Quantum hypothesis testing of non-mixed-unitarity: A multifaceted hierarchy of quantum channel discrimination
Abstract
Given multiple uses of an unknown quantum channel, we determine whether it is a specified non-mixed-unitary channel or belongs to the set of mixed-unitary channels. Formulating this as a composite channel hypothesis testing problem, we characterize the Stein exponents achievable by parallel strategies under progressively weaker restrictions on probe states and auxiliary memory. In particular, we consider block-i.i.d. probes, which allow arbitrary correlations within blocks of fixed size while remaining i.i.d. across different blocks, and derive finite-letter expressions of the corresponding Stein exponents. Varying the block size, which interpolates between fully i.i.d. and arbitrary probes, together with further restrictions on intra-block correlations and access to auxiliary memory, results in a multifaceted hierarchy. We establish several strict separations within this hierarchy. Without auxiliary memory, we prove that fully i.i.d. probes yield a vanishing Stein exponent for every unital non-mixed-unitary channel, while blocks of three product probes suffice to obtain a strictly positive exponent for the qutrit Werner-Holevo channel. For block size two, although product probes seem to be insufficient for O(3)-covariant channels, an entangled probe achieves a strictly positive exponent for the qutrit Werner-Holevo channel, even though every maximally entangled probe fails. In contrast, access to auxiliary memory makes fully i.i.d. probes sufficient by yielding a strictly positive exponent for every non-mixed-unitary channel, even without requiring input-reference entanglement, and this exponent admits a lower bound determined by the diamond-norm distance from the mixed-unitary set. Moreover, for odd-dimensional Werner-Holevo channels, we find that this exponent is infinite, with every full-Schmidt-rank pure state being optimal.
Related
- Essential Unitarity for Higher-Order Quantum Computation
- Quantum communication: a discrimination approach
- A Sum-of-Squares Hierarchy with Quadratic Convergence for Quantum Channel Coding
- A Spectrum-Based Converse for Quantum State Discrimination and Its Applications to Classical-Quantum Channel Coding
- Optimal quantum discrimination at Liouvillian exceptional points
BibTeX
@misc{ghosal2026quantum,
title = {{Quantum hypothesis testing of non-mixed-unitarity: A multifaceted hierarchy of quantum channel discrimination}},
author = {Pratik Ghosal and Pritam Halder and Ayan Patra and Aditi Sen De},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.40355},
eprint = {2609.40355},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40355},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum hypothesis testing of non-mixed-unitarity: A multifaceted hierarchy of quantum channel discrimination
AU - Pratik Ghosal
AU - Pritam Halder
AU - Ayan Patra
AU - Aditi Sen De
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.40355
UR - https://arxiv.org/abs/2609.40355
AB - Given multiple uses of an unknown quantum channel, we determine whether it is a specified non-mixed-unitary channel or belongs to the set of mixed-unitary channels. Formulating this as a composite channel hypothesis testing problem, we characterize the Stein exponents achievable by parallel strategies under progressively weaker restrictions on probe states and auxiliary memory. In particular, we consider block-i.i.d. probes, which allow arbitrary correlations within blocks of fixed size while remaining i.i.d. across different blocks, and derive finite-letter expressions of the corresponding Stein exponents. Varying the block size, which interpolates between fully i.i.d. and arbitrary probes, together with further restrictions on intra-block correlations and access to auxiliary memory, results in a multifaceted hierarchy. We establish several strict separations within this hierarchy. Without auxiliary memory, we prove that fully i.i.d. probes yield a vanishing Stein exponent for every unital non-mixed-unitary channel, while blocks of three product probes suffice to obtain a strictly positive exponent for the qutrit Werner-Holevo channel. For block size two, although product probes seem to be insufficient for O(3)-covariant channels, an entangled probe achieves a strictly positive exponent for the qutrit Werner-Holevo channel, even though every maximally entangled probe fails. In contrast, access to auxiliary memory makes fully i.i.d. probes sufficient by yielding a strictly positive exponent for every non-mixed-unitary channel, even without requiring input-reference entanglement, and this exponent admits a lower bound determined by the diamond-norm distance from the mixed-unitary set. Moreover, for odd-dimensional Werner-Holevo channels, we find that this exponent is infinite, with every full-Schmidt-rank pure state being optimal.
ER -