Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uncertainty and Complementarity Relations in Weak Measurement   We prove uncertainty relations that quantitatively express the impossibility
of jointly sharp preparation of pre- and post-selected quantum states for
measuring incompatible observables during the weak measurement. By defining a
suitable operator whose average in the pre-selected quantum state gives the
weak value, we show that one can have new uncertainty relations for variances
of two such operators corresponding to two non-commuting observables. These
generalize the recent stronger uncertainty relations that give non-trivial
lower bounds for the sum of variances of two observables which fully capture
the concept of incompatible observables. Furthermore, we show that weak values
for two non-commuting projection operators obey a complementarity relation.
Specifically, we show that for a pre-selected state if we measure a projector
corresponding to an observable $A$ weakly followed by the strong measurement of
another observable $B$ (for the post-selection) and, for the same pre-selected
state we measure a projector corresponding to an observable $B$ weakly followed
by the strong measurement of the observable $A$ (for the post-selection), then
the product of these two weak values is always less than one. This shows that
even though individually they are complex and can be large, their product is
always bounded.

11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
18
The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg