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arXiv:2208.07772

Achieving Heisenberg limit in the phase measurement through three-qubit graph states

Subhasish Bag, Sarkar, Ramita, Prasanta Kumar Panigrahi

Published Aug 16, 2022• 0 citations
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Abstract

We study the reciprocal of the mean quantum Fisher information (RMQFI), $χ^2$ for general three qubit states, having graph and hypergraph states as special cases, for identifying genuine multi party entanglement characterized by $χ^2 <1$. We demonstrate that the most symmetric graph state and the GHZ state have the lowest RMQFI values leading to the highest statistical speed showing that both these states attain the Heisenberg limit in phase sensitivity. Unlike the GHZ state, graph states have the same RMQFI values for measurement through different parameters, a property shared by the hypergraph states. Three qubit graph and hypergraph states can violate Bell's inequality as $F_Q > N$. Both the GHZ state and the most symmetric graph state have the highest concurrence equalling 3 and the maximum QFI values.

DOI
10.48550/arxiv.2208.07772

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Graph states and hypergraph states are of wide interest in quantum information processing and foundational studies. Efficient verification of these states is a key to various applications. Here we propose a simple method for verifying hypergraph states, which requires only two distinct Pauli measurements for each party, yet its efficiency is comparable to the best strategy based on entangling measurements. For a given state, the overhead is bounded by the chromatic number and degree of the underlying hypergraph. Our protocol is dramatically more efficient than all previous protocols based on local measurements, including tomography and direct-fidelity estimation. It enables the verification of hypergraph states and genuine multipartite entanglement of thousands of qubits. The protocol can also be generalized to the adversarial scenario, while achieving almost the same efficiency. This merit is particularly appealing to demonstrating blind measurement-based quantum computation and quantum supremacy.