| G. Lindblad, "Entropy, information, and quantum measurements," Communications in Mathematical Physics, vol. 33, pp. 305--322, 1973. |
....inequality: I c (ae; E) I(ae; DE) 7.14) This was first shown in [17] using strong subadditivity. It is also easily shown from the monotonicity of relative entropy under trace preserving operations (as also noted by Allaverdyan and Saakian [52] The latter was established by Lindblad [53], and a more general version found by Uhlmann [54] 7.1.3 An upper bound We wish to establish an upper bound, given by a coherent information, on the rate at which entanglement may be transmitted through a quantum channel. The rate will be given by the limiting entropy of the n block density ....
G. Lindblad, "Entropy, information, and quantum measurements," Communications in Mathematical Physics, vol. 33, pp. 305--322, 1973.
....that the compression rate q must satisfy q (E) M. Horodecki [11] has independently derived the lower bound of Theorem 17, using the nonincrease of the Holevo quantity under completely positive maps. This nonincrease is an easy consequence of the monotonicity of relative entropy under such maps [24, 25], and therefore of Lieb s fundamental concavity theorem [26] A good treatment of all of these is to be found in [27] A special case of Theorem 17 is the lower bound of S(ae) qubits per source signal on the rate of compression of ensembles of pure states. This lower bound was established for ....
G. Lindblad, "Entropy, information, and quantum measurements," Communications in Mathematical Physics, vol. 33, pp. 305--322, 1973.
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