Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum State Isomorphism   We consider a problem we call StateIsomorphism: given two quantum states of n
qubits, can one be obtained from the other by rearranging the qubit subsystems?
Our main goal is to study the complexity of this problem, which is a natural
quantum generalisation of the problem StringIsomorphism. We show that
StateIsomorphism is at least as hard as GraphIsomorphism, and show that these
problems have a similar structure by presenting evidence to suggest that
StateIsomorphism is an intermediate problem for QCMA. In particular, we show
that the complement of the problem, StateNonIsomorphism, has a two message
quantum interactive proof system, and that this proof system can be made
statistical zero-knowledge. We consider also StabilizerStateIsomorphism (SSI)
and MixedStateIsomorphism (MSI), showing that the complement of SSI has a
quantum interactive proof system that uses classical communication only, and
that MSI is QSZK-hard.

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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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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: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph