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Related Concept Videos

Computed Tomography01:10

Computed Tomography

Tomography refers to imaging by sections. Computed tomography (CT) is a non-invasive imaging technique that uses computers to analyze several cross-sectional X-rays to reveal minute details about structures in the body.
The technique was invented in the 1970s and is based on the principle that as X-rays pass through the body, they are absorbed or reflected at different levels. In the technique, a patient lies on a motorized platform while a computerized axial tomography (CAT) scanner rotates...
Imaging Studies III: Computed Tomography01:27

Imaging Studies III: Computed Tomography

DefinitionComputed Tomography (CT) of the genitourinary (GU) tract is a non-invasive imaging modality that utilizes X-rays and computer processing to generate detailed cross-sectional images of the urinary system, encompassing the kidneys, ureters, bladder, and adjacent structures such as the adrenal glands.PurposeCT scans of the GU tract serve several diagnostic and therapeutic purposes, including:Diagnosis of Urinary Tract Diseases: Detects kidney stones, tumors, cysts, and congenital...
Electron Microscope Tomography and Single-particle Reconstruction01:07

Electron Microscope Tomography and Single-particle Reconstruction

Transmission electron microscopy (TEM) can be used to determine the 3D structure of biological samples with the help of techniques such as electron microscope tomography and single-particle reconstruction. While single-particle reconstruction can examine macromolecules and macromolecular complexes in vitro conditions only, tomography permits the study of cell components or small cells in vivo.
Electron Tomography
Electron tomography can be performed either in TEM or STEM (scanning transmission...
Positron Emission Tomography01:29

Positron Emission Tomography

Positron emission tomography (PET) is a medical imaging technique involving radiopharmaceuticals — substances that emit short-lived radiation. Although the first PET scanner was introduced in 1961, it took 15 more years before radiopharmaceuticals were combined with the technique and revolutionized its potential.
One of the main requirements of a PET scan is a positron-emitting radioisotope, which is produced in a cyclotron and then attached to a substance used by the part of the body being...
2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)01:19

2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)

Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
Imaging Studies II: Positron Emission Tomography and Scintigraphy01:25

Imaging Studies II: Positron Emission Tomography and Scintigraphy

Positron Emission Tomography (PET) is a medical imaging technique that provides crucial insights into the body's physiological functions at a molecular level. It is an indispensable resource for diagnosing, staging, and monitoring various illnesses, notably cancer, neurological disorders, and cardiovascular conditions.
Fundamental Principles of PET

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Lensless Fluorescent Microscopy on a Chip
11:23

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Published on: August 17, 2011

Quantum state tomography via compressed sensing.

David Gross1, Yi-Kai Liu, Steven T Flammia

  • 1Institute for Theoretical Physics, Leibniz University Hannover, 30167 Hannover, Germany.

Physical Review Letters
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

We developed compressed sensing methods for quantum state tomography, significantly improving large quantum system analysis. These techniques require fewer measurements and are robust for experimental use.

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Area of Science:

  • Quantum information science
  • Quantum computing
  • Quantum physics

Background:

  • Quantum state tomography is crucial for characterizing quantum systems.
  • Standard tomography methods are resource-intensive, especially for large systems.
  • Developing efficient tomography protocols is essential for advancing quantum technologies.

Purpose of the Study:

  • To introduce novel compressed sensing-based methods for quantum state tomography.
  • To enhance the efficiency and scalability of reconstructing quantum states.
  • To provide a robust and experimentally feasible approach for characterizing quantum states.

Main Methods:

  • Utilizing compressed sensing principles for quantum state reconstruction.
  • Developing algorithms tailored for fairly pure quantum states.
  • Employing simple Pauli measurements and fast convex optimization techniques.

Main Results:

  • Reconstruction of a density matrix of dimension d and rank r using O(rdlog²d) settings, a significant reduction from d².
  • Demonstrated applicability to approximately low-rank states.
  • Methods are stable against noise and do not require a priori purity assumptions.

Conclusions:

  • The developed methods offer a significant performance improvement for quantum state tomography on large systems.
  • The techniques are practical for experimental implementation due to their reliance on simple measurements and robust optimization.
  • The approach allows for certification of state purity without prior knowledge.