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Keywords
(5)
Maximum Principle
Mutual Information
Quantum Measurement
unitarily invariant norm
Upper and Lower Bounds
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Bounds on Shannon distinguishability in terms of partitioned measures
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Bounds on Shannon distinguishability in terms of partitioned measures
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Citations: 3
)
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Alexey E. Rastegin
A family of quantum measures like the Shannon distinguishability is presented. These measures are defined over the two classes of POVM measurements and related to separate parts in the expression for mutual information. Changes of Ky Fan’s norms and the partitioned trace distances under the operation of partial trace are discussed.
Upper and lower bounds
on the introduced quantities are obtained in terms of partitioned trace distances and Uhlmann’s partial fidelities. These inequalities provide a kind of generalization of the well-known bounds on the Shannon distinguishability. The notion of cryptographic exponential indistinguishability for quantum states is revisited. When exponentially fast convergence is required, all the metrics induced by unitarily invariant norms are shown to be equivalent.
Journal:
Quantum Information Processing - QUANTUM INF PROCESS
, vol. 10, no. 1, pp. 123-138, 2011
DOI:
10.1007/s11128-010-0184-z
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Citation Context
(2)
...Some results have also been obtained for Uhlmann’s partial fidelities [30] and the Ky Fan norms [
33
]...
Alexey E. Rastegin
.
Some General Properties of Unified Entropies
...For instance, all the metrics induced by unitarily invariant norms are tantamount in posing the cryptographic exponential indistinguishability [
18
]...
Alexey E. Rastegin
.
Continuity and Stability of Partial Entropic Sums
References
(27)
On “partial” fidelities
(
Citations: 8
)
Armin Uhlmann
Journal:
Reports on Mathematical Physics - REP MATH PHYS
, vol. 45, no. 3, pp. 407-418, 2000
The “transition probability” in the state space of a *-algebra
(
Citations: 142
)
A. Uhlmann
Journal:
Reports on Mathematical Physics - REP MATH PHYS
, vol. 9, no. 2, pp. 273-279, 1976
Quantum-state disturbance versus information gain: Uncertainty relations for quantum information
(
Citations: 46
)
Christopher A. Fuchs
,
Asher Peres
Journal:
Physical Review A - PHYS REV A
, vol. 53, no. 4, pp. 2038-2045, 1996
Cryptographic Distinguishability Measures for Quantum-Mechanical States
(
Citations: 71
)
Christopher A. Fuchs
,
Jeroen Van De Graaf
Journal:
IEEE Transactions on Information Theory - TIT
, vol. 45, no. 4, pp. 1216-1227, 1999
Security of Quantum Key Distribution against All Collective Attacks
(
Citations: 23
)
Eli Biham
,
Michel Boyer
,
Gilles Brassard
,
Jeroen Van De Graaf
,
Tal Mor
Journal:
Algorithmica
, vol. 34, no. 4, pp. 372-388, 2002
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Citations
(3)
Some General Properties of Unified Entropies
Alexey E. Rastegin
Published in 2011.
Continuity and Stability of Partial Entropic Sums
(
Citations: 2
)
Alexey E. Rastegin
Published in 2010.
Some general properties of unified entropies
Alexey E. Rastegin
Published in 2010.