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

Linear Circuits01:17

Linear Circuits

872
A linear circuit is characterized by its output having a direct proportionality to its input, adhering to the linearity property, which encompasses the principles of homogeneity (scaling) and additivity. Homogeneity dictates that when the input, also referred to as the excitation, is multiplied by a constant factor, the output, known as the response, is correspondingly scaled by the same constant factor. For instance, if the current is multiplied by a constant 'k,' the voltage likewise...
872
Linear Equations01:27

Linear Equations

475
Linear equations form the foundation of many algebraic and real-world applications, characterized by their simplicity and utility. A linear equation is an algebraic statement in which each term is either a constant or a product of a constant and a single variable. These equations represent straight lines when plotted on a Cartesian coordinate plane, reflecting a constant rate of change between two quantities.A typical linear equation in one variable has the form: ax + b = c, where a, b, and c...
475
Linear Momentum00:55

Linear Momentum

18.2K
The term momentum is used in various ways in everyday language, most of which are consistent with the precise scientific definition. Generally, momentum implies a tendency to continue on course—to move in the same direction; we tend to speak of sports teams or politicians gaining and maintaining the momentum to win.  Momentum is also associated with great mass and speed and is often considered when talking about collisions. For example, when rugby players collide and fall to the...
18.2K
Linearization and Approximation01:26

Linearization and Approximation

59
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
59
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

90
A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
90
Linear Differential Equations01:27

Linear Differential Equations

70
The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law...
70

You might also read

Related Articles

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

Sort by
Same author

Chernoff Information Bottleneck for Covert Quantum Target Sensing.

Physical review letters·2026
Same author

Robust quantum classifiers via NISQ adversarial learning.

Nature computational science·2024
Same author

Generating Haar-Uniform Randomness Using Stochastic Quantum Walks on a Photonic Chip.

Physical review letters·2022
Same author

Bounding the Benefit of Adaptivity in Quantum Metrology Using the Relative Fidelity.

Physical review letters·2021
Same author

Optimal Quantum Spatial Search with One-Dimensional Long-Range Interactions.

Physical review letters·2021
Same author

Molecular docking with Gaussian Boson Sampling.

Science advances·2020

Related Experiment Video

Updated: Jan 31, 2026

Serial Two-Photon Tomography of the Whole Marmoset Brain for Neuroanatomical Analyses
04:02

Serial Two-Photon Tomography of the Whole Marmoset Brain for Neuroanatomical Analyses

Published on: January 17, 2025

1.0K

Multiphoton Tomography with Linear Optics and Photon Counting.

Leonardo Banchi1, W Steven Kolthammer1, M S Kim1

  • 1QOLS, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom.

Physical Review Letters
|January 5, 2019
PubMed
Summary
This summary is machine-generated.

Fully characterizing quantum states requires fewer measurement bases than previously thought. Researchers demonstrate a practical method using linear optics and photon counting to determine unknown quantum states efficiently.

More Related Videos

Micron-scale Resolution Optical Tomography of Entire Mouse Brains with Confocal Light Sheet Microscopy
09:49

Micron-scale Resolution Optical Tomography of Entire Mouse Brains with Confocal Light Sheet Microscopy

Published on: October 8, 2013

17.2K
Integrated Photoacoustic Ophthalmoscopy and Spectral-domain Optical Coherence Tomography
11:21

Integrated Photoacoustic Ophthalmoscopy and Spectral-domain Optical Coherence Tomography

Published on: January 15, 2013

12.0K

Related Experiment Videos

Last Updated: Jan 31, 2026

Serial Two-Photon Tomography of the Whole Marmoset Brain for Neuroanatomical Analyses
04:02

Serial Two-Photon Tomography of the Whole Marmoset Brain for Neuroanatomical Analyses

Published on: January 17, 2025

1.0K
Micron-scale Resolution Optical Tomography of Entire Mouse Brains with Confocal Light Sheet Microscopy
09:49

Micron-scale Resolution Optical Tomography of Entire Mouse Brains with Confocal Light Sheet Microscopy

Published on: October 8, 2013

17.2K
Integrated Photoacoustic Ophthalmoscopy and Spectral-domain Optical Coherence Tomography
11:21

Integrated Photoacoustic Ophthalmoscopy and Spectral-domain Optical Coherence Tomography

Published on: January 15, 2013

12.0K

Area of Science:

  • Quantum Information Science
  • Quantum Optics
  • Quantum State Tomography

Background:

  • Characterizing unknown quantum states is crucial for quantum information processing.
  • Current methods often require complex experimental setups and numerous measurement bases.
  • Efficient state determination is essential for advancing quantum technologies.

Purpose of the Study:

  • To determine the minimum number of measurement bases required for full quantum state characterization.
  • To investigate practical methods using linear optics and photon counting.
  • To explore the role of unitary designs in state reconstruction.

Main Methods:

  • Studying projective measurements using linear optics and photon counting.
  • Deriving the theoretical lower bound for measurement settings.
  • Numerical simulations with random linear optics configurations (Haar random unitaries).
  • Utilizing unitary 2N designs for analytical state reconstruction protocols.

Main Results:

  • A practical set of projective measurements using linear optics and photon counting can fully characterize multimode quantum states.
  • The minimum number of required measurement settings was derived.
  • The derived lower bound is saturated by random linear optics configurations.
  • Analytical state reconstruction protocols can be derived from unitary 2N designs for N photons.

Conclusions:

  • Full characterization of quantum states with a definite number of photons is achievable with a reduced number of measurement bases.
  • Linear optics and photon counting offer a practical experimental approach.
  • The findings provide a theoretical framework and practical guidelines for quantum state tomography.