A reasonable quantum information theory for fermions must respect the parity superselection rule to comply with the special theory of relativity and the no-signaling principle. This rule restricts the possibility of any quantum state to have a superposition between even- and odd-parity fermionic states. thereby characterizing the set of physically allowed fermionic quantum states. Here we introduce the physically allowed quantum operations, in congruence with the parity superselection rule, that map the set of allowed fermionic states onto itself. We first introduce unitary and projective measurement operations of the fermionic states. We further extend the formalism to general quantum operations in the forms of Stinespring dilation, operator-sum representation, and axiomatic completely positive and trace-preserving maps. We explicitly show the equivalence between these three representations of fermionic quantum operations. We discuss the possible implications of our results in characterization of correlations in fermionic systems.

中文翻译：

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费米子信息论中的量子运算

一个合理的费米子量子信息理论必须尊重奇偶超选规则，以符合狭义相对论和无信号原理。该规则限制了任何量子态在偶数和奇数费米子态之间叠加的可能性。从而表征物理上允许的费米子量子态集。在这里，我们介绍了物理上允许的量子操作，与奇偶超选择规则一致，将允许的费米子态集映射到自身上。我们首先介绍费米态的幺正和投影测量操作。我们进一步将形式主义扩展到 Stinespring 膨胀、算子和表示以及公理完全正和迹保留映射等形式的一般量子运算。我们明确地展示了费米子量子操作的这三种表示之间的等价性。我们讨论了我们的结果对费米子系统相关性表征的可能影响。