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Related Concept Videos

Gauss's Law01:07

Gauss's Law

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If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
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Gauss's Law: Problem-Solving01:10

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Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...
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Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...
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Gauss's Law in Dielectrics01:17

Gauss's Law in Dielectrics

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Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...
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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Gaussian Intrinsic Entanglement.

Ladislav Mišta1, Richard Tatham1

  • 1Department of Optics, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic.

Physical Review Letters
|December 24, 2016
PubMed
Summary
This summary is machine-generated.

We introduce Gaussian intrinsic entanglement (GIE), a new measure for quantum entanglement in Gaussian systems. GIE is computable, physically meaningful, and linked to secure key distribution, offering a practical entanglement quantification method.

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Area of Science:

  • Quantum Information Science
  • Quantum Optics
  • Quantum Computing

Background:

  • Quantifying entanglement is crucial for understanding quantum systems and developing quantum technologies.
  • Existing entanglement measures can be difficult to compute or lack clear operational meaning.
  • Gaussian states are fundamental in quantum optics and continuous-variable quantum information processing.

Purpose of the Study:

  • To introduce a novel, cryptographically motivated quantifier for entanglement in bipartite Gaussian systems, termed Gaussian intrinsic entanglement (GIE).
  • To establish the properties of GIE, including its vanishing on separable states and monotonicity under relevant quantum operations.
  • To explore the relationship between GIE and other entanglement measures in specific quantum states.

Main Methods:

  • Defined GIE as the optimized mutual information of a Gaussian distribution conditioned on measurements of a purifying subsystem.
  • Analyzed the behavior of GIE under Gaussian local trace-preserving operations and classical communication.
  • Computed GIE for various pure and mixed two-mode Gaussian states.

Main Results:

  • Demonstrated that GIE is zero if and only if the quantum state is separable.
  • Proved that GIE is monotonic under Gaussian local operations and classical communication.
  • Found that GIE is equal to Gaussian Rényi-2 entanglement for all pure and several important classes of mixed two-mode Gaussian states.

Conclusions:

  • GIE provides a computable and physically meaningful measure of entanglement for Gaussian systems.
  • Its operational link to secret-key agreement protocols highlights its practical relevance.
  • GIE offers a valuable compromise between calculability and physical interpretation in entanglement quantification.