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.