of the real and fictious modes in the thermo entangled state representation, we solve the quantum master equation describing the diffusion channel and obtain the Kraus operator-sum representation of its analytical solution. we find that the pure coherent states evolve into the new mixed thermal superposed states in the diffusion channel. Also, we investigate the statistical properties of the initial coherent states and their entropy evolutions in the diffusion channel, and find that the entropy evolutions are only related to the decay time and without the amplitudes of the initial coherent states.
In quantum statistics theory, very few systems’ quantum entropy can be evaluated, since the quantum entropy’s formula by von-Neumann is [Formula: see text] where [Formula: see text] is density operator, [Formula: see text] is the Boltzmann constant, and the natural logarithm [Formula: see text] is quite difficult to treat. In this work, we tackle how to derive the entropy evolution of an initial coherent state undergoing a quantum diffusion process. We employ the method of integration within ordered product (IWOP) of operators to derive the final mixed state, which is a displaced chaotic state, and then deduce its entropy.