Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Detection and Classification of Three-qubit States Using $l_{1}$ Norm of
  Coherence   Entanglement is a purely quantum mechanical phenomenon and thus it has no
classical analogue. On the other hand, coherence is a well known phenomenon in
classical optics and in quantum mechanics. Recent research shows that quantum
coherence may act as an useful resource in quantum information theory. We will
employ here quantum coherence to detect and classify the entanglement property
of three-qubit states. We have formulated few equality type necessary
conditions based on $l_{1}$ norm of coherence for both three-qubit pure
biseparable and separable states. We have shown that if the pure three-qubit
state under investigation does not satisfy the corresponding equality
conditions then the state does not belong to either the set of biseparable
state or the set of separable states or both the sets. Moreover, we provide
another set of necessary conditions, which is based on coherence based
inequalities for the detection of pure and mixed three-qubit biseparable
states. We have shown that if any three-qubit state (pure or mixed) violate the
derived coherence based inequality then the given three-qubit state cannot be a
biseparable state. Since there are only three categories of states for
three-qubit system so if we detect that the state under probe is neither a
separable nor a biseparable state then we can definitely conclude that the
given three-qubit state is a genuine entangled state. We have illustrated our
result with few examples.

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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: math
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat