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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
Consider a situation in which two quantum operations Φ0 and Φ1 are fixed. A single evaluation
, 2008
"... Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary system needed to optimally distinguish quantum operations ar ..."
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Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary system needed to optimally distinguish quantum operations are known in several situations. For instance, the dimension of the auxiliary space never needs to exceed the dimension of the input space [Smi83, Kit97] of the operations for optimal distinguishability, while no auxiliary system whatsoever is needed to optimally distinguish unitary operations [AKN98, CPR00]. Another bound, which follows from work of R. Timoney [Tim03], is that optimal distinguishability is always possible when the dimension of the auxiliary system is twice the number of operators needed to express the difference between the quantum operations in Kraus form. This paper provides an alternate proof of this fact that is based on concepts and tools that are familiar to quantum information theorists. 1