Optimal verification of stabilizer states
- URL: http://arxiv.org/abs/2007.09713v1
- Date: Sun, 19 Jul 2020 16:49:01 GMT
- Title: Optimal verification of stabilizer states
- Authors: Ninnat Dangniam, Yun-Guang Han, Huangjun Zhu
- Abstract summary: We investigate systematically optimal verification of entangled stabilizer states using Pauli measurements.
For experimentalists, optimal protocols and protocols with the minimum number of settings are explicitly provided for all equivalent classes of stabilizer states up to seven qubits.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Statistical verification of a quantum state aims to certify whether a given
unknown state is close to the target 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 work, we investigate systematically
optimal verification of entangled stabilizer states using Pauli measurements.
First, we provide a lower 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. Then we propose a simple algorithm
for constructing optimal protocols based on Pauli measurements. Our
calculations suggest that optimal protocols based on Pauli measurements can
saturate the above bound for all entangled stabilizer states, and this claim is
verified explicitly for states up to seven qubits. Similar results are derived
when each party can choose only two measurement settings, say X and Z.
Furthermore, by virtue of the chromatic number, we provide an upper bound for
the minimum number of settings required to verify any graph state, which is
expected to be tight. For experimentalists, optimal protocols and protocols
with the minimum number of settings are explicitly provided for all equivalent
classes of stabilizer states up to seven qubits. For theorists, general results
on stabilizer states (including graph states in particular) and related
structures derived here may be of independent interest beyond quantum state
verification.
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