Erlangen 2018 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 46: Quantum Information (Concepts and Methods) IV

Q 46.3: Talk

Wednesday, March 7, 2018, 14:30–14:45, K 1.019

New no-go theorems regarding phase space negativity and contextuality as resources — •Felipe Montealegre Mora, Huangjun Zhu, and David Gross — University of Cologne, Cologne, Germany

It has been proven recently that both negativity in the discrete Wigner function and contextuality with respect to stabilizer measurements may be considered resources in several variants of the model of quantum computing with magic states. They are also known not to be resources when working over qubits, and when including all operations taken from the stabilizer world into the model. This is arguably the most relevant case, as quantum algorithms are commonly understood in this framework.

Here we derive two new no-go theorems extending the results above. The first result considers phase space representations, a wider class of representations than discrete Wigner functions. We show that no phase space representation is covariant with respect to the real Clifford group. This result implies that negativity also fails to be a resource in this wider context whenever all real Clifford unitaries are part of the computational model. The second result considers a set of Pauli measurements subject to a certain uniformity condition. It is shown that if such a measurement set is large enough, then it contains some Clifford transform of the Mermin-Peres square with high probability.