A.S. Holevo and R.F.Werner: "Evaluating capacities of Bosonic Gaussian channels", quant-ph/9912067, to appear in Phys.Rev. A Home/Search Document Not in Database Summary Related Articles Check |
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Radon-Nikodym Derivatives of Quantum Operations - Raginsky (2003) (Correct)
....2. 3 The norm of complete boundedness In many information theoretic studies of noisy quantum channels one needs a quantitative measure of the noisiness of a channel; this is, in fact, a natural departure point for various de nitions of information carrying capacities of quantum channels [15, 18, 36]. A good candidate for such a measure is the norm kT id k , where the question mark refers to the fact that we have not yet speci ed a suitable norm. The choice of the proper norm turns out to be a tricky matter [18] Let A and B be C algebras, and consider a linear map : A B. We cannot ....
....we will always write k k cb , even when working with . In fact, the norm (11) was introduced by Kitaev [19] under the name diamond norm (Kitaev used the notation k k ) The equivalence of the diamond norm and the CB norm has been alluded to in the literature on quantum information theory [15] but, to the best of our knowledge, no proof of the equivalence was ever presented. The duality relation between : B(H ) B(K ) and : T (K ) T (H ) implies that we can also write id n k 1 ; where k k 1 = supfk (A)k 1 j A 2 T (K ) kAk 1 1g and kAk 1 = Tr jAj Tr A is ....
A.S. Holevo and R.F. Werner, \Evaluating capacities of bosonic Gaussian channels," Phys. Rev. A 63, 032312 (2001).
Quantum Information Theory - an Invitation - Werner (2001) (2 citations) Self-citation (Werner) (Correct)
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A.S. Holevo and R.F.Werner: "Evaluating capacities of Bosonic Gaussian channels", quant-ph/9912067, to appear in Phys.Rev. A
Quantum Information Theory - an Invitation - Werner (2001) (2 citations) Self-citation (Werner) (Correct)
....For example, a Gaussian channel (this is a special type of infinite dimensional channel) has infinite capacity for classical information, no matter how much noise we add. But its quantum capacity drops to zero, if we add more classical noise than specified by the Heisenberg uncertainty relations [16]. A standard technique for stabilizing classical information is redundancy:just send a classical bit three times, and decide at the end by majority vote which bit to take. It is easy to see that this reduces the probability of error from order # to order # 2 . But quantum mechanically this ....
....(T# # ) 6.31) in analogy to (6.21) So far there are some good heuristic arguments [27, 28] in that direction, but a full proof remains one of the main challenges in the field. An interesting upper bound on C q (T ) can be written in terms of the transpose operation # on the output system [16]: one has C q (T ) # log 2 ##T# cb . 6.32) Hence if #T happens to be completely positive (as for any channel with an intermediate classical state) this map is a channel, hence has cb norm 1, and C q (T ) 0. This criterion can also be used to show that whenever there is su#ciently high ....
A.S. Holevo and R.F.Werner: "Evaluating capacities of Bosonic Gaussian channels", quant-ph/9912067, to appear in Phys.Rev. A
Dynamical Aspects of Information Storage in Quantum-Mechanical.. - Raginsky (2002) (Correct)
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A.S. Holevo and R.F. Werner, \Evaluating capacities of bosonic Gaussian channels," Phys. Rev. A 63, 032312 (2001).
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