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Multiple quantum channels are said to be incompatible if they cannot be realized as the marginals of a single joint channel [1]. Quantum channel incompatibility provides a unified perspective on various phenomena, such as the no-broadcasting theorem [2] and the no-information-without-disturbance principle [3]. In this talk, we address the question of how accurately incompatible quantum channels can be approximated by the marginals of a single joint channel. We quantify the quality of such an approximation using the minimum total diamond-norm error and establish upper and lower bounds on this error in terms of the generalized robustness of incompatibility (RoI) [4, 5], a measure of channel incompatibility. We examine the tightness of these bounds by analytically determining both the RoI and the minimum total error for identity channels. By applying our bounds to quantum measurements, we also derive a tradeoff among measurement informativeness, measurement error, and the resulting disturbance. This talk is based on our work [6].

[1] T. Heinosaari and T. Miyadera, J. Phys. A: Math. Theor. 50, 135302 (2017).

[2] H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa, and B. Schumacher, Phys. Rev. Lett. 76, 2818 (1996).

[3] P. Busch, “No Information Without Disturbance”: Quantum Limitations of Measurement. In: Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle. The Western Ontario Series in Philosophy of Science, vol 73. Springer, Dordrecht (2009).

[4] E. Haapasalo, J. Phys. A: Math. Theor. 48, 255303 (2015).

[5] J. Mori, Phys. Rev. A 101, 032331 (2020).

[6] S. Minagawa, R. Takakura, and K. Torii, arXiv:2605.11924 (2026).