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

¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.0K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
1.0K
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

903
NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
903
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

1.2K
In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
1.2K
¹H NMR Signal Multiplicity: Splitting Patterns01:13

¹H NMR Signal Multiplicity: Splitting Patterns

5.0K
When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
5.0K
Molecular Spectroscopy: Absorption and Emission01:14

Molecular Spectroscopy: Absorption and Emission

2.0K
Molecules possess discrete energy levels called quantum states. Unlike atoms, which have simpler energy levels, molecules possess additional rotational and vibrational energy levels.  Each energy level is separated by an energy gap, with the gaps between adjacent electronic, vibrational, and rotational levels varying significantly. The three types of energy levels in a diatomic molecule are shown in Figure 1.
2.0K
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

35.8K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
35.8K

You might also read

Related Articles

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

Sort by
Same author

Asymptotic Survival of Genuine Multipartite Entanglement in Noisy Quantum Networks Depends on the Topology.

Physical review letters·2022
Same author

Genuine Multipartite Nonlocality Is Intrinsic to Quantum Networks.

Physical review letters·2021
Same author

Resource Theory of Entanglement with a Unique Multipartite Maximally Entangled State.

Physical review letters·2019
Same author

Structure of multidimensional entanglement in multipartite systems.

Physical review letters·2013

Related Experiment Video

Updated: Jun 16, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
00:07

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.4K

Maximally Entangled Mixed States for a Fixed Spectrum Do Not Always Exist.

Julio I de Vicente1

  • 1Departamento de Matemáticas, <a href="https://ror.org/03ths8210">Universidad Carlos III de Madrid</a>, E-28911, Leganés (Madrid), Spain and <a href="https://ror.org/05e9bn444">Instituto de Ciencias Matemáticas (ICMAT)</a>, E-28049 Madrid, Spain.

Physical Review Letters
|August 19, 2024
PubMed
Summary

Maximally entangled states do not exist for all fixed spectra in quantum mechanics. Even under broader nonentangling operations, specific spectral states cannot be transformed into all other isospectral states, challenging previous assumptions.

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

8.9K
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.5K

Related Experiment Videos

Last Updated: Jun 16, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
00:07

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.4K
Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

8.9K
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.5K

Area of Science:

  • Quantum Information Theory
  • Quantum Entanglement
  • Quantum State Characterization

Background:

  • Entanglement is a key quantum resource manipulated via local operations assisted by classical communication (LOCC).
  • A maximally entangled state within a set can be transformed into all other states in that set via LOCC.
  • The d-dimensional Bell state is known as the maximally entangled state for all bipartite states of local dimension d.

Purpose of the Study:

  • To investigate the existence of maximally entangled states within sets of mixed quantum states sharing the same spectrum.
  • To determine if a single state can maximize all entanglement measures for a fixed spectrum, particularly in practical, noisy quantum systems.

Main Methods:

  • Analysis of rank-2 quantum states with fixed spectra.
  • Examination of state transformations under local operations assisted by classical communication (LOCC).
  • Extension of analysis to the broader class of nonentangling operations.

Main Results:

  • Demonstrated that maximally entangled states do not exist for all fixed spectra in general.
  • For specific eigenvalues of rank-2 states, no single state can be transformed into all other isospectral states, even under nonentangling operations.
  • This implies that the state maximizing entanglement depends on the chosen entanglement measure for a fixed spectrum.

Conclusions:

  • The concept of a universally maximally entangled state for a fixed spectrum is not generally valid.
  • The findings highlight the complexity of entanglement in mixed states and the limitations of LOCC and nonentangling operations for certain spectral distributions.
  • Future research may need to consider measure-specific maximal entanglement for mixed states with identical spectra.