Pranjal Agarwal, Nada Ali, Camilla Polvara, Martin Isbjörn Trappe, Berthold-Georg Englert, Mark Hillery
{"title":"Unsupervised state learning from pairs of states","authors":"Pranjal Agarwal, Nada Ali, Camilla Polvara, Martin Isbjörn Trappe, Berthold-Georg Englert, Mark Hillery","doi":"arxiv-2409.11120","DOIUrl":null,"url":null,"abstract":"Suppose you receive a sequence of qubits where each qubit is guaranteed to be\nin one of two pure states, but you do not know what those states are. Your task\nis to either determine the states or to construct a POVM (Positive Operator\nValued Measure) that will discriminate them. This can be viewed as a quantum\nanalog of unsupervised learning. A problem is that without more information,\nall that can be determined is the density matrix of the sequence, and, in\ngeneral, density matrices can be decomposed into pure states in many different\nways. To solve the problem additional information, either classical or quantum,\nis required. We show that if an additional copy of each qubit is supplied, that\nis, one receives pairs of qubits, both in the same state, rather than single\nqubits, the task can be accomplished. We then simulate numerically the\nmeasurement of a sequence of qubit pairs and show that the unknown states and\ntheir respective probabilities of occurrence can be found with high accuracy.","PeriodicalId":501226,"journal":{"name":"arXiv - PHYS - Quantum Physics","volume":"197 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Quantum Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11120","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Suppose you receive a sequence of qubits where each qubit is guaranteed to be
in one of two pure states, but you do not know what those states are. Your task
is to either determine the states or to construct a POVM (Positive Operator
Valued Measure) that will discriminate them. This can be viewed as a quantum
analog of unsupervised learning. A problem is that without more information,
all that can be determined is the density matrix of the sequence, and, in
general, density matrices can be decomposed into pure states in many different
ways. To solve the problem additional information, either classical or quantum,
is required. We show that if an additional copy of each qubit is supplied, that
is, one receives pairs of qubits, both in the same state, rather than single
qubits, the task can be accomplished. We then simulate numerically the
measurement of a sequence of qubit pairs and show that the unknown states and
their respective probabilities of occurrence can be found with high accuracy.