Related Experiment Video
Updated: Oct 2, 2025
07:56
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
8.6K
A Characterization of Maximally Entangled Two-Qubit States
Junjun Duan1, Lin Zhang1, Quan Qian1
1School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China.
Entropy (Basel, Switzerland)
|February 25, 2022
Summary
Researchers explored bipartite quantum states with minimal partial-transpose eigenvalues of -1/2. For two-qubit systems, this indicates maximal entanglement, a finding not generalizable to higher-dimension two-qudit systems.
Area of Science:
- Quantum Information Theory
- Quantum Entanglement
- Quantum State Characterization
Background:
- Rana's prior work established that eigenvalues of partial-transposed bipartite states are bounded within [-1/2, 1].
- Bipartite quantum states are fundamental to quantum information processing and understanding entanglement properties.
Purpose of the Study:
- To investigate a specific family of bipartite quantum states characterized by a minimal eigenvalue of -1/2 in their partial transpose.
- To determine the conditions under which this minimal eigenvalue of -1/2 occurs in bipartite quantum states.
Main Methods:
- Analysis of eigenvalues of partial-transposed bipartite states.
- Mathematical derivation for two-qubit systems.
- Comparison with two-qudit systems of higher dimensions.
Main Results:
- For a two-qubit system, a minimal eigenvalue of -1/2 for the partial-transposed state is a necessary and sufficient condition for maximal entanglement.
- This direct correlation between the minimal eigenvalue and maximal entanglement is specific to the two-qubit case.
- The result does not extend to two-qudit systems where the dimensions exceed two.
Conclusions:
- Maximal entanglement in two-qubit states is precisely characterized by the -1/2 minimal eigenvalue of their partial transpose.
- The dimensionality of the quantum system plays a crucial role in the relationship between partial-transpose eigenvalues and entanglement.
- Further research is needed to explore entanglement characterization in higher-dimensional bipartite systems.
Related Concept Videos
01:03Atomic Nuclei: Nuclear Spin State Overview
1.2K
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...
1.2K
03:06The Pauli Exclusion Principle
53.0K
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:
53.0K
03:25Free Energy Changes for Nonstandard States
11.8K
The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
where R is the gas constant (8.314 J/K·mol), T is the absolute temperature in kelvin, and Q is the reaction quotient. This equation may be used to predict the spontaneity of a process under any given set of conditions.
Reaction Quotient...
where R is the gas constant (8.314 J/K·mol), T is the absolute temperature in kelvin, and Q is the reaction quotient. This equation may be used to predict the spontaneity of a process under any given set of conditions.
Reaction Quotient...
11.8K
04:08The Uncertainty Principle
27.0K
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
27.0K
02:45The Quantum-Mechanical Model of an Atom
51.1K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
51.1K
01:14Atomic Nuclei: Nuclear Spin State Population Distribution
1.3K
Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
1.3K