Valid and efficient entanglement verification with finite copies of a quantum state

Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme’s validity via the probability that the signal comes from a separable state, offering a meaning...

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Bibliographic Details
Published in:npj quantum information 2024-01, Vol.10 (1), p.14-10, Article 14
Main Authors: Cieśliński, Paweł, Dziewior, Jan, Knips, Lukas, Kłobus, Waldemar, Meinecke, Jasmin, Paterek, Tomasz, Weinfurter, Harald, Laskowski, Wiesław
Format: Article
Language:English
Subjects:
639/766/483/1139
639/766/483/481
Bayesian analysis
Certification
Classical and Quantum Gravitation
Datasets
Efficiency
Hypotheses
Hypothesis testing
Physics
Physics and Astronomy
Probability
Quantum Computing
Quantum Field Theories
Quantum Information Technology
Quantum Physics
Relativity Theory
Spintronics
Statistical inference
String Theory
Validity
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Summary:Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme’s validity via the probability that the signal comes from a separable state, offering a meaningful figure of merit for big datasets. Yet, with limited samples, avoiding experimental data misinterpretations requires considering not only the probabilities concerning separable states but also the probability that the signal came from an entangled state, i.e. the detection scheme’s efficiency. We demonstrate this explicitly and apply a general method to optimize both the validity and the efficiency in small data sets providing examples using at most 20 state copies. The method is based on an analytical model of finite statistics effects on correlation functions which takes into account both a Frequentist as well as a Bayesian approach and is applicable to arbitrary entanglement witnesses.
ISSN:2056-6387
2056-6387
DOI:10.1038/s41534-024-00810-3