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Perturbation theory of von Neumann Entropy
, 902
"... In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the dimension is infinite. We develop the perturbation theory sys ..."
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In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the dimension is infinite. We develop the perturbation theory
von Neumann and the von Neumann Entropy
 in John von Neumann and the Foundations of Quantum Physics
, 2001
"... The highway of the development of entropy is marked by many great names, for example, Clausius, Gibbs, Boltzmann, Szilárd, von Neumann, Shannon, Jaynes, and several others. In this article the emphasis is put on von Neumann and on quantum mechanics. The selection of the subjects reflects the taste ( ..."
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Cited by 8 (2 self)
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The highway of the development of entropy is marked by many great names, for example, Clausius, Gibbs, Boltzmann, Szilárd, von Neumann, Shannon, Jaynes, and several others. In this article the emphasis is put on von Neumann and on quantum mechanics. The selection of the subjects reflects the taste
Distinguishability of states and von Neumann entropy
 Physical Review A
"... Let {ψ1〉,...,ψn〉;p1,...,pn} be an ensemble of pure quantum states. We show that it is possible to increase all of the pairwise overlaps 〈ψiψj〉  i.e. make each constituent pair of the states more parallel (while keeping the prior probabilities the same), in such a way that the von Neumann entrop ..."
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Cited by 18 (5 self)
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entropy S is increased, and dually, make all pairs more orthogonal while decreasing S. We show that this phenomenon cannot occur for ensembles in two dimensions but that it is a feature of almost all ensembles of three states in three dimensions. It is known that the von Neumann entropy characterises
A new inequality for the von Neumann entropy
 Commun. Math. Phys
, 2005
"... Strong subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. Here we prove a new inequality for the von Neumann entropy which we prove is independent of ..."
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Cited by 10 (1 self)
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Strong subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. Here we prove a new inequality for the von Neumann entropy which we prove is independent
The Von Neumann Entropy: A Reply to Shenker
, 2003
"... Shenker has claimed that Von Neumann's argument for identifying the quantum mechanical entropy with the Von Neumann entropy, Sr#ktrr log r, is invalid. Her claim rests on a misunderstanding of the idea of a quantum mechanical pure state. I demonstrate this, and provide a further explanation of ..."
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Shenker has claimed that Von Neumann's argument for identifying the quantum mechanical entropy with the Von Neumann entropy, Sr#ktrr log r, is invalid. Her claim rests on a misunderstanding of the idea of a quantum mechanical pure state. I demonstrate this, and provide a further explanation
The von Neumann entropy asymptotics in multidimensional fermionic systems
, 706
"... We study the von Neumann entropy asymptotics of pure translationinvariant quasifree states of ddimensional fermionic systems. It is shown that the entropic area law is violated by all these states: apart from the trivial cases, the entropy of a cubic subsystem with edge length L cannot grow slower ..."
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We study the von Neumann entropy asymptotics of pure translationinvariant quasifree states of ddimensional fermionic systems. It is shown that the entropic area law is violated by all these states: apart from the trivial cases, the entropy of a cubic subsystem with edge length L cannot grow
KERNEL INTEGRATION USING VON NEUMANN ENTROPY
, 2009
"... Kernel methods provide a computational framework to integrate heterogeneous biological data from different sources for a wide range of learning algorithms by designing a kernel for each different information source and combining them in a unique kernel through simple mathematical operations. We deve ..."
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develop here a novel technique for weighting kernels based on their von Neumann entropy. This permits to assess the kernel quality without using label information, and to integrate kernels before the beginning of the learning process. Moreover, we carry out a comparison with the unweighted kernel
1 The von Neumann Entropy of EPR Spin Correlation for the Relativistic Multiple Pairs
, 712
"... Taking the spinsinglet state in the center of mass frame, the von Neumann entropy in the laboratory frame is calculated from the reduced density matrix obtained by taking the trace over 4momentum after the Lorentz transformation. As the model to discuss the EPR spin correlation, it is supposed tha ..."
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Taking the spinsinglet state in the center of mass frame, the von Neumann entropy in the laboratory frame is calculated from the reduced density matrix obtained by taking the trace over 4momentum after the Lorentz transformation. As the model to discuss the EPR spin correlation, it is supposed
Markov property and Strong additivity of von Neumann entropy for graded quantum systems
, 2006
"... It is easily verified that the quantum Markov property is equivalent to the strong additivity of von Neumann entropy for graded quantum systems. However, the structure of Markov states for graded systems is different from that for tensorproduct systems which have trivial grading. For threecomposed ..."
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Cited by 1 (0 self)
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It is easily verified that the quantum Markov property is equivalent to the strong additivity of von Neumann entropy for graded quantum systems. However, the structure of Markov states for graded systems is different from that for tensorproduct systems which have trivial grading. For three
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