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(3)
Density Operator
Quantum Information Processing
Singular Value
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Partitioned trace distances
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Partitioned trace distances
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Citations: 6
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Alexey E. Rastegin
New quantum distance is introduced as a half-sum of several singular values of difference between two density operators. This is, up to factor, the metric induced by so-called Ky Fan norm. The partitioned trace distances enjoy similar properties to the standard trace distance, including the unitary invariance, the strong convexity and the close relations to the classical distances. The partitioned distances cannot increase under quantum operations of certain kind including bistochastic maps. All the basic properties are re-formulated as majorization relations. Possible applications to
quantum information processing
are briefly discussed.
Journal:
Quantum Information Processing - QUANTUM INF PROCESS
, vol. 9, no. 1, pp. 61-73, 2010
DOI:
10.1007/s11128-009-0128-7
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Citation Context
(2)
...The k-th partitioned trace distance between ρ0 and ρ1 is expressed by [
20
]...
...The partitioned distances enjoy many properties of the trace norm distance, including the unitary invariance and the strong convexity [
20
]...
...where the maximum is actually reached by the one-rank PVM [
20
]...
...and A = B − C. Since A is also Hermitian, there holds � A� (k) = Tr (P − Q) A for some mutually orthogonal projectors P and Q that satisfy rank(P + Q) ≤ k [
20
]...
Alexey E. Rastegin
.
Bounds on Shannon distinguishability in terms of partitioned measures
...So we will examine differences between kth partial sums of Tsallis entropy of two m-dimensional probability vectors p and q. It is natural to estimate this difference in terms of partitioned classical distances G(k)(p −q) .T hese distances and their quantum extensions via Ky Fan’s norms were introduced in [
17
]...
...Remark 10. The inequalities (37) and (43) are expressed in terms of the distances � ρ − � � (k) that enjoy similar properties to the standard trace distance [
17
]...
Alexey E. Rastegin
.
Continuity and Stability of Partial Entropic Sums
References
(34)
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
Separable States Are More Disordered Globally than Locally
(
Citations: 39
)
M. A. Nielsen
,
J. Kempe
Journal:
Physical Review Letters - PHYS REV LETT
, vol. 86, no. 22, pp. 5184-5187, 2001
Relative error of state-dependent cloning
(
Citations: 4
)
A. E. Rastegin
Journal:
Physical Review A - PHYS REV A
, vol. 66, no. 4, 2002
How to mix a density matrix
(
Citations: 2
)
Ingemar Bengtsson
,
Asa Ericsson
Journal:
Physical Review A - PHYS REV A
, vol. 67, no. 1, 2003
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Citations
(6)
Bounds on Shannon distinguishability in terms of partitioned measures
(
Citations: 3
)
Alexey E. Rastegin
Journal:
Quantum Information Processing - QUANTUM INF PROCESS
, vol. 10, no. 1, pp. 123-138, 2011
Metrics On Unitary Matrices, Bounds On Eigenvalues Of Product Of Unitary Matrices, And Measures Of Non-commutativity Between Two Unitary Matrices
(
Citations: 2
)
H. F. Chau
Published in 2010.
Continuity and Stability of Partial Entropic Sums
(
Citations: 2
)
Alexey E. Rastegin
Published in 2010.
A Shrinking Factor for Unitarily Invariant Norms under a Completely Positive Map
Alexey E. Rastegin
Published in 2010.
Some properties of partial fidelities
(
Citations: 5
)
Alexey E. Rastegin
Published in 2009.