Graph States as a Resource for Quantum Metrology

Abstract

By using highly entangled states, quantum metrology guarantees precision impossible with classical measurements. Unfortunately such states can be very susceptible to noise, and it is a great challenge of the field to maintain quantum advantage in realistic conditions. In this study we investigate the practicality of graph states for quantum metrology. Graph states are a natural resource for much of quantum information, and here we characterize their quantum Fisher information (QFI) for an arbitrary graph state. We then construct families of graph states which attain a QFI of at least of at least n 2−log n k , we call these states bundled graph states. We also quantify the number of n qubit stabilizer states that are useful as a resource for quantum metrology. We demonstrate that bundled graph states maintain a quantum advantage after being subjected to iid dephasing or finite erasures. This shows that these graph states are good resources for robust quantum metrology.Quantum metrology describes the framework for estimation strategies which surpass the precision limit of classical strategies [1][2][3][4]. A classical estimation strategy can be emulated by using non-entangled single qubit quantum states to estimate an unknown parameter θ. The highest precision we can achieve in this way is such that the mean squared error, ∆θ 2 , scales inversely with the number of quantum states (n); ∆θ 2 ≥ 1/n. Using an n qubit entangled state, it is possible to gain a quadratic advantage in precision; ∆θ 2 ≥ 1/n 2 , otherwise known as the Heisenberg limit (HL).Given a quantum resource, ρ, the highest achievable precision attainable is bounded by Q(ρ), the quantum Fisher information (QFI): ∆θ 2 ≥ 1/Q(ρ). There are many different proposals for which quantum states make ideal candidates for quantum metrology, including, but not limited to, spin squeezed states [5], 2D cluster states [6], and symmetric states [7,8]. A fundamental issue in this area is how to tolerate noise [9,10]. For example, the GHZ state is the canonical, optimal, resource for quantum metrology [1,3,11], but it is very fragile to noise, losing all quantum advantage if only one system is lost [12,13]. In this study we explore the practicality of graph states as a resource for quantum metrology.Graph states are incredibly useful resources with applications spanning many quantum information processes including cryptography [14,15], quantum networks [16,17], computation [18,19], and quantum error correction [20,21]. Furthermore, they can be implemented using different techniques, such as, ion traps [22], super conducting qubits [23], NV centers [24] and discrete [25][26][27] and continuous variable [28,29] optics. Here we show that they can also be effective resources for practical quantum metrology in the presence of noise.

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“…Given the steady-state property and high decay rate of the qubits FJ y is even below the standard quantum limit (SQL) in most parameter regions. Nonetheless, one still is able to identify areas that FJ y > 1, though slightly, which signals passing the SQL as it is expected from a graph state [27] as well as a multiparticle entangled state [48]. This behavior is studied for larger systems and the optimal values are shown in Fig.…”

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