An entropy inequality

@article{Hellmund2008AnEI,
  title={An entropy inequality},
  author={M. Hellmund and A. Uhlmann},
  journal={Quantum Information & Computation},
  year={2008},
  volume={9},
  pages={622-627}
}
Let S(ρ) = -Tr(ρ log ρ) be the von Neumann entropy of an N-dimensional quantum state ρ and e2(ρ) the second elementary symmetric polynomial of the eigenvalues of ρ. We prove the inequality S(ρ)≤c(N)√e2(ρ) where c(N) = log(N) √2N/N-1. This generalizes an inequality given by Fuchs and Graaf [1] for the case of one qubit, i.e., N = 2. Equality is achieved if and only if ρ is either a pure or the maximally mixed state. This inequality delivers new bounds for quantities of interest in quantum… Expand
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References

SHOWING 1-10 OF 15 REFERENCES
Universal state inversion and concurrence in arbitrary dimensions
Cryptographic Distinguishability Measures for Quantum-Mechanical States
Mixed-state entanglement and quantum error correction.
Entanglement of formation and concurrence
  • W. Wootters
  • Computer Science, Mathematics
  • Quantum Inf. Comput.
  • 2001
Convex Optimization
Physical Review A 54 , 3824 ( 1996 ) , quant - ph / 9604024 . [ 5 ] W . K . Wootters
  • Convex Optimization
  • 2004
Physical Review A 69
  • 032304
  • 2004
Towards a geometrical interpretation of quantuminformation compression
  • Physical Review A 69(3):032304,
  • 2004
Phys
  • Rev. A 64, 042315
  • 2001
...
1
2
...