A preprint posted to arXiv — not yet peer-reviewed — addresses a fundamental question in quantum channel discrimination: given repeated access to an unknown channel, how efficiently can one determine whether it belongs to the set of mixed-unitary channels, or is definitively outside it? The authors frame this as a composite quantum hypothesis testing problem and analyze the achievable Stein exponents — the exponential rates at which error probabilities can be suppressed — under parallel measurement strategies with varying levels of probe sophistication and auxiliary memory.
The analysis reveals a multifaceted hierarchy depending on two key resources: the degree of correlation permitted within probe states (parametrized by block size, interpolating between fully independent and arbitrary probes) and access to auxiliary quantum memory. A notable finding is that without auxiliary memory, fully i.i.d. probes yield a vanishing Stein exponent for every unital non-mixed-unitary channel, yet blocks of just three product probes suffice to achieve a strictly positive exponent for the qutrit Werner-Holevo channel. For block size two, entangled probes can succeed where product probes appear insufficient, but crucially, maximally entangled probes fail while a specific non-maximally entangled state succeeds. The paper establishes several strict separations within this hierarchy, meaning no resource can substitute for another in general.
With auxiliary memory, the picture changes substantially: fully i.i.d. probes become sufficient for every non-mixed-unitary channel, achieving a strictly positive exponent bounded below by the diamond-norm distance from the mixed-unitary set, and requiring no input-reference entanglement. For odd-dimensional Werner-Holevo channels specifically, this exponent is found to be infinite, with every full-Schmidt-rank pure state serving as an optimal probe. These results, if confirmed through peer review, would substantially clarify the resource requirements for certifying the non-mixed-unitarity of quantum channels.