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Related Concept Videos

Quantum Numbers02:43

Quantum Numbers

49.9K
It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
49.9K
Titration Calculations: Strong Acid - Strong Base02:28

Titration Calculations: Strong Acid - Strong Base

33.8K
Calculating pH for Titration Solutions: Strong Acid/Strong Base
A titration is carried out for 25.00 mL of 0.100 M HCl (strong acid) with 0.100 M of a strong base NaOH. The pH at different volumes of added base solution can be calculated as follows:
(a) Titrant volume = 0 mL. The solution pH is due to the acid ionization of HCl. Because this is a strong acid, the ionization is complete and the hydronium ion molarity is 0.100 M. The pH of the solution is then:
33.8K
Strong Acid and Base Solutions03:22

Strong Acid and Base Solutions

35.6K
A strong acid is a compound that dissociates completely in an aqueous solution and produces a concentration of hydronium ions equal to the initial concentration of acid. For example, 0.20 M hydrobromic acid will dissociate completely in water and produces 0.20 M of hydronium ions and 0.20 M of bromide ions.
35.6K
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

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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.
57.1K
Titration of a Strong Acid with a Strong Base01:23

Titration of a Strong Acid with a Strong Base

10.5K
During the titration of a strong acid with a strong base, pH calculations are primarily based on the concentration of residual hydronium or hydroxide ions. Initially, a strong acid like hydrochloric acid fully dissociates, creating hydronium and chloride ions, resulting in a low pH. The addition of a strong base like sodium hydroxide alters the concentration of hydronium ions by neutralizing them. As more base is added, the pH gradually increases. At the equivalence point, all hydronium ions...
10.5K
Titration Calculations: Weak Acid - Strong Base03:55

Titration Calculations: Weak Acid - Strong Base

49.2K
Calculating pH for Titration Solutions: Weak Acid/Strong Base
For the titration of 25.00 mL of 0.100 M CH3CO2H with 0.100 M NaOH, the reaction can be represented as:
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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Strong Quantum Nonlocality without Entanglement.

Saronath Halder1, Manik Banik2, Sristy Agrawal3

  • 1Department of Mathematics, Indian Institute of Science Education and Research Berhampur, Transit Campus, Government ITI, Berhampur 760010, Odisha, India.

Physical Review Letters
|February 16, 2019
PubMed
Summary
This summary is machine-generated.

Researchers found locally irreducible quantum states that demonstrate nonlocality without entanglement. These product states, even when prepared separately, exhibit unique nonlocal properties in multiparty systems, challenging previous assumptions.

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Area of Science:

  • Quantum Information Science
  • Quantum Foundations
  • Multiatom Quantum Systems

Background:

  • Quantum nonlocality is typically linked to entangled states violating Bell inequalities.
  • Unentangled systems can also exhibit nonlocal properties, termed 'quantum nonlocality without entanglement' (NWoE).
  • NWoE occurs when product states are locally indistinguishable via local operations and classical communication (LOCC).

Purpose of the Study:

  • To introduce and investigate 'local irreducibility' as a stronger form of NWoE in multiparty quantum systems.
  • To demonstrate the existence of locally irreducible orthogonal product bases.
  • To explore the implications for quantum resource requirements in multiparty measurements.

Main Methods:

  • Definition of local irreducibility for multiparty orthogonal quantum states.
  • Construction of orthogonal product bases in C^d ⊗ C^d ⊗ C^d for d=3 and d=4.
  • Analysis of local indistinguishability and local irreducibility properties.

Main Results:

  • First examples of orthogonal product bases exhibiting local irreducibility across all bipartitions for d=3 and d=4.
  • The d=3 construction achieves the minimum dimension required for such states.
  • Locally irreducible sets are locally indistinguishable, but the converse is not always true.

Conclusions:

  • Locally irreducible product states represent a significant manifestation of quantum nonlocality without entanglement.
  • The existence of these states implies that implementing multiparty separable measurements may necessitate entangled resources across all bipartitions.
  • This work expands the understanding of nonlocality in quantum mechanics, particularly in the context of unentangled systems.