Probability and statistics seminar
Wednesday, 7th February at 3 pm
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Venue: Ramanujan Hall
Host: Debraj Das
Speaker: Dr. Samriddha Lahiry
Affiliation: Harvard University
Title: Quantum Statistical Inference
Abstract: Recent advancements in quantum technology, such as quantum
computing, communication, and metrology, have given rise to questions
related to quantum measurements, which can be elegantly formulated in the
language of mathematical statistics. However, quantum mechanics,
inherently noncommutative, yields inferential results that are distinctly
non-trivial, compared to their counterparts in classical statistics.
In classical statistics, a fundamental paradigm involves approximating
complex models with simpler ones. One commonly establishes asymptotic
equivalence between i.i.d models, characterized by a local parameter, and
a Gaussian shift model. This approximation, known as local asymptotic normality (LAN),
facilitates the construction of an estimator based on a procedure in the
Gaussian model, offering comparable risk bounds.
Notably, local asymptotic equivalence can be extended to quantum scenarios,
linking quantum i.i.d. models with quantum Gaussian models. In this context,
we obtain optimal estimators in the complex former models based on optimal
estimators in the simpler latter models.