Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How well can we guess the outcome of measurements of non-commuting
  observables?   According to Heisenberg's uncertainty relation, there is an ultimate limit to
how precisely we may predict the outcome of position and momentum measurements
on a quantum system. We show that this limit may be violated by an arbitrarily
large factor if one aims, instead, to guess the unknown value of a past
measurement. For experiments on a single quantum system, the precise assignment
of past position and momentum measurement outcomes is accompanied by large
uncertainty about their linear combinations, while we show that entanglement
with an ancillary system permits accurate retrodiction of any such linear
combination. Finally, we show that the outcomes of experiments that jointly
measure multiple linear combinations of position and momentum observables by
means of ancillary probe particles can also be guessed with no formal lower
limit. We present quantitative results for projective measurements and for
generalized measurements where all components are prepared in Gaussian states.

19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th