{"status":"public","abstract":[{"text":"Classical shadows are succinct classical representations of quantum states\r\nwhich allow one to encode a set of properties P of a quantum state rho, while\r\nonly requiring measurements on logarithmically many copies of rho in the size\r\nof P. In this work, we initiate the study of verification of classical shadows,\r\ndenoted classical shadow validity (CSV), from the perspective of computational\r\ncomplexity, which asks: Given a classical shadow S, how hard is it to verify\r\nthat S predicts the measurement statistics of a quantum state? We show that\r\neven for the elegantly simple classical shadow protocol of [Huang, Kueng,\r\nPreskill, Nature Physics 2020] utilizing local Clifford measurements, CSV is\r\nQMA-complete. This hardness continues to hold for the high-dimensional\r\nextension of said protocol due to [Mao, Yi, and Zhu, PRL 2025]. Among other\r\nresults, we also show that CSV for exponentially many observables is complete\r\nfor a quantum generalization of the second level of the polynomial hierarchy,\r\nyielding the first natural complete problem for such a class.","lang":"eng"}],"publication":"International Colloquium on Automata, Languages, and Programming (ICALP)","type":"conference","language":[{"iso":"eng"}],"user_id":"71541","external_id":{"arxiv":["2510.08515"]},"_id":"61777","citation":{"ama":"Karaiskos G, Rudolph D, Meyer JJ, Eisert J, Gharibian S. How hard is it to verify a classical shadow? In: <i>International Colloquium on Automata, Languages, and Programming (ICALP)</i>. ; 2026.","ieee":"G. Karaiskos, D. Rudolph, J. J. Meyer, J. Eisert, and S. Gharibian, “How hard is it to verify a classical shadow?,” 2026.","chicago":"Karaiskos, Georgios, Dorian Rudolph, Johannes Jakob Meyer, Jens Eisert, and Sevag Gharibian. “How Hard Is It to Verify a Classical Shadow?” In <i>International Colloquium on Automata, Languages, and Programming (ICALP)</i>, 2026.","apa":"Karaiskos, G., Rudolph, D., Meyer, J. J., Eisert, J., &#38; Gharibian, S. (2026). How hard is it to verify a classical shadow? <i>International Colloquium on Automata, Languages, and Programming (ICALP)</i>.","bibtex":"@inproceedings{Karaiskos_Rudolph_Meyer_Eisert_Gharibian_2026, title={How hard is it to verify a classical shadow?}, booktitle={International Colloquium on Automata, Languages, and Programming (ICALP)}, author={Karaiskos, Georgios and Rudolph, Dorian and Meyer, Johannes Jakob and Eisert, Jens and Gharibian, Sevag}, year={2026} }","short":"G. Karaiskos, D. Rudolph, J.J. Meyer, J. Eisert, S. Gharibian, in: International Colloquium on Automata, Languages, and Programming (ICALP), 2026.","mla":"Karaiskos, Georgios, et al. “How Hard Is It to Verify a Classical Shadow?” <i>International Colloquium on Automata, Languages, and Programming (ICALP)</i>, 2026."},"year":"2026","title":"How hard is it to verify a classical shadow?","author":[{"full_name":"Karaiskos, Georgios","last_name":"Karaiskos","first_name":"Georgios"},{"first_name":"Dorian","last_name":"Rudolph","full_name":"Rudolph, Dorian"},{"first_name":"Johannes Jakob","full_name":"Meyer, Johannes Jakob","last_name":"Meyer"},{"full_name":"Eisert, Jens","last_name":"Eisert","first_name":"Jens"},{"first_name":"Sevag","last_name":"Gharibian","full_name":"Gharibian, Sevag"}],"date_created":"2025-10-10T13:45:07Z","date_updated":"2026-04-20T13:55:08Z"}