Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the geometric distance between quantum states with positive partial
  transposition and private states   We prove an analytic positive lower bound for the geometric distance between
entangled positive partial transpose (PPT) states of a broad class and any
private state that delivers one secure key bit. Our proof holds for any Hilbert
space of finite dimension. Although our result is proven for a specific class
of PPT states, we show that our bound nonetheless holds for all known entangled
PPT states with non-zero distillable key rates whether or not they are in our
special class.

27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
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The categories of this paper are: eess
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th