Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
Estimation of the Physical Quantities01:05

Estimation of the Physical Quantities

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
Chebyshev's Theorem to Interpret Standard Deviation01:15

Chebyshev's Theorem to Interpret Standard Deviation

Chebyshev’s theorem, also known as Chebyshev’s Inequality, states that the proportion of values of a dataset for K standard deviation is calculated using the equation:
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Quantum limits on the time-bandwidth product of an optical resonator.

Optics letters·2018
Same author

Far-Field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit.

Physical review letters·2016
Same author

Interferometric superlocalization of two incoherent optical point sources.

Optics express·2016
Same author

Quantum-limited mirror-motion estimation.

Physical review letters·2013
Same author

Continuous quantum hypothesis testing.

Physical review letters·2012
Same author

Quantum nonlocality in weak-thermal-light interferometry.

Physical review letters·2012
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Related Experiment Videos

Ziv-Zakai error bounds for quantum parameter estimation.

Mankei Tsang1

  • 1Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117583. eletmk@nus.edu.sg

Physical Review Letters
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Quantum Ziv-Zakai bounds offer a new approach to quantum parameter estimation. These bounds provide tighter error limits than quantum Cramér-Rao bounds for certain quantum states, improving precision in quantum measurements.

Related Experiment Videos

Area of Science:

  • Quantum Information Science
  • Quantum Metrology
  • Statistical Estimation Theory

Background:

  • Quantum parameter estimation is crucial for advancing quantum technologies.
  • Quantum Cramér-Rao bounds are widely used but have limitations.
  • Existing bounds may not be optimal for all quantum states and measurement regimes.

Purpose of the Study:

  • To introduce quantum versions of the Ziv-Zakai bounds as alternatives to quantum Cramér-Rao bounds.
  • To explore the implications of these new bounds for quantum parameter estimation precision.
  • To analyze the performance of quantum Ziv-Zakai bounds in specific quantum optical scenarios.

Main Methods:

  • Derivation of quantum Ziv-Zakai bounds from a simplified form.
  • Analysis of derived bounds, yielding Heisenberg-like and Cramér-Rao-like error limits.
  • Application of the bounds to optical phase estimation problems with varying photon number statistics.

Main Results:

  • The proposed quantum Ziv-Zakai bounds yield a Heisenberg error limit dependent on average energy.
  • A quantum Cramér-Rao-like bound scaling with energy variance is also derived.
  • For non-Gaussian states, quantum Ziv-Zakai bounds can be significantly tighter than quantum Cramér-Rao bounds in specific regimes.

Conclusions:

  • Quantum Ziv-Zakai bounds offer a valuable alternative for quantum parameter estimation.
  • These bounds provide tighter estimations for states with non-Gaussian photon number statistics.
  • The derived bounds complement existing methods, offering improved precision in quantum measurements.