Related papers: Ziv-Zakai Error Bounds for Quantum Parameter Estim…
A common feature of collapse models and an expected signature of the quantization of gravity at energies well below the Planck scale is the deviation from ordinary quantum-mechanical behavior. Here, we analyze the general consequences of…
When standard light sources are employed, the precision of the phase determination is limited by the shot noise. Quantum entanglement provides means to exceed this limit with the celebrated example of N00N states that saturate the ultimate…
The quantum fisher information and quantum correlation parameters are employed to study the application of non-classical light to the problem of parameter estimation. It is shown that the optimal measurement sensitivity of a quantum state…
The Holevo Cram\'er Rao bound is a lower bound on the sum of the mean square error of estimates for parameters of a state. We provide a method for calculating the Holevo Cram\'er-Rao bound for estimation of quadrature mean parameters of a…
A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…
Variational quantum time evolution allows us to simulate the time dynamics of quantum systems with near-term compatible quantum circuits. Due to the variational nature of this method the accuracy of the simulation is a priori unknown. We…
Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of the phase shift. We compare the two frameworks and their sensitivity bounds to the estimation of…
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2)…
Performance bounds for parameter estimation play a crucial role in statistical signal processing theory and applications. Two widely recognized bounds are the Cram\'{e}r-Rao bound (CRB) in the non-Bayesian framework, and the Bayesian CRB…
Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit…
The phase resolution of interferometers is limited by the so-called Heisenberg limit, which states that the optimum phase sensitivity is inversely proportional to the number of interfering particles N, a 1/sqrt{N} improvement over the…
Quantum-enhanced sensing promises to improve the performance of sensing tasks using non-classical probes and measurements that require far fewer scene-modulated photons than the best classical schemes, thereby granting…
This review aims at gathering the most relevant quantum multi-parameter estimation methods that go beyond the direct use of the Quantum Fisher Information concept. We discuss in detail the Holevo Cram\'er-Rao bound, the Quantum Local…
The Heisenberg limit traditionally provides a lower bound on the phase uncertainty scaling as 1/<N>, where <N> is the mean number of photons in the probe. However, this limit has a number of loopholes which potentially might be exploited,…
Several current ultra-wide band applications, such as millimeter wave radar and communication systems, require high sampling rates and therefore expensive and energy-hungry analogto-digital converters (ADCs). In applications where cost and…
We develop a hybrid framework for quantum parameter estimation in the presence of nuisance parameters. In this Bayes-point scheme, the parameters of interest are treated as fixed non-random parameters while nuisance parameters are…
We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally…
A rigorous lower bound is obtained for the average resolution of any estimate of a shift parameter, such as an optical phase shift or a spatial translation. The bound has the asymptotic form k_I/<2|G|> where G is the generator of the shift…
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…
We theoretically present the quantum Cram\'{e}r-Rao bounds (QCRB) of an SU(1,1) interferometer for Gaussian states input with and without the internal photonic losses. The phase shifts in the single arm and in the double arms are studied…