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Quantum Information and Entropy
2007
International Journal of Theoretical Physics
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In view of this, we propose a new measure for the informational entropy of a quantum state that includes information in the pure states and the thermodynamic entropy. ...
Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. ...
We propose a measure for informational entropy and show that it may be seen as the sum of information in the pure states and the thermodynamic entropy. ...
doi:10.1007/s10773-006-9245-6
fatcat:rzvbz6b5cvbvzh4djmgreomyhi
Quantum information entropies and orthogonal polynomials
2001
Journal of Computational and Applied Mathematics
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This is a survey of the present knowledge on the analytical determination of the Shannon information entropies for simple quantum systems: single-particle systems in central potentials. ...
These results have allowed us to ÿnd the position and momentum entropies of the ground and excited states of the physical systems mentioned above. ...
Concluding remarks and open problems The study of the Shannon information entropies of simple quantum systems in both position and momentum spaces requires the analytical determination of entropic integrals ...
doi:10.1016/s0377-0427(00)00633-6
fatcat:ctxl4xkvgrboxhho7acb5kx3w4
Entanglement, quantum entropy and mutual information
2002
Proceedings of the Royal Society A
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The relative entropy of the d-compound and entangled states leads to two different types of entropy for a given quantum state: the von Neumann entropy, which is achieved as the maximum of mutual information ...
The d- and q- information of a quantum noisy channel are respectively defined via the input d- and q- encodings, and the q-capacity of a quantum noiseless channel is found as the logarithm of the dimensionality ...
We also discuss the informational degree of entanglement and entangled quantum mutual entropy and quantum capacity. ...
doi:10.1098/rspa.2001.0867
fatcat:lsvgrpyvtvd2nbwomtxemfufda
Entanglement, quantum entropy and mutual information
[chapter]
2008
Selected Papers of M Ohya
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The relative entropy of the d-compound and entangled states leads to two di¤erent types of entropy for a given quantum state: the von Neumann entropy, which is achieved as the maximum of mutual information ...
The d-and q-information of a quantum noisy channel are respectively de...ned via the input dand q-encodings, and the q-capacity of a quantum noiseless channel is found as the logarithm of the dimensionality ...
We also discuss the informational degree of entanglement and entangled quantum mutual entropy and quantum capacity. ...
doi:10.1142/9789812794208_0008
fatcat:k7ajtmjqrbczdk5z44lohmoprm
QUANTUM MEASUREMENTS, INFORMATION AND ENTROPY PRODUCTION
1999
International Journal of Modern Physics B
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The notion of heat and work in measurements is made manifest in this approach, and the relationship between information entropy and thermodynamic entropy is explored. ...
In order to understand the Landau-Lifshitz conjecture on the relationship between quantum measurements and the thermodynamic second law, we discuss the notion of "diabatic" and "adiabatic" forces exerted ...
In Sec.10, the information entropy is introduced within the context of projective measurements. The relationship between information entropy and thermodynamic entropy is explored. ...
doi:10.1142/s0217979299003076
fatcat:sckigrz4xbfmnbr6ihvpfp3dxa
Quantum Information Dimension and Geometric Entropy
[article]
2024
arXiv
pre-print
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dimension that is the rate of geometric quantum state compression and the dimensional geometric entropy that monitors information stored in quantum states. ...
This opens the door to revisiting foundational questions and issues, such as the nature of quantum entropy, from a geometric perspective. ...
ACKNOWLEDGMENTS F.A. thanks Akram Touil, Martin Savage, Sebastian Deffner, Marina Radulaski, Davide Pastorello, and Davide Girolami for various discussions on the quantum geometric formalism. ...
arXiv:2111.06374v2
fatcat:6prk4hwhajdb3oox7as7tnhg2a
Black hole entropy and quantum information
[article]
2007
arXiv
pre-print
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We review some recently established connections between the mathematics of black hole entropy in string theory and that of multipartite entanglement in quantum information theory. ...
In the case of N=2 black holes and the entanglement of three qubits, the quartic [SL(2)]^3 invariant, Cayley's hyperdeterminant, provides both the black hole entropy and the measure of tripartite entanglement ...
We are grateful to Murat Gunaydin for pointing out the connection between our entanglement diagram, Figure 1 , and the multiplication table of the octonions. ...
arXiv:hep-th/0612036v3
fatcat:2qurasuwhfes5lswcvlvebf5ci
Information and Entropy in Quantum Theory
[article]
2004
arXiv
pre-print
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We then examine the relationship between information and entropy. ...
We look at certain thought experiments based upon the 'delayed choice' and 'quantum eraser' interference experiments, which present a complementarity between information gathered from a quantum measurement ...
In this thesis we will be examining some of these relationships between information, thermodynamic entropy, and quantum theory. ...
arXiv:quant-ph/0411172v1
fatcat:p7coxumaizf4faqiyvlfkm63fm
Mutual Entropy in Quantum Information and Information Genetics
[article]
2004
arXiv
pre-print
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In this paper, first we review the quantum mutual entropy and discuss its uses in quantum information theory, and secondly we show how the classical mutual entropy can be used to analyze genomes, in particular ...
Shannon's important discovery is to give a mathematical expression of the mutual entropy (information), information transmitted from an input system to an output system, by which communication processes ...
Part I Quantum Information 2 Quantum Mutual Entropy The quantum mutual entropy was introduced in [23] for a quantum input and quantum output, namely, for purely quantum channel, and it was generalized ...
arXiv:quant-ph/0406228v1
fatcat:f77lfwurqrfoxlqbg5kavf36rq
Negative Entropy and Information in Quantum Mechanics
1997
Physical Review Letters
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A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement ...
Unlike in classical (Shannon) information theory, quantum (von Neumann) conditional entropies can be negative when considering quantum entangled systems, a fact related to quantum non-separability. ...
The mutual entropy corresponds to the information gained about A by measuring B. It is symmetric, i.e., H͑A:B͒ H͑B:A͒, and can be viewed as the amount of entropy shared by A and B. ...
doi:10.1103/physrevlett.79.5194
fatcat:abjxdumu3zerjcrtnrutcehfdy
Information and Entropy in Quantum Brownian Motion
2008
Journal of statistical physics
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2007 accepted arXiv:0710.1716v2 fatcat:c6a6nm7ocjgqtg5mfyp4x7ai5mOther Versions
We compare the thermodynamic entropy of a quantum Brownian oscillator derived from the partition function of the subsystem with the von Neumann entropy of its reduced density matrix. ...
We give an explanation for these findings and point out that these deviations become important in cases where statements about the information capacity of the subsystem are associated with thermodynamic ...
In quantum information theory it is a commonly used measure of entanglement and decoherence [7] and can be understood as a measure of the amount of information gained by a unique quantum measurement ...
doi:10.1007/s10955-008-9640-x
fatcat:z4uwr3dydnee5lhejseekycj3q
Smooth Entropies and the Quantum Information Spectrum
2009
IEEE Transactions on Information Theory
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2008 pre-print arXiv:0801.0282v1 fatcat:is45jquaq5b4hds2bhl2jh3zbi
To overcome this limitation, two different techniques, the information spectrum method and the smooth entropy framework, have been developed independently. ...
More precisely, the spectral entropy rate can be seen as the asymptotic limit of the smooth entropy. Our results apply to the quantum setting and thus include the classical setting as a special case. ...
In the quantum regime, spectral entropy rates have mostly been used to characterize information sources, communication channels and entanglement manipulations. ...
doi:10.1109/tit.2009.2018340
fatcat:h7x63x7nerbrnpzy3qg3bwb5ue
Instruments and mutual entropies in quantum information
[article]
2004
arXiv
pre-print
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Then, by using mutual entropies on von Neumann algebras and the identification of instruments and channels, many old and new informational inequalities are obtained in a unified manner. ...
In this paper the mathematical formalization is given of the idea that an instrument is a channel which accepts a quantum state as input and produces a probability and an a posteriori state as output. ...
Instruments, mutual entropies, informational bounds. 3.1. The letter states and the measurement. In quantum statistics, the following problem of identification of states is a natural one. ...
arXiv:quant-ph/0412116v1
fatcat:bv4oao5cgffyvmppsu6lfbatti
Information entropy and squeezing of quantum fluctuations
1997
Physical Review A. Atomic, Molecular, and Optical Physics
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Quantum-mechanical entropies of position and momentum operators in a given state are shown to be reasonable and sensitive measures for squeezing of quantum fluctuations. ...
A much more satisfactory measure of quantum uncertainty is given by the information entropy of the given probability distribution. ...
A much more satisfactory measure of quantum uncertainty is given by the information entropy of the given probability distribution. ...
doi:10.1103/physreva.56.2545
fatcat:nj6skt3iqzgjlp2jt5ltommudm
Quantum information and entropy in random matrix ensembles
[article]
2003
arXiv
pre-print
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Measures of quantum chaos and quantum integrability with respect to eigenergies of quantum systems are defined and calculated. ...
The distribution function for the random matrix ensembles is derived from the maximum entropy principle. Information functional is defined as negentropy (opposite of entropy or minus entropy). ...
The information functional I β is the opposite of entropy I β (f X ) = −S β (f X ) = (+k B ln f X (X))f X (X)dX. ( 20 ) Information is negentropy, and entropy is neginformation. ...
arXiv:cond-mat/0306447v2
fatcat:xn5jcxw2xje3fmzsubbl4pzdm4
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