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Unifying theory of quantum state estimation using past and future information


The term ``quantum state estimation'' is often used to refer to the quantum state tomography, where outcomes of multiple projective measurements, applied on unknown quantum systems, are analyzed to optimally estimate the unknown state ``before'' such measurements (retrodiction). However, learning from classical state estimation theory, one can easily see that the more recent quantum measurement theory is also a type of ``state estimation'', where measurement outcomes, from either weak or strong measurements, are processed to optimally estimate the quantum state ``after'' such measurements (prediction). In this talk, I will present our recent theoretical work, extending the quantum state estimation theory beyond this, and introducing the concept of estimation using measurement information both in the past and future to estimate a state at present. In the quantum regime, there are mainly three existing formalisms that take into account the information both before and after the estimation time, i.e., the weak-value formalism [Phys. Rev. Lett. 60 1351 (1988)], the quantum most-likely path [Phys. Rev. A 88 042110 (2013)], and the quantum state smoothing [Phys. Rev. Lett. 115, 180407 (2015)]. Considering a partially observed quantum system, in which there exist both observed and unobserved records from continuous monitoring of the system, we give a common formulation that establishes the connection among three existing formalisms. The state estimators are calculated based on the expected cost minimization, either in the state space or the unknown record space. Our theory not only unifies existing formalisms for quantum state estimation, but also suggests new estimators that can be applied in practical scenarios. (Co-authors: Ivonne Guevara, Kiarn T. Laverick, and Howard M. Wiseman) Join Zoom Meeting:

Meeting ID: 942 4307 1494
Password: 487616

Link to seminar recording:

Unifying theory of quantum state estimation using past and future information