# Unifying theory of quantum state estimation using past and future information

Date and time |
Jul 14, 2020 from 11:00 AM to 12:00 PM |
---|---|

Location | Zoom meeting |

Host | Aephraim Steinberg |

## Areeya Chantasri

**
Department of Physics, Faculty of Science, Mahidol University, Bangkok
**

## Abstract:

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:

https://zoom.us/j/94243071494?pwd=VHpCVk0rci9McEVETlpGNUszTUdDUT09

Meeting ID: 942 4307 1494

Password: 487616

Link to seminar recording: https://play.library.utoronto.ca/00179e36f976a4fc86560c477d9d39de