Unsupervised classification of quantum data

Gael Sentís, Alex Monràs, John Calsamiglia, Ramon Muñoz-Tapia, Emilio Bagan

Research output: Contribution to journalArticleResearch

13 Citations (Scopus)


We introduce the problem of unsupervised classification of quantum data, namely, of systems whose quantum states are unknown. We derive the optimal single-shot protocol for the binary case, where the states in a disordered input array are of two types. Our protocol is universal and able to automatically sort the input under minimal assumptions, yet partially preserves information contained in the states. We quantify analytically its performance for an arbitrary size and dimension of the data. We contrast it with the performance of its classical counterpart, which clusters data that have been sampled from two unknown probability distributions. We find that the quantum protocol fully exploits the dimensionality of the quantum data to achieve a much higher performance, provided the data are at least three dimensional. For the sake of comparison, we discuss the optimal protocol when the classical and quantum states are known.

Original languageEnglish
Article number041029
Pages (from-to)041029-1-041029-22
JournalPhysical Review X
Issue number4
Publication statusPublished - 8 Nov 2019


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