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Related Concept Videos

Entropy02:39

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
Entropy01:18

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Continuous Charge Distributions01:17

Continuous Charge Distributions

Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...
The Entropy as a State Function01:14

The Entropy as a State Function

Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
Calculation of First-Law Quantities II01:24

Calculation of First-Law Quantities II

The first law of thermodynamics establishes that the change in internal energy of a system is given by ΔU = q + w, where q is the heat exchanged, and w is the work performed. For a perfect gas, both internal energy (U) and enthalpy (H) depend solely on temperature. Consequently, for any change of state, whether reversible or irreversible, the internal energy change is determined by integrating the heat capacity at constant volume, and the enthalpy change by integrating the heat capacity at...

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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Quantification and scaling of multipartite entanglement in continuous variable systems.

Gerardo Adesso1, Alessio Serafini, Fabrizio Illuminati

  • 1Dipartimento di Fisica E. R. Caianiello, Università di Salerno, Via S. Allende, 84081 Baronissi (SA), Italy.

Physical Review Letters
|December 17, 2004
PubMed
Summary

We developed a method to measure multipartite entanglement in Gaussian states. This technique simplifies complex systems to equivalent two-mode states for easier analysis and experimental verification.

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Area of Science:

  • Quantum Information Science
  • Quantum Optics
  • Condensed Matter Physics

Background:

  • Multipartite entanglement is crucial for quantum information processing.
  • Quantifying multipartite entanglement in continuous variable systems is challenging.
  • Gaussian states are fundamental in quantum optics and quantum information.

Purpose of the Study:

  • To develop a theoretical method for determining multipartite entanglement in Gaussian states.
  • To simplify the quantification of multipartite entanglement in symmetric Gaussian states.
  • To provide a pathway for reliable experimental estimation of multipartite entanglement.

Main Methods:

  • Theoretical analysis of multipartite entanglement in multimode Gaussian states.
  • Derivation of the exact expression for logarithmic negativity.
  • Reduction of multipartite entanglement to an equivalent two-mode Gaussian state problem.

Main Results:

  • An exact expression for logarithmic negativity in symmetric Gaussian states was determined.
  • Multipartite entanglement was shown to be equivalent to two-mode entanglement.
  • The scaling of multipartite entanglement with the number of modes was demonstrated.

Conclusions:

  • The proposed method offers an exact and simplified approach to quantify multipartite entanglement.
  • The equivalence to two-mode states facilitates experimental verification.
  • Direct measurements of global and local purities enable reliable entanglement estimation.