Chain rules for quantum Renyi entropies
| Authors | |
|---|---|
| Year of publication | 2015 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Mathematical Physics |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1063/1.4907981 |
| Field | Theoretical physics |
| Keywords | quantum information; renyi entropy |
| Description | We present chain rules for a new definition of the quantum Renyi conditional entropy sometimes called the "sandwiched" Renyi conditional entropy. More precisely, we prove analogues of the equation H(AB|C) = H(A|BC) + H(B|C), which holds as an identity for the von Neumann conditional entropy. In the case of the Rnyi entropy, this relation no longer holds as an equality but survives as an inequality of the form H-alpha(AB|C) > H-beta(A|BC) + H-gamma(B|C), where the parameters alpha, beta, gamma obey the relation alpha/alpha-1 = beta/beta-1 + gamma/gamma-1 and (alpha - 1)(beta - 1)(gamma - 1) > 1; if (alpha - 1)(beta - 1)(gamma - 1) < 1, the direction of the inequality is reversed. |
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