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UID:www.tcs.tifr.res.in/event/1385
DTSTAMP:20240125T054532Z
SUMMARY:Quantum Statistical Inference
DESCRIPTION:Speaker: Dr. Samriddha Lahiry (Harvard University\, Cambridge)\
n\nAbstract: \nQuantum state estimation is a fundamental problem in quantu
m information theory with applications in quantum computing and communicat
ion. To determine the state of a quantum system\, researchers often perfor
m measurements on a set of identically prepared quantum states\, which are
indexed by a parameter. These measurements provide information not only a
bout the parameter itself but also about the quantum states. While questio
ns related to optimal quantum measurements can be elegantly formulated in
the language of mathematical statistics\, the underlying non-commutative s
tructure yields inferential results that are distinctly non-trivial compar
ed to their counterparts in classical statistics. Furthermore\, in contras
t to classical models\, where estimates are constructed solely based on me
asurement outcomes\, quantum models introduce an additional layer of compl
exity because the optimal estimator depends on the choice of measurement a
s well. In classical statistics\, a fundamental paradigm involves approxim
ating complex models with simpler ones. One commonly establishes asymptoti
c equivalence between i.i.d. models\, characterized by a local parameter\,
and a Gaussian shift model. This approximation\, known as local asymptoti
c normality (LAN)\, facilitates the construction of an estimator based on
a procedure in the Gaussian model\, offering comparable risk bounds. Notab
ly\, local asymptotic equivalence can be extended to quantum scenarios\, l
inking quantum i.i.d. models with quantum Gaussian models. In this context
\, we obtain optimal estimators in the complex former models based on opti
mal estimators in the simpler latter models.\nShort Bio:\nSamriddha Lahir
y is a postdoctoral fellow at Harvard University in the Department of Stat
istics. He received his Ph.D. in Statistics from Cornell University in 202
2. His research focuses on asymptotic methods in quantum statistical infer
ence and high-dimensional statistics.\n
URL:https://www.tcs.tifr.res.in/web/events/1385
DTSTART;TZID=Asia/Kolkata:20240206T160000
DTEND;TZID=Asia/Kolkata:20240206T170000
LOCATION:A-201 (STCS Seminar Room)
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