The present paper deals with a connection between quantum quadratic operators (QQOs) and quasi QQOs on 𝕄2(ℂ). We show that QQOs and quasi QQOs on 𝕄2(ℂ) coincide in the class of Volterra type of operators. To establish this result, we first describe these two kind of operators on the commutative part of 𝕄2(ℂ). Furthermore, in the last section, we introduce a quantum analogue of Volterra operators and provide concrete examples of such kind of operators. It is established that the considered examples also satisfy quasiness condition as well. The obtained results will allow to produce (with explicit conditions) a class of unital, but not trace-preserving positive maps of 𝕄2(ℂ).

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关于 𝕄2(ℂ) 上的拟量子二次算子的几点说明

本论文处理 𝕄 上的量子二次算子 (QQO) 和准 QQO 之间的联系2(ℂ)。我们在 𝕄 上展示了 QQO 和准 QQO2(ℂ) 符合 Volterra 类型的运算符。为了确定这个结果，我们首先在𝕄的交换部分上描述这两种算子2(ℂ)。此外，在最后一节中，我们介绍了 Volterra 算子的量子模拟，并提供了此类算子的具体示例。确定所考虑的示例也满足准条件。获得的结果将允许（在明确的条件下）产生一类单一但不保留痕迹的𝕄正映射2(ℂ)。