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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...
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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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Uncertainty: Overview00:59

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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...
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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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.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...

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Uncertainty relation for smooth entropies.

Marco Tomamichel1, Renato Renner

  • 1Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland. marcoto@phys.ethz.ch

Physical Review Letters
|April 8, 2011
PubMed
Summary
This summary is machine-generated.

This study generalizes quantum uncertainty relations using smooth entropies, providing practical bounds for predicting measurement outcomes. This directly ensures the security of quantum key distribution protocols, even with imperfect devices.

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Area of Science:

  • Quantum Information Theory
  • Quantum Cryptography

Background:

  • Uncertainty relations set limits on predicting outcomes of incompatible measurements.
  • Existing relations typically assume classical data, not quantum information.
  • A recent extension considers quantum information but lacks operational relevance.

Purpose of the Study:

  • To generalize existing uncertainty relations using smooth entropies.
  • To establish a practical uncertainty relation with direct applications.
  • To demonstrate the security of quantum key distribution (QKD) protocols.

Main Methods:

  • Formulation of uncertainty relations in terms of smooth entropies.
  • Direct implication of the generalized uncertainty relation for QKD security.
  • Analysis of security under arbitrary deviations from theoretical models.

Main Results:

  • A novel uncertainty relation is formulated using smooth entropies.
  • The relation directly quantifies security for quantum key distribution.
  • Security is proven robust against imperfections in measurement devices.

Conclusions:

  • The generalized uncertainty relation offers practical insights into quantum information processing.
  • It provides a powerful tool for proving security in quantum cryptographic protocols.
  • This work enhances the understanding and application of uncertainty relations in quantum information.