Quantum memory precludes mixed-unitary dynamics

• URL: http://arxiv.org/abs/2603.17010v1
• Date: Tue, 17 Mar 2026 18:00:51 GMT
• Title: Quantum memory precludes mixed-unitary dynamics
• Abstract summary: Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations.<n>Characterizing channels that do not admit such a decomposition is in general a hard problem.<n>We establish a link between mixed-unitarity of unital channels and the (quantum) nature of the memory effects in non-Markovian dynamics.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of unitary evolutions. Characterizing channels that do not admit such a decomposition is in general a hard problem with significant implications for noise mitigation in quantum technologies and for fundamental problems in quantum information theory. Here we establish a link between mixed-unitarity of unital channels and the (quantum) nature of the memory effects in non-Markovian dynamics. Translating the problem into the language of process tensors, this connection yields a hierarchy of semidefinite programs that provides numerically efficient witnesses for non-mixed-unitary behavior, outperforming existing criteria. We demonstrate the power of this approach through illustrative examples of unital channels in dimensions three and four.

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