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Chinese Physics Letters

Fluctuation of Quantum Information Density in Curved Time–Space

Bi Qiao

Published Apr 1, 2007• 0 citations
Publisher

Abstract

A dynamical equation for quantum information density (QID) in curved spacetime is presented. The related fluctuation of QID with quantum Einstein equation is also discussed, which reveals the measuring of the dynamical mutual information condition using a Gaussian quantum channel.
DOI
10.1088/0256-307x/24/4/004

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We establish several dynamical equations for quantum information density. It is demonstrated that quantum information density shares the same formalism of the Liouville equation, subdynamics kinetic equation and Fokker–Planck equation as the density operator and also possesses the superposition property. These allow one to use quantum information density directly to model quantum information. The kinetic equations for quantum information density reveal that the dynamical process of quantum information may be related to dissipative, Markovian, or diffusional information flows, together causing irreversibility. Finally, we discuss superposition of quantum information density, which allows us to construct a quantum information channel in the coherent state representation using harmonic oscillator based encoded quantum information, and obtain a formula for quantum dynamical mutual information.
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Starting from the quantum Fokker–Planck equation, a viable quantum Gaussian channel is constructed in a quantum information network. It is shown that the solution of this equation satisfies a Gaussian distribution channel. Transforming the solution of the Fokker–Planck equation and substituting it into the information formula, a quantum dynamical mutual information equation is obtained in the coherent state representation. On the basis of this equation, a new scheme is proposed to implement parallel quantum information processing in the quantum Gaussian channel. The proposed scheme takes the coefficients related to the encryption states of photons as the signal, and encodes the information that will be passed in the quantum Gaussian channel from the input terminal. Information is then accessed by extracting and decoding the coefficients from the output terminal. Compared with a classical Gaussian channel, this approach offers the advantage of quantum parallelism.
Quantum mutual information is a fundamental quantity for characterizing correlations among quantum systems. In this work, we investigate the dynamic evolution of the quantum mutual information based on Rényi-2 entropy for three-mode Gaussian states in the background of a Schwarzschild black hole. We find that the physically inaccessible mutual information increases with Hawking temperature and eventually saturates, while the physically accessible mutual information exhibits nonmonotonic temperature dependence: it first rises, reaches a peak, then declines toward a finite asymptotic value. This nonmonotonic behavior differs from the monotonic degradation typically observed for Gaussian entanglement and steering in curved spacetime. Furthermore, we establish several constraint relations governing the distribution of mutual information among subsystems. These findings contribute to understanding the quantumness of quantum correlations for continuous variable in Schwarzschild spacetime.
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