Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear Gaussian Quantum State Smoothing: Understanding the optimal
  unravelings for Alice to estimate Bob's state   Quantum state smoothing is a technique to construct an estimate of the
quantum state at a particular time, conditioned on a measurement record from
both before and after that time. The technique assumes that an observer, Alice,
monitors part of the environment of a quantum system and that the remaining
part of the environment, unobserved by Alice, is measured by a secondary
observer, Bob, who may have a choice in how he monitors it. The effect of Bob's
measurement choice on the effectiveness of Alice's smoothing has been studied
in a number of recent papers. Here we expand upon the Letter which introduced
linear Gaussian quantum (LGQ) state smoothing [Phys. Rev. Lett., 122, 190402
(2019)]. In the current paper we provide a more detailed derivation of the LGQ
smoothing equations and address an open question about Bob's optimal
measurement strategy. Specifically, we develop a simple hypothesis that allows
one to approximate the optimal measurement choice for Bob given Alice's
measurement choice. By 'optimal choice' we mean the choice for Bob that will
maximize the purity improvement of Alice's smoothed state compared to her
filtered state (an estimated state based only on Alice's past measurement
record). The hypothesis, that Bob should choose his measurement so that he
observes the back-action on the system from Alice's measurement, seems contrary
to one's intuition about quantum state smoothing. Nevertheless we show that it
works even beyond a linear Gaussian setting.

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The categories of this paper are: q-fin
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th