Optimal verification of stabilizer states

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September 10, 2020 2:00 PM

Quantum tomography completely identifies an arbitrary unknown quantum state at the cost that is exponential in the number of qubits. Alternative, more feasible approaches to characterize quantum states aim to provide only partial, but important information such as a certification that an unknown state is close to the desired state with confidence.

So far, sample-optimal verification protocols based on local measurements have been found only for disparate groups of states: bipartite pure states, GHZ states, and antisymmetric basis states. In this talk, I will discuss our recent result [1] that gives a bound on the sample complexity of any verification protocol based on separable measurements, which is independent of the number of qubits and the specific stabilizer state, and provides evidence that the bound can be attained using only non-adaptive Pauli measurements. The latter is done by algorithmically constructing such an optimal verification scheme for every stabilizer state up to seven qubits, making use of the structure of stabilizer states and concepts such as canonical and admissible test projectors that we introduce along the way, which also apply to verification of quantum states in general.

[1] N. Dangniam, Y-G. Han and H. Zhu, http://arxiv.org/abs/2007.09713  

Zoom meeting details

Topic: Quantum Information and Quantum Computing Working Group
Time: September 10, 2020, 2:00 PM Warsaw

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Meeting ID: 92227103826
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