Related papers: Parameter estimation of qubit states with unknown …
We study quantum-limited 3D magnetometry using two qubits. Two qubits form the smallest multi-qubit system for 3D magnetometry, the simultaneous estimation of three phases, as it is impossible with a single qubit. We provide an analytical…
We prove a concise factor-of-2 estimate for the failure rate of optimally distinguishing an arbitrary ensemble of mixed quantum states, generalizing work of Holevo [Theor. Probab. Appl. 23, 411 (1978)] and Curlander [Ph.D. Thesis, MIT,…
I propose quantum versions of the Ziv-Zakai bounds as alternatives to the widely used quantum Cram\'er-Rao bounds for quantum parameter estimation. From a simple form of the proposed bounds, I derive both a "Heisenberg" error limit that…
Phase diffusion invariably accompanies all phase estimation strategies -- quantum or classical. A precise estimation of the former can often provide valuable understanding of the physics of the phase generating phenomena itself. We…
The Cram\'er-Rao bound captures completely the performance of single-parameter quantum sensors. On the other hand, its extension to multiple parameters demands more caution. Different aspects need to be captured at once, including,…
The goal of this paper is to characterize the best achievable performance for the problem of estimating an unknown parameter having a sparse representation. Specifically, we consider the setting in which a sparsely representable…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
We demonstrate the application of pattern recognition algorithms via hidden Markov models (HMM) for qubit readout. This scheme provides a state-path trajectory approach capable of detecting qubit state transitions and makes for a robust…
The aim of this thesis is to develop a theoretical framework to study parameter estimation of quantum channels. We study the task of estimating unknown parameters encoded in a channel in the sequential setting. A sequential strategy is the…
In quantum computation, amplitude estimation is a fundamental subroutine that is utilized in various quantum algorithms. A general important task of such estimation problems is to characterize the estimation lower bound, which is referred…
For a fixed average energy, the simultaneous estimation of multiple phases can provide a better total precision than estimating them individually. We show this for a multimode interferometer with a phase in each mode, using Gaussian inputs…
We study the sensitivity of phase estimation using a generic class of path-symmetric entangled states $|\varphi\rangle|0\rangle+|0\rangle|\varphi\rangle$, where an arbitrary state $|\varphi\rangle$ occupies one of two modes in quantum…
The uniformly accelerated Unruh-DeWitt detector serves as a fundamental model in relativistic quantum metrology. While previous studies have mainly concentrated on single-parameter estimation via quantum Cram\'er-Rao bound, the…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
We explore optical quantum engineering of phase-parameterized continuous-variable (CV) probe states to exploit nonclassical light to solve the problem of precise phase estimation. The optical interferometer consists of a single beam…
The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum Cramer-Rao bound. For Gaussian stationary statistics, and a phase spectrum scaling asymptotically as…
Quantum parameter estimation holds significant promise for achieving high precision through the utilization of the most informative measurements. While various lower bounds have been developed to assess the best accuracy for estimates, they…
We study the frontier between learnable and unlearnable hidden Markov models (HMMs). HMMs are flexible tools for clustering dependent data coming from unknown populations. The model parameters are known to be fully identifiable (up to…
Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems $Hv = \lambda v$, such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to…
For decoherence processes induced by weak interactions with the environment, a general quantum channel with one noise parameter has been formulated. This channel is called low-noise channel and very useful for investigating the parameter…