Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extensions of the Mandelstam-Tamm quantum speed limit to systems in
  mixed states   The Mandelstam-Tamm quantum speed limit puts a bound on how fast a closed
system in a pure state can evolve. In this paper, we derive several extensions
of this quantum speed limit to closed systems in mixed states. We also compare
the strengths of these extensions and examine their tightness. The most widely
used extension of the Mandelstam-Tamm quantum speed limit originates in
Uhlmann's energy dispersion estimate. We carefully analyze the underlying
geometry of this estimate, an analysis that makes apparent that the Bures
metric, or equivalently the quantum Fisher information, will rarely give rise
to tight extensions. This observation leads us to address whether there is a
tightest general extension of the Mandelstam-Tamm quantum speed limit. Using a
geometric construction similar to that developed by Uhlmann, we prove that this
is indeed the case. In addition, we show that tight evolutions of mixed states
are typically generated by time-varying Hamiltonians, which contrasts with the
case for systems in pure states.

24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat