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Testing quantum expanders is coQMAcomplete
, 2012
"... A quantum expander is a unital quantum channel that is rapidly mixing, has only a few Kraus operators, and can be implemented efficiently on a quantum computer. We consider the problem of estimating the mixing time (i.e., the spectral gap) of a quantum expander. We show that this problem is coQMAc ..."
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A quantum expander is a unital quantum channel that is rapidly mixing, has only a few Kraus operators, and can be implemented efficiently on a quantum computer. We consider the problem of estimating the mixing time (i.e., the spectral gap) of a quantum expander. We show that this problem is coQMAcomplete. This has applications to testing randomized constructions of quantum expanders, and studying thermalization of open quantum systems. 1
Variations on classical and quantum extractors
 In Information Theory (ISIT), 2014 IEEE International Symposium on
, 2014
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Local tests of global entanglement and a counterexample to the generalized area law
"... We introduce a technique for applying quantum expanders in a distributed fashion, and use it to solve two basic questions: testing whether a bipartite quantum state shared by two parties is the maximally entangled state and disproving a generalized area law. In the process these two questions which ..."
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We introduce a technique for applying quantum expanders in a distributed fashion, and use it to solve two basic questions: testing whether a bipartite quantum state shared by two parties is the maximally entangled state and disproving a generalized area law. In the process these two questions which appear completely unrelated turn out to be two sides of the same coin. Strikingly in both cases a constant amount of resources are used to verify a global property. Introduction. In this paper we address two basic questions: 1. Can Alice and Bob test whether their joint state is maximally entangled while exchanging only a constant number of qubits? More precisely, Alice and Bob hold two halves of a quantum state ψ 〉 on a D2dimensional space for large D, and would like to check whether ψ 〉 is the maximally entangled state φD 〉 = 1√D ∑x x〉x 〉 or whether it is orthogonal to that state. So far, all known protocols for