Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Masking quantum information into a tripartite syste   Since masking of quantum information was introduced by Modi et al. in [PRL
120, 230501 (2018)], many discussions on this topic have been published. In
this paper, we consider relationship between quantum multipartite maskers
(QMMs) and quantum error-correcting codes (QECCs). We say that a subset $Q$ of
pure states of a system $K$ can be masked by an operator $S$ into a
multipartite system $\H^{(n)}$ if all of the image states $S|\psi\>$ of states
$|\psi\>$ in $Q$ have the same marginal states on each subsystem. We call such
an $S$ a QMM of $Q$. By establishing an expression of a QMM, we obtain a
relationship between QMMs and QECCs, which reads that an isometry is a QMM of
all pure states of a system if and only if its range is a QECC of any
one-erasure channel. As an application, we prove that there is no an isometric
universal masker from $\C^2$ into $\C^2\otimes\C^2\otimes\C^2$ and then the
states of $\C^3$ can not be masked isometrically into
$\C^2\otimes\C^2\otimes\C^2$. This gives a consummation to a main result and
leads to a negative answer to an open question in [PRA 98, 062306 (2018)].
Another application is that arbitrary quantum states of $\C^d$ can be
completely hidden
  in correlations between any two subsystems of the tripartite system
$\C^{d+1}\otimes\C^{d+1}\otimes\C^{d+1}$, while arbitrary quantum states cannot
be completely hidden in the correlations between subsystems of a bipartite
system [PRL 98, 080502 (2007)].

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
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The categories of this paper are: econ
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat