Cauchy Inequality and Uncertainty Relations for Mixed States

This paper is the continuation of a study into the information paradox problem started by the author in his earlier works. As before, the key instrument is a deformed density matrix in quantum mechanics of the early universe. It is assumed that the latter represents quantum mechanics with fundamental length. It is demonstrated that the obtained results agree well with the canonical viewpoint that in the processes involving black holes pure states go to the mixed ones in the assumption that all measurements are performed by the observer in a well-known quantum mechanics. Also it is shown that high entropy for Planck's remnants of black holes appearing in the assumption of the generalized uncertainty relations may be explained within the scope of the density matrix entropy introduced by the author previously. It is noted that the suggested paradigm is consistent with the holographic principle. Because of this, a conjecture is made about the possibility for obtaining the generalized uncertainty relations from the covariant entropy bound at high energies in the same way as Bousso has derived Heisenberg's uncertainty principle for the flat space.

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Stronger uncertainty relations of mixed states

Quantum Information Processing ◽

10.1007/s11128-020-02761-y ◽

2020 ◽

Vol 19 (8) ◽

Author(s):

Yajing Fan ◽

Huaixin Cao ◽

Liang Chen ◽

Huixian Meng

Keyword(s):

Uncertainty Relations ◽

Mixed States

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Sum uncertainty relations for mixed states

International Journal of Quantum Information ◽

10.1142/s0219749917500307 ◽

2017 ◽

Vol 15 (04) ◽

pp. 1750030

Author(s):

Kan He ◽

Dahong Wei ◽

Li Wang

Keyword(s):

Standard Deviation ◽

Uncertainty Relation ◽

Uncertainty Relations ◽

Mathematical Approach ◽

Mixed States ◽

Pure States

In this paper, we extend existing variance-based sum uncertainty relations for pure states to those for mixed states by a mathematical approach. Furthermore, we show that the monotonicity of the standard deviation of observables induces a variance-based sum uncertainty relation. Finally, the multiobservable case is also discussed.

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Improvement of uncertainty relations for mixed states

Journal of Mathematical Physics ◽

10.1063/1.1876874 ◽

2005 ◽

Vol 46 (4) ◽

pp. 042109 ◽

Cited By ~ 9

Author(s):

Yong Moon Park

Keyword(s):

Uncertainty Relations ◽

Mixed States

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The Classification of Two-Particle Spin States and BellCHSH Inequalities for Mixed States

Acta Physica Hungarica B) Quantum Electronics ◽

10.1556/aph.20.2004.1-2.32 ◽

2004 ◽

Vol 20 (1-2) ◽

pp. 157-160

Author(s):

V.I. Man'ko ◽

V.A. Andreev

Keyword(s):

Spin States ◽

Mixed States ◽

Particle Spin ◽

Chsh Inequalities

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The Uncertainty Principle Derived by The Finite Transmission Speed of Light and Information

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v3i3.2059 ◽

2014 ◽

Vol 3 (3) ◽

pp. 257-266 ◽

Cited By ~ 1

Author(s):

Piero Chiarelli

Keyword(s):

Uncertainty Principle ◽

Large Scale ◽

Uncertainty Relations ◽

Speed Of Light ◽

Energy Fluctuation ◽

Hydrodynamic Analogy ◽

Non Local ◽

Minimum Uncertainty ◽

Quantum Hydrodynamic ◽

Transmission Speed

This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle is fully compatible with the postulate of finite transmission speed of light and information. The theory shows that the measurement process performed in the large scale classical limit in presence of background noise, cannot have a duration smaller than the time need to the light to travel the distance up to which the quantum non-local interaction extend itself. The product of the minimum measuring time multiplied by the variance of energy fluctuation due to presence of stochastic noise shows to lead to the minimum uncertainty principle. The paper also shows that the uncertainty relations can be also derived if applied to the indetermination of position and momentum of a particle of mass m in a quantum fluctuating environment.

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