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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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One-parameter class of uncertainty relations based on entropy power.
Petr Jizba1,2, Yue Ma3, Anthony Hayes4
1FNSPE, Czech Technical University in Prague, Břehová 7, 115 19 Praha 1, Czech Republic.
Physical Review. E
|July 15, 2016
Summary
We introduce a new class of uncertainty relations using entropy power, applicable to conjugate observables in infinite-dimensional spaces. This framework reveals higher-order statistics and aids in characterizing information distribution functions.
Area of Science:
- Quantum Information Theory
- Mathematical Physics
Background:
- Uncertainty relations are fundamental in quantum mechanics, quantifying the inherent limits on the precision of simultaneously measured conjugate observables.
- Existing uncertainty relations often focus on second-order statistics, limiting the full characterization of quantum states.
Purpose of the Study:
- To derive a generalized class of information-theoretic uncertainty relations for conjugate observables in infinite-dimensional Hilbert spaces.
- To extend uncertainty relations beyond second-order statistics using the concept of entropy power.
- To provide a method for characterizing information distribution functions through entropy power measurements.
Main Methods:
- Utilized the concept of entropy power to formulate a one-parameter class of uncertainty relations.
- Applied the derived relations to infinite-dimensional Hilbert spaces.
- Investigated higher-order statistics of information distributions.
Main Results:
- Derived a one-parameter family of information-theoretic uncertainty relations.
- Established a connection between entropy powers and the shape of information-distribution functions.
- Demonstrated the framework's applicability to specific quantum states, including superpositions of vacuum and squeezed states, and Cauchy-type heavy-tailed wave functions.
Conclusions:
- The proposed class of uncertainty relations offers a more comprehensive understanding of quantum uncertainty.
- Entropy power serves as a powerful tool for characterizing information distributions in quantum systems.
- The framework has practical implications for analyzing complex quantum states and their associated uncertainties.
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