Related papers: The quantum Bell-Ziv-Zakai bounds and Heisenberg l…
Using a quantum version of the Bell-Ziv-Zakai bound, I derive a Heisenberg limit to multiparameter estimation for any Gaussian prior probability density. The mean-square error lower bound is shown to have a universal quadratic scaling with…
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…
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…
When measuring a time-varying phase, the standard quantum limit and Heisenberg limit as usually defined, for a constant phase, do not apply. If the phase has Gaussian statistics and a power-law spectrum $1/|\omega|^p$ with $p>1$, then the…
We apply the variational method to obtain the universal and analytical lower bounds for parameter precision in some noisy systems. We first derive a lower bound for phase precision in lossy optical interferometry at non-zero temperature.…
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,…
We study the generalized limit for parameter sensitivity in quantum estimation theory considering the effects of repeated and adaptive measurements. Based on the quantum Ziv-Zakai bound, we derive some lower bounds for parameter sensitivity…
We derive fundamental lower bounds on the performance of optical metrology and communication systems in a Bayesian framework. The derivation uses classical rate-distortion theory in conjunction with bounds on the capacity to transmit…
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 provide evidence that the uncertainty in detection of small and deterministic phase-shift deviations from a working point can be lower than the Heisenberg bound, for fixed finite mean number of photons. We achieve that by exploiting…
Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
The ultimate precision of phase estimation is limited by the Heisenberg scaling $\Delta\phi_0 = K/N$, where $K\sim1$ is a numerical prefactor and $N$ is the mean number of photons interacting with the phase shifting object(s). However,…
Adaptive techniques make practical many quantum measurements that would otherwise be beyond current laboratory capabilities. For example: they allow discrimination of nonorthogonal states with a probability of error equal to the Helstrom…
The problem of measuring a time-varying phase, even when the statistics of the variation is known, is considerably harder than that of measuring a constant phase. In particular, the usual bounds on accuracy - such as the $1/(4\bar{n})$…
The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously…
The measurement of physical parameters is one of the main pillars of science. A classic example is the measurement of the optical phase enabled by optical interferometry where the best sensitivity achievable with N photons scales as 1/N -…
In this work, we address the central problem about how to effectively find the available precision limit of unknown parameters. In the framework of the quantum Ziv-Zakai bound (QZZB), we employ noiseless linear amplification (NLA)techniques…
Modern precision measurements, such as interferometry for detecting gravitational waves, rely on the estimation of optical phases encoded in light fields. Here, we propose to exploit the collectively enhanced output field of a…
Understanding the fundamental limits on the precision to which an optical phase can be estimated is of key interest for many investigative techniques utilized across science and technology. We study the estimation of a fixed optical phase…