Timeline for How to estimate the quantum fidelity between two given states
Current License: CC BY-SA 3.0
13 events
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| Apr 21, 2013 at 5:38 | comment | added | Lin Zhang | @Peter Shor: There is no closed formulae for the mentioned quantities above. It is left open. | |
| Apr 21, 2013 at 5:32 | comment | added | Lin Zhang | The fidelity deals with the similarity between two states. However, the relative entropy or the trace-distance deals with the dissimilarity. Since the difficulty exist in estimating the relative entropy, I turn to another way---estimating the fideility to do this problem. | |
| Apr 21, 2013 at 5:27 | comment | added | Lin Zhang | Along with the above line, I proposed an approach---self-commutator--- to this problems. The following link can be visited: arxiv.org/abs/1212.5023v2 arxiv.org/abs/1010.1750 arxiv.org/abs/1210.3181 arxiv.org/abs/1210.4720v3 | |
| Apr 21, 2013 at 5:18 | comment | added | Lin Zhang | In fact, I mean all the quantities above are known. On the one hand, I am interested in a univeral lower bound of $S(\rho||\sigma) - S(\Phi(\rho)||\Phi(\sigma))$. Since if the lower bound is obtained, we can use it to lower bounding the quantum conditional mutual information, defined by $$ I(A:C|B)_\rho := S(\rho_{AB}) + S(\rho_{BC}) - S(\rho_{ABC}) - S(\rho_B). $$ That is because the conditional mutual information can be represented by the difference of two relative entropy. On the other hand, I would like to consider the perturbation of Markov chain states, i.e. $I(A:C|B)_\rho =0$ | |
| Apr 19, 2013 at 21:05 | comment | added | Peter Shor | Aren't there exact formulas for all the quantities above? Why do we need any estimation? | |
| Apr 19, 2013 at 7:51 | history | edited | Lin Zhang | CC BY-SA 3.0 |
The title is changed.
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| Apr 15, 2013 at 1:40 | comment | added | Lin Zhang | I find a work [Koenraad M.R. Audenaert, On the asymmetry of the relative entropy, arXiv:1304.0409], deal with the amount of asymmetry by providing a sharp upper bound in terms of two parameters the trace norm distance between the two states, and the smallest of the smallest eigenvalues of both states. This amounts to give the estimate of the following quantity: $$ |S(\rho||\Phi^\dagger_\sigma\circ\Phi(\rho)) - S(\Phi^\dagger_\sigma\circ\Phi(\rho)) ||\rho)|. $$ | |
| Apr 13, 2013 at 23:55 | comment | added | Lin Zhang | The resolution of this problem can give a good estimate of conditional mutual information. | |
| Apr 13, 2013 at 23:48 | history | edited | Lin Zhang | CC BY-SA 3.0 |
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| Apr 11, 2013 at 7:20 | history | edited | Lin Zhang | CC BY-SA 3.0 |
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| Apr 11, 2013 at 7:05 | history | edited | Lin Zhang | CC BY-SA 3.0 |
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| Apr 11, 2013 at 6:59 | history | edited | Lin Zhang | CC BY-SA 3.0 |
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| Apr 11, 2013 at 6:52 | history | asked | Lin Zhang | CC BY-SA 3.0 |