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Article Dans Une Revue Quantum Année : 2023

The quantum switch is uniquely defined by its action on unitary operations

Qingxiuxiong Dong
Marco Túlio Quintino
Akihito Soeda
Mio Murao

Résumé

The quantum switch is a quantum process that creates a coherent control between different unitary operations, which is often described as a quantum process which transforms a pair of unitary operations ( U 1 , U 2 ) into a controlled unitary operation that coherently applies them in different orders as |0><0| \otimes U_1U_2 + |1><1| \otimes U_2U_1 . This description, however, does not directly define its action on non-unitary operations. The action of the quantum switch on non-unitary operations is then chosen to be a ``natural'' extension of its action on unitary operations. In general, the action of a process on non-unitary operations is not uniquely determined by its action on unitary operations. It may be that there could be a set of inequivalent extensions of the quantum switch for non-unitary operations. We prove, however, that the natural extension is the only possibility for the quantum switch for the 2-slot case. In other words, contrary to the general case, the action of the quantum switch on non-unitary operations (as a linear and completely CP preserving supermap) is completely determined by its action on unitary operations. We also discuss the general problem of when the complete description of a quantum process is uniquely determined by its action on unitary operations and identify a set of single-slot processes which are completely defined by their action on unitary operations.
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Dates et versions

hal-04273568 , version 1 (10-01-2024)

Identifiants

Citer

Qingxiuxiong Dong, Marco Túlio Quintino, Akihito Soeda, Mio Murao. The quantum switch is uniquely defined by its action on unitary operations. Quantum, 2023, 7, pp.1169. ⟨10.22331/q-2023-11-07-1169⟩. ⟨hal-04273568⟩
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