Consequences of preserving reversibility in quantum superchannels
- URL: http://arxiv.org/abs/2003.05682v5
- Date: Tue, 27 Apr 2021 12:26:58 GMT
- Title: Consequences of preserving reversibility in quantum superchannels
- Authors: Wataru Yokojima, Marco T\'ulio Quintino, Akihito Soeda, Mio Murao
- Abstract summary: Quantum superchannels with multiple slots are deterministic transformations which take independent quantum operations as inputs.
We show that the reversibility preserving condition restricts all pure superchannels with two slots to be either a quantum circuit only consisting of unitary operations or a coherent superposition of two unitary quantum circuits.
- Score: 4.014524824655106
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Similarly to quantum states, quantum operations can also be transformed by
means of quantum superchannels, also known as process matrices. Quantum
superchannels with multiple slots are deterministic transformations whichtake
independent quantum operations as inputs. While they are enforced to respect
the laws of quantum mechanics, the use of input operations may lack a definite
causal order, and characterizations of general superchannels in terms of
quantum objects with a physical implementation have been missing. In this
paper, we provide a mathematical characterization for pure superchannels with
two slots (also known as bipartite pure processes), which are superchannels
preserving the reversibility of quantum operations. We show that the
reversibility preserving condition restricts all pure superchannels with two
slots to be either a quantum circuit only consisting of unitary operations or a
coherent superposition of two unitary quantum circuits where the two input
operations are differently ordered. The latter may be seen as a generalization
of the quantum switch, allowing a physical interpretation for pure two-slot
superchannels. An immediate corollary is that purifiable bipartite processes
cannot violate device-independent causal inequalities.
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