Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time reversal symmetry of generalized quantum measurements with past and
  future boundary conditions   We expand the time reversal symmetry arguments of quantum mechanics,
originally proposed by Wigner in the context of unitary dynamics, to contain
situations including generalized measurements for monitored quantum systems. We
propose a scheme to derive the time reversed measurement operators by
considering the Schr\"{o}dinger picture dynamics of a qubit coupled to a
measuring device, and show that the time reversed measurement operators form a
Positive Operator Valued Measure (POVM) set. We present three particular
examples to illustrate time reversal of measurement operators: (1) the Gaussian
spin measurement, (2) a dichotomous POVM for spin, and (3) the measurement of
qubit fluorescence. We then propose a general rule to unravel any rank two
qubit measurement, and show that the backward dynamics obeys the retrodicted
equations of the forward dynamics starting from the time reversed final state.
We demonstrate the time reversal invariance of dynamical equations using the
example of qubit fluorescence. We also generalize the discussion of a
statistical arrow of time for continuous quantum measurements introduced by
Dressel et al. [Phys. Rev. Lett. 119, 220507 (2017)]: we show that the backward
probabilities can be computed from a process similar to retrodiction from the
time reversed final state, and extend the definition of an arrow of time to
ensembles prepared with pre- and post-selections, where we obtain a
non-vanishing arrow of time in general. We discuss sufficient conditions for
when time's arrow vanishes and show our method also captures the contributions
to time's arrow due to natural physical processes like relaxation of an atom to
its ground state. As a special case, we recover the time reversibility of the
weak value as its complex conjugate using our method, and discuss how our
conclusions differ from the time-symmetry argument of
Aharonov-Bergmann-Lebowitz (ABL) rule.

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The categories of this paper are: math
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: stat
26
The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: cs