Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faithful Squashed Entanglement   Squashed entanglement is a measure for the entanglement of bipartite quantum
states. In this paper we present a lower bound for squashed entanglement in
terms of a distance to the set of separable states. This implies that squashed
entanglement is faithful, that is, strictly positive if and only if the state
is entangled. We derive the bound on squashed entanglement from a bound on
quantum conditional mutual information, which is used to define squashed
entanglement and corresponds to the amount by which strong subadditivity of von
Neumann entropy fails to be saturated. Our result therefore sheds light on the
structure of states that almost satisfy strong subadditivity with equality. The
proof is based on two recent results from quantum information theory: the
operational interpretation of the quantum mutual information as the optimal
rate for state redistribution and the interpretation of the regularised
relative entropy of entanglement as an error exponent in hypothesis testing.
The distance to the set of separable states is measured by the one-way LOCC
norm, an operationally-motivated norm giving the optimal probability of
distinguishing two bipartite quantum states, each shared by two parties, using
any protocol formed by local quantum operations and one-directional classical
communication between the parties. A similar result for the Frobenius or
Euclidean norm follows immediately. The result has two applications in
complexity theory. The first is a quasipolynomial-time algorithm solving the
weak membership problem for the set of separable states in one-way LOCC or
Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show
that multiple provers are not more powerful than a single prover when the
verifier is restricted to one-way LOCC operations thereby providing a new
characterisation of the complexity class QMA.

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The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
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The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg