Equation of motion for estimation fidelity of monitored oscillating qubits

• Published in: Physics letters. A Vol. 381; no. 29; pp. 2293 - 2297
• Main Authors: Bassa, Humairah, Konrad, Thomas, Diósi, Lajos, Uys, Hermann
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 05.08.2017
• Subjects: Quantum measurement; Quantum state estimation; Qubits; Unsharp measurement; Weak measurement; Quantum state estimation; Weak measurement; Quantum measurement; Qubits; Unsharp measurement
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2017.05.013

We study the convergence properties of state estimates of an oscillating qubit being monitored by a sequence of discrete, unsharp measurements. Our method derives a differential equation determining the evolution of the estimation fidelity from a single incremental step. If the oscillation frequency Ω is precisely known, the estimation fidelity converges exponentially fast to unity. For imprecise knowledge of Ω we derive the asymptotic estimation fidelity. •A method for investigating state estimation fidelity during unsharp measurement is proposed.•The analysis relies on calculating fidelity changes in an incremental step of the protocol.•The method is used to study state estimation during qubit oscillations.•A differential equation is obtained describing the estimation fidelity convergence.•Asymptotic behaviour of the fidelity is studied given imprecise knowledge of that Hamiltonian.