A. Uhlmann, "The `transition probability' in the state space of a #-algebra.," Reports on Mathematical Physics, vol. 9, pp. 273--279, 1976. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
The Trouble with Quantum Bit Commitment - Mayers (1996) (11 citations) (Correct)
....[10] that (1 Gamma BW ) K=2. Therefore, we have BW (1 Gamma 4 Theta 2 Gammaffn ) Furthermore, in [4, 12] it is shown that the minimum of BW over all possible measurement is the fidelity F between ae 0 and ae 1 . So, we have F (1 Gamma 4 Theta 2 Gammaffn ) A theorem due to Uhlmann [6, 11] says that the fidelity between two mixed states ae 0 and ae 1 on a system H is given by F = max jhOE 0 jOE 1 ij 2 where the maximum is taken over the purifications OE 0 and OE 1 of ae 0 and ae 1 respectively. Let OE 0 and OE 1 be two purifications such that jhOE 0 jOE 1 ij 2 = F (1 Gamma ....
A. Uhlmann, "The `transition probability' in the state space of a --algebra", Reports on Mathematical Physics, vol. 9, pp. 273 -- 279, 1976.
Towards a Formal Definition of Security for Quantum Protocols - Graaf (1997) (1 citation) (Correct)
....In particular, using the formula jh 0 j 1 ij = j 0 jj 1 j cos ff and recalling that state vectors are usually normalized, we can define overlap(j 0 i; j 1 i) jh 0 j 1 ij as a measure of distinguishability. The question is: what to do for mixed states The answer was given by Uhlmann [UH76] and simplified by Jozsa [JO94] If ae 0 is the density matrix of a mixed state in the Hilbert space H 1 , then we can always extend the Hilbert space such that ae 0 becomes a pure state in the combined Hilbert space H 1 Omega H 2 . More precisely, we can always find an extension H 2 of H 1 and ....
....leading to the following definition. 3.12 Definition The (generalized) overlap between two density matrices is defined by overlap(ae 0 ; ae 1 ) def = max jh 0 j 1 ij; 3.14) where the maximum is taken over all purifications j 0 i and j 1 i of ae 0 and ae 1 respectively. It can be shown [UH76] [JO94] that overlap(ae 0 ; ae 1 ) Tr q p ae 0 ae 1 p ae 0 ; 3.15) but for dimensions higher than 2 this formula is difficult to evaluate, unless the eigenvalues of ae 0 and ae 1 are known. However, overlap(ae 0 ; ae 1 ) has the nice property 65 that it is multiplicative over ....
UHLMANN, A., "The `transition probability' in the state space of a -algebra", Reports on Mathematical Physics 9 (1976), pp. 273-- 279.
Interaction in Quantum Communication and the.. - Klauck, Nayak.. (2003) (5 citations) (Correct)
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A. Uhlmann, "The `transition probability' in the state space of a #-algebra.," Reports on Mathematical Physics, vol. 9, pp. 273--279, 1976.
Interaction in Quantum Communication - Klauck, Nayak, Ta-Shma, Zuckerman (Correct)
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A. Uhlmann, "The `transition probability' in the state space of a #-algebra.," Reports on Mathematical Physics, vol. 9, pp. 273--279, 1976.
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