Orbit-injective Covariant Quantum Channels
Orbit-injective Covariant Quantum Channels
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DOI：
10.1016/j.laa.2023.03.018
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发表时间：
2023-03
影响因子：
1.1
通讯作者：
Kai Liu;Chuangxun Cheng;D. Han
中科院分区：
文献类型：
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作者：
Kai Liu;Chuangxun Cheng;D. Han
本文的目的是研究在群酉表示π作用下保留并分离纯态轨道的量子通道。这样的量子通道将被称为π轨道内射。我们证明，对于有限群和复杂的希尔伯特空间情况，这样的通道必然会分离所有的纯状态。然而，对于作用于真实希尔伯特空间的量子通道，或作用于具有（无限）紧群表示的复杂希尔伯特空间的量子通道，情况不再如此。在这两种情况下，我们都获得了量子通道是轨道内射的必要和/或充分条件。这些条件根据群的特征（更一般地，不可约表示）的所谓属性（H）给出，并且属性（H）的表征针对实数和复值乘法特征给出。
The purpose of this paper is to investigate the quantum channels that preserve and also separate the orbits of pure states under the action of a group unitary representationπ. Such a quantum channel will be calledπ-orbit injective. We prove that for finite group and complex Hilbert space cases, such a channel necessarily separates all the pure states. However, this is no longer true for quantum channels acting on real Hilbert spaces, or quantum channels acting on complex Hilbert spaces with (infinite) compact group representations. In both cases, we obtain necessary and/or sufficient conditions under which the quantum channel is orbit injective. These conditions are given in terms of the so called property (H) of characters (more generally, irreducible representations) of the group, and characterizations of property (H) are presented for real and complex valued multiplicative characters.