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Related Concept Videos

Entropy Change in Reversible Processes01:10

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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.
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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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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.
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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...
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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...
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Purity-Based Continuity Bounds for von Neumann Entropy.

Junaid Ur Rehman1, Hyundong Shin2

  • 1Department of Electronic Engineering, Kyung Hee University, 1732 Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do, 17104, Korea.

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This summary is machine-generated.

We developed new continuity bounds for quantum qubit entropy using purity differences. These bounds offer tighter estimations than existing methods, aiding in calculating complex information-theoretic quantities.

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Area of Science:

  • Quantum Information Theory
  • Quantum Computing

Background:

  • Continuity bounds are essential for quantifying changes in quantum states.
  • Existing bounds based on trace distance have limitations in precision.
  • Von Neumann entropy is a key measure of quantum information.

Purpose of the Study:

  • To propose novel continuity bounds for the von Neumann entropy of qubits.
  • To establish a new distance measure for quantum states based on purity difference.
  • To demonstrate the improved tightness of these new bounds compared to existing methods.

Main Methods:

  • Developing continuity bounds for von Neumann entropy.
  • Utilizing the difference in purity between two qubits as a distance metric.
  • Comparing the proposed bounds with trace distance-based bounds.

Main Results:

  • Proposed continuity bounds for von Neumann entropy based on purity difference.
  • Demonstrated that these bounds are tighter than existing trace distance-based bounds.
  • Showcased the utility of continuity bounds for hard-to-compute information-theoretic quantities.

Conclusions:

  • Continuity bounds based on purity difference provide a more accurate measure for quantum state comparisons.
  • These novel bounds enhance the analysis of quantum information and entropy.
  • The proposed method offers a valuable tool for quantum information theory research.