One-to-one parametrization of quantum channels

Fujiwara, Akio; Algoet, P.

doi:10.1103/physreva.59.3290

Cited by 143 publications

(217 citation statements)

References 3 publications

Supporting

Mentioning

213

Contrasting

Order By: Relevance

“…As was shown in [11] (and also in [1]), the allowed diagonal entries of Φ in (54) lie in the tetrahedron with corners at the points (1, 1, 1), (1, −1, −1), (−1, −1, 1), (−1, 1, −1…”

Section: Proof Of Theoremmentioning

confidence: 99%

Additivity for unital qubit channels

King¹

2002

Journal of Mathematical Physics

181

231

View full text Add to dashboard Cite

Additivity of the Holevo capacity is proved for product channels, under the condition that one of the channels is a unital qubit channel, with the other completely arbitrary. As a byproduct this proves that the Holevo bound is the ultimate information capacity of such qubit channels (assuming no prior entanglement between sender and receiver). Additivity of minimal entropy and multiplicativity of p-norms are also proved under the same assumptions. The proof relies on a new bound for the p-norm of an output state from the phase-damping channel.

show abstract

Section: Proof Of Theoremmentioning

confidence: 99%

Additivity for unital qubit channels

King¹

2002

Journal of Mathematical Physics

181

231

View full text Add to dashboard Cite

show abstract

“…Obviously, this does neither change the determinant, nor complete positivity. For the latter it is necessary that λ is contained in a tetrahedron spanned by the four corners of the unit cube with λ 1 λ 2 λ 3 = 1 [23,24]. Fortunately, all these points can indeed be reached by unital channels (v = 0) for which this criterion becomes also sufficient for complete positivity.…”

Section: Definition 8 (Divisibility) Consider the Set T ∈ {T T + } mentioning

confidence: 99%

“…Expressing complete positivity in terms of v and λ is rather involved and discussed in detail in [23][24][25]. A necessary condition for complete positivity is that…”

Section: Qubit Channelsmentioning

confidence: 99%

Dividing Quantum Channels

Wolf

Cirac

2008

Commun. Math. Phys.

288

344

View full text Add to dashboard Cite

Abstract:We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible' channels which can not be written as non-trivial products of other channels and study the set of 'infinitesimal divisible' channels which are elements of continuous completely positive evolutions. For qubit channels we obtain a complete characterization of the sets of indivisible and infinitesimal divisible channels. Moreover, we identify those channels which are solutions of time-dependent master equations for both positive and completely positive evolutions. For arbitrary finite dimension we prove a representation theorem for elements of continuous completely positive evolutions based on new results on determinants of quantum channels and Markovian approximations.

show abstract

“…(The special case t 1 = t 2 = 0 was considered earlier in [7].) One expects the generic behavior of non-unital qubit channels to be quite different from that of unital ones.…”

Section: Qubit Channelsmentioning

confidence: 99%

Maximal output purity and capacity for asymmetric unital qudit channels

Datta

Ruskai

2005

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

We consider generalizations of depolarizing channels to maps of the formWe show that one can construct unital channels of this type for which the input which achieves maximal output purity is unique. We give conditions on V k under which multiplicativity of the maximal p-norm and additivity of the minimal output entropy can be proved for Φ ⊗ Ω with Ω arbitrary. We also show that the Holevo capacity need not equal log d − S min (Φ) as one might expect for a convex combination of unitary conjugations.

show abstract

One-to-one parametrization of quantum channels

Cited by 143 publications

References 3 publications

Additivity for unital qubit channels

Additivity for unital qubit channels

Dividing Quantum Channels

Maximal output purity and capacity for asymmetric unital qudit channels

Contact Info

Product

Resources

About