Quantum memory precludes mixed-unitary dynamics

TL;DR

This paper links the property of unital quantum channels being mixed-unitary to the nature of memory effects in non-Markovian dynamics, providing efficient numerical tools to identify channels that are not mixed-unitary.

Contribution

It introduces a hierarchy of semidefinite programs to efficiently witness non-mixed-unitary unital channels using process tensor formalism.

Findings

Outperforms existing criteria in detecting non-mixed-unitary channels

Demonstrates the approach with examples in dimensions three and four

Establishes a connection between mixed-unitarity and quantum memory effects

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.