Universal upper bound for the Holevo information induced by a quantum operation

Lin Zhang, Junde Wu, and Shao-Ming Fei

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Submission date: 01. Feb. 2013
published in: Physics Letters / A, 376 (2012) 47/48, p. 3588-3592 
DOI number (of the published article): 10.1016/j.physleta.2012.10.014
Bibtex
Keywords and phrases: quantum state, Quantum operation, von Neumann entropy, Holevo quantity
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Abstract:
Let _A ⊗_B be a bipartite system and ρ_AB a quantum state on _A ⊗_B, ρ_A = Tr_B, ρ_B = Tr_A. Then each quantum operation Φ_B on quantum system _B can induce a quantum ensemble {(p_μ,ρ_A,μ)} on quantum system _A. In this paper, we show that the Holevo quantity χ{(p_μ,ρ_A,μ)} of the quantum ensemble {(p_μ,ρ_A,μ)} can be upper bounded by S(ρ_B). By using the result, we answer partly a conjecture of Fannes, de Melo, Roga and Życzkowski.