Tuesday, July 30, 2013

1307.7171 (Victor Veitch et al.)

The Resource Theory of Stabilizer Computation    [PDF]

Victor Veitch, Seyed Ali Hamed Mousavian, Daniel Gottesman, Joseph Emerson
Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the theory of entanglement, for resources for stabilizer codes. We introduce two quantitative measures - monotones - for the amount of non-stabilizer resource. As an application we give absolute bounds on the efficiency of magic state distillation. One of these monotones is the sum of the negative entries of the discrete Wigner representation of a quantum state, thereby resolving a long-standing open question of whether the degree of negativity in a quasi-probability representation is an operationally meaningful indicator of quantum behaviour.
View original: http://arxiv.org/abs/1307.7171

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