Counterexample to an additivity conjecture for output purity of quantum channels
By Reinhard F. Werner, Alexander S. Holevo. 2002
222 citations recorded by the source corpus.
A conjecture arising naturally in the investigation of additivity of classical information capacity of quantum channels states that the maximal purity of outputs from a quantum channel, as measured by the p-norm, should be multiplicative with respect to the tensor product of channels. We disprove this conjecture for p>4.79. The same example (with p=∞) also disproves a conjecture for the multiplicativity of the injective norm of Hilbert space tensor products.
Subfields: Artificial Intelligence, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4bd52002b60262b5b6ed06dfa832aee3e2122a3f
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In Artificial Intelligence
- Mary Beth Ruskai
- Otfried Gühne
- Géza Tóth
- Keiji Matsumoto
- Michael Nathanson
- Ion Nechita
- Benoît Collins
- Christopher K. King
In Mathematical Physics
- Keiji Matsumoto
- Géza Tóth
- Ion Nechita
- Otfried Gühne
- Mary Beth Ruskai
- Benoît Collins
- Christopher K. King
- Michael Nathanson
Citations in the corpus
- Properties of Conjugate Channels with Applications to Additivity and Multiplicativity (2005, methodology): “) Their work extended an argument used by Alicki-Fannes [1] to prove multiplicativity of the Werner Holevo channel [31]; however, the question of additivity in the form (d) for the WH channel seems open.”
- Entanglement detection (2008, background): “This is then a lower bound on the relative entropy of |ψ〉, however, it is still not additive [288] and its convex roof is no longer an entanglement monotone [289].”
- Inequalities for quantum entropy: A review with conditions for equality (2002, background): “Despite the results mentioned above, many open conjectures remain; see [2, 8, 20, 21, 48 ] for further details.”
- Random matrix techniques in quantum information theory (2015, methodology): “S IN QUANTUM INFORMATION THEORY 23 Theorem 7.1. For every p2[1;1], there exist quantum channels and such that Hmin p ( ) <H p min() + H p min(#TAB#): (7.1) Except for some particular cases (p>4:73, [WH02] and p>2, [GHP10]), the proof of this theorem uses the random method, i.e. the channels”