Quantum channels describe the most general dynamics of open quantum systems. A quantum channel, as a linear map on vectorized quantum states, can be represented by a single matrix, whose spectrum is called the channel spectrum. Here, we propose a general method to measure the channel spectrum and apply this method to Hamiltonian parameter estimation. We first demonstrate that the channel spectrum can be measured by tracking the probability of a specific outcome in repeated application of the same channel. Then, we construct and analyze a class of concatenated channels, with each one being a unitary channel on a target quantum system followed by a weak-measurement channel induced by a Ramsey measurement on a probe qubit. We show that the spectrum measurement of such concatenated channels can be utilized for estimating the parameters in the free Hamiltonians generating the unitary channels of the target system. As practical examples, we numerically demonstrate that a probe spin qubit can accurately sense nuclear spin clusters for nanoscale nuclear magnetic resonance.

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• Open quantum systems & decoherence
• Quantum channels
• Quantum measurements
• Quantum parameter estimation
• Quantum sensing
• Non-Hermitian systems