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arXiv:1110.5979 · Physics Letters A

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

Lin Zhang, Junde Wu, Shao-Ming Fei

Published Oct 11, 2012• 4 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2012.10.014

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For a given probability distribution 1;:::; m we deter- mine the structure of all such maps dened on a dense subset of density operators which leave the Holevo bound invariant i.e. which satisfy S( m X k=1 k ( k)) m X k=1 kS( ( k)) = S( m X k=1 k k) m X k=1 kS( k) for all possible collections 1;:::; m of density operators. The Holevo bound (or Holevo information) plays a distinguished role in quantum information theory. It provides an upper limit (which can be achieved in certain cases) of the accessible information in a quantum mea- surement, it gives an upper bound on how well we can infer the value of an unknown random variable based on the knowledge of another one. The denition
The mutual information between the sender of a classical message encoded in quantum carriers and a receiver is fundamentally limited by the Holevo quantity. Using strong subadditivity of entropy, we prove that the Holevo quantity is not larger than an exchange entropy. This implies an upper bound for coherent information. Moreover, restricting our attention to classical information, we bound the transmission distance between probability distributions by their entropic distance, which is a concave function of their Hellinger distance.
We show that the recently discovered universal upper bound on the thermal conductance of a single channel comprising particles obeying arbitrary fractional statistics is in fact a consequence of a more general universal upper bound, involving the averaged entropy and energy currents of a single channel connecting heat reservoirs with arbitrary temperatures and chemical potentials. The latter upper bound in turn leads, via Holevo's theorem, to a universal (i.e., statistics-independent) upper bound on the optimum capacity for classical information transmission down a single, wideband quantum channel.