The incompatibility of quantum channels in general probabilistic
theories
- URL: http://arxiv.org/abs/2403.01392v1
- Date: Sun, 3 Mar 2024 04:28:25 GMT
- Title: The incompatibility of quantum channels in general probabilistic
theories
- Authors: Masataka Yamada, Takayuki Miyadera
- Abstract summary: In quantum theory, there exist sets of operations that cannot be performed simultaneously.
In this paper, we introduce min-tensor-compatibility using the min-tensor on the composite system of effect spaces.
We find that the set of min-tensor-compatible channel pairs is strictly broader than the set of quantum-compatible channel pairs.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In quantum theory, there exist sets of operations that cannot be performed
simultaneously. These sets of operations are referred to as incompatible. While
this definition of incompatibility extends to general probabilistic theories,
the dependency of the set of compatible sets on the definition of composite
systems has not been thoroughly investigated. In the context of quantum
channels, compatibility is defined using the tensor product of Hilbert spaces,
employing the usual composite system. However, in the context of general
probabilistic theories, composite systems are not uniquely determined, and the
set of states can range from min tensor to max tensor, forming various convex
sets. In this paper, in addition to quantum compatibility using the usual
composite system, we introduce min-tensor-compatibility using the min-tensor on
the composite system of effect spaces and investigate their relationship using
noisy identity channels on qubits. As a result, we found that the set of
min-tensor-compatible channel pairs is strictly broader than the set of
quantum-compatible channel pairs. Furthermore, we introduce the concept of
almost quantum compatible channel pairs from an operational perspective. This
concept corresponds to cases where the correlation functions appearing in the
verification of compatibility can be realized through a channel and local
reinterpretation of effects. We demonstrate that the set of all almost quantum
compatible channel pairs is strictly narrower than the set of all
min-tensor-compatible channel pairs.
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