Uhlmann, A.: Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory, Commun. Math. Phys. 54, 123 (1977).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....p i # i , Holevo s chi quantity equals #(E) S(#) p i S(# i ) Note that the # quantity depends not only on #, but also on the specific pairs (# i , p i ) The following monotonicity property of Lindblad and Uhlmann will be very useful later on. Fact 20 (Lindblad Uhlmann monotonicity [68, 101]) Let i , p i ) be an ensemble, and S a completely positive, trace preserving mapping. For every such and S, it holds that: #(S(E) #(E) where S(E) is the transformed ensemble (S(# i ) p i ) 7.5. Symmetric Subspaces 71 The entropy of finite systems is robust against small ....

Armin Uhlmann. Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory. Reviews in Mathematical Physics, 54:21--32, 1977.

....of the most general form of the pure state lower bound. M. Horodecki [11] has independently derived the lower bound, 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] We were also aware of the possibility of such a derivation of the lower bound. Indeed, we originally informally formulated the argument as conditional upon giving the ....

A. Uhlmann, \Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory," Communications in Mathematical Physics, vol. 54, pp. 21-32, 1977.

....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 matrix of a source which the channel can send ....

A. Uhlmann, "Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory," Communications in Mathematical Physics, vol. 54, pp. 21--32, 1977.

....chi quantity equals (E) S(ae) Gamma X i p i S(ae i ) Note that the quantity depends not only on ae, but also on the specific pairs (p i ; ae i ) The following monotonicity property of Lindblad and Uhlmann will be very useful later in the paper. Theorem 3 Lindblad Uhlmann monotonicity [13, 19]: Let E = f(ae i ; p i )g be an ensemble, and a completely positive, trace preserving mapping. For every such E and , it holds that: E) E) where (E) is the transformed ensemble f( ae i ) p i )g. The entropy of finite systems is robust against small changes. This continuity of S over ....

Armin Uhlmann, "Relative Entropy and the WignerYanase -Dyson-Lieb Concavity in an Interpolation Theory", Reviews in Mathematical Physics, Volume 54, pp. 21--32 (1977)

....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 ....

A. Uhlmann, "Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory," Communications in Mathematical Physics, vol. 54, pp. 21--32, 1977.

....quantum measurement theory. The first published proof appeared in [Holevo 1973] It is worthwhile to mention also that this bound is closely related to the fundamental property of decrease of quantum relative entropy under completely positive maps developed in [Lindblad 1973 1975] and in [Uhlmann 1977] (see [Yuen and Ozawa 1993] for history and some generalizations of the entropy bound) In the same way we can consider the product channel in the tensor product Hilbert space H Omega n = H Omega : Omega H with the input alphabet A n consisting of words w = i 1 ; i n ) of length n, ....

A. Uhlmann, "Relative entropy and the Wigner-YanaseDyson -Lieb concavity in an interpolation theory," Commun. Math. Phys., vol. 54, pp. 21-32 1977.

.... i.e. a property of whole types of input sequences, not just individual sequences (see Csisz ar, Korner [4] Also, it may be interesting to note that the proof of the converse did not use the Holevo bound [6] which usually is derived from Uhlmann s monotonocity of the quantum I divergence [17], which in turn is a consequence of a deep concavity result, the Wigner Yanase Dyson conjecture, first proved by Lieb [12] Thus in turn we get a new proof of the Holevo bound. Finally some general remarks: note that our proof of the coding theorem follows the original idea of Feinstein [5] ....

A. Uhlmann,"Relative Entropy and the Wigner--Yanase--Dyson--Lieb Concavity in an Interpolation Theory", Comm. Math. Phys. 54 (1977), 21--32

.... Gamma ffi 2 Now generally for two states ae; oe and complementary positive operators S; D (i.e. S D = 1) one has Tr (aeS) log Tr (aeS) Tr (oeS) Tr (aeD) log Tr (aeD) Tr (oeD) D(aekoe) January 12, 1999 DRAFT 12 This follows immediately from Uhlmann s monotonicity of quantum I divergence [9], applied to the completely positive, trace preserving map L(H) Gamma C 2 ff 7 Gamma Tr (ffS)e 1 Tr (ffD)e 2 From this we get by elementary operations Tr (oeS) exp Gamma D(aekoe) h(Tr (aeS) Tr (aeS) Applying this to ae = V f(m) oe = W f(m) and S = Sm , D = Dm we find Tr (W ....

A. Uhlmann,"Relative Entropy and the Wigner--Yanase--Dyson--Lieb Concavity in an Interpolation Theory", Comm. Math. Phys. 54 (1977), 21--32

.... Gamma ffi n k 1 1 4 So by Markov s inequality there is a subset C ae P n with P n (C) 1 Gamma 2 p and 8 n 2 C k n Gamma ffi n k 1 p Now form the state oe = P n 2P n P n ( n ) n , then by Uhlmann s monotonocity of the quantum I divergence [12] 8 n 2 P n D( n koe) D(ffi n kffi oe) Averaging we obtain X n 2P n P n ( n )D( n koe) X n 2P n P n ( n )D(ffi n kffi oe) February 12, 1999 DRAFT 8 Now it is straightforward to calculate the l.h.s. of this to H(oe) Gamma P n ....

A. Uhlmann,"Relative Entropy and the Wigner--Yanase--Dyson--Lieb Concavity in an Interpolation Theory", Comm. Math. Phys. 54 (1977), 21--32

No context found.

Uhlmann, A.: Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory, Commun. Math. Phys. 54, 123 (1977).

No context found.

A. Uhlmann, Relative Entropy and the Wigner-Yanase-Dyson-Lieb Concavity in an Interpolation Theory, Commun. Math. Phys. 54, 21-32 (1977) 14

No context found.

A. Uhlmann, Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory, Commun. Math. Phys. 54, 21--32 (1977).

No context found.

A. Uhlmann, \Relative Entropy and the Wigner-Yanase-Dyson-Lieb Concavity in an Interpolation Theory", Commun. Math. Phys. 54, 21 - 32 (1977).

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC