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2003 | 1 | 4 | 695-707
Tytuł artykułu

On entanglement distillation and quantum error correction for unknown states and channels

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the problem of invariance of distillable entanglement D and quantum capacities Q under erasure of information about single copy of quantum state or channel respectively. We argue that any 2 ⊗N two-way distillable state is still two-way distillable after erasure of single copy information. For some known distillation protocols the obtained two-way distillation rate is the same as if Alice and Bob knew the state from the very beginning. The isomorphism between quantum states and quantum channels is also investigated. In particular it is pointed out that any transmission rate down the channel is equal to distillation rate with formal LOCC-like superoperator that uses in general nonphysical Alice actions. This allows to we prove that if given channel Λ has nonzero capacity (Q → or Q ⟺) then the corresponding quantum state ϱ(Λ) has nonzero distillable entanglement (D → or D ⟺). Follwoing the latter arguments are provided that any channel mapping single qubit into N level system allows for reliable two-way transmission after erasure of information about single copy. Some open problems are discussed.
Wydawca

Czasopismo
Rocznik
Tom
1
Numer
4
Strony
695-707
Opis fizyczny
Daty
wydano
2003-12-01
online
2003-12-01
Twórcy
  • Facully of Applied Physics and Mathematics, Gdańsk University of Technology, 80-952, Gdańsk, Poland
Bibliografia
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  • [11] If the state of bipartite system is defined on Hilbert space \(\mathcal{H}_A \otimes \mathcal{H}_B \) and \(d_A = dim\mathcal{H}_A \) , \(d_B = dim\mathcal{H}_B \) then we deal withd A⊗d B system.
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  • [18] P. Horodecki, M. Horodecki and R. Horodecki: “Binding entanglement channels”, J. Mod. Opt., Vol. 47, (2000), pp. 347–354. D. DiVincenzo, T. Mor, P. Shor, J. Smolin, and B.M. Terhal: “Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement”, Commun. Math. Phys., Vol. 238, pp. 379–410. http://dx.doi.org/10.1080/095003400148259[Crossref]
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  • [22] Here, in general \(\vec p \in R^{15} \) since two qubit density matrix is described by 15 parameters. In analysis of hashing of Bell diagnonal states [21] effectively one can choose \(\vec p \in R^{15} \) since Bell diagnonal states depend effectively on 3 parameters.
  • [23] G.M. D'Ariano, M.G.A. Paris, M.F. Sacchi: “Quantum Tomography”, (quantph/0302028), http://arxiv.org/abs/quant-ph/0302028.
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  • [26] P. Horodecki, PhD thesis, Technical University of Gdansk, Gdansk 1999.
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_BF02475911
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