Bernoulli泛函上基于典则酉对合的量子熵

Quantum Entropy Based onCanonical Unitary Involutionon Bernoulli Functional

摘要: 量子 Bernoulli 噪声(QBNs)是作用于平方可积Bernoulli 泛函空间上的湮灭和增生算子族，满足等时典则反交换关系(CAR)。湮灭与增生算子的和算子是Bernoulli 泛函空间上的一列自伴算子，称为Bernoulli 泛函上的典则酉对合，本文基于Bernoulli 泛函空间的子空间上的典则酉对合，构造了一类密度算子，考虑了该密度算子的量子熵以及量子熵的若干性质。

Abstract: Quantum Bernoulli noises (QBNs) are the family of annihilation and creation operators acting on the space of square integrable Bernoulli functional, which satisfy a canonical anti-commutation relation (CAR) in equal time. The sum operator of annihilation and creation operator is a series of self-adjoint operator on Bernoulli functional space, which is called canonical unitary involution on Bernoulli functional. In this paper, based on the canonical unitary involution on the subspace of the Bernoulli functional space, we construct a class of density operators, and consider the quantum entropy of the density operator and some properties of the quantum entropy.