Abstract
| Language | English |
|---|---|
| Pages | 472-489 |
| Number of pages | 18 |
| Journal | Quantum Information & Computation |
| Volume | 12 |
| Issue number | 5-6 |
| Publication status | Published - 1 May 2012 |
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Keywords
- fidelity matrices
- gram matrices
- Holevo quantity
- quantum ensembles
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Matrices of fidelities for ensembles of quantum states and the Holevo quantity. / Fannes, M.; De Melo, F.; Roga, W.; Zyczkowski, K.
In: Quantum Information & Computation, Vol. 12, No. 5-6, 01.05.2012, p. 472-489.Research output: Contribution to journal › Article
TY - JOUR
T1 - Matrices of fidelities for ensembles of quantum states and the Holevo quantity
AU - Fannes, M.
AU - De Melo, F.
AU - Roga, W.
AU - Zyczkowski, K.
PY - 2012/5/1
Y1 - 2012/5/1
N2 - The entropy of the Gram matrix of a joint purification of an ensemble of K mixed states yields an upper bound for the Holevo information χ of the ensemble. In this work we combine geometrical and probabilistic aspects of the ensemble in order to obtain meaningful bounds for χ. This is done by constructing various correlation matrices involving fidelities between every pair of states from the ensemble. For K = 3 quantum states we design a matrix of root fidelities that is positive and the entropy of which is conjectured to upper bound χ. Slightly weaker bounds are established for arbitrary ensembles. Finally, we investigate correlation matrices involving multi-state correlations in relation to the Holevo quantity.
AB - The entropy of the Gram matrix of a joint purification of an ensemble of K mixed states yields an upper bound for the Holevo information χ of the ensemble. In this work we combine geometrical and probabilistic aspects of the ensemble in order to obtain meaningful bounds for χ. This is done by constructing various correlation matrices involving fidelities between every pair of states from the ensemble. For K = 3 quantum states we design a matrix of root fidelities that is positive and the entropy of which is conjectured to upper bound χ. Slightly weaker bounds are established for arbitrary ensembles. Finally, we investigate correlation matrices involving multi-state correlations in relation to the Holevo quantity.
KW - fidelity matrices
KW - gram matrices
KW - Holevo quantity
KW - quantum ensembles
UR - http://www.rintonpress.com/journals/qic/
M3 - Article
VL - 12
SP - 472
EP - 489
JO - Quantum Information & Computation
T2 - Quantum Information & Computation
JF - Quantum Information & Computation
IS - 5-6
ER -