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Abstract
The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A 78, 062324 (2008)] the authors put forward an important isomorphism between storing quantum information in a dimension D and transmission of quantum information in a D+1 -dimensional network. We show that it is possible to obtain long-distance entanglement in a noisy two-dimensional (2D) network, even when taking into account that encoding and decoding of a state is exposed to an error. For 3D networks we propose a simple encoding and decoding scheme based solely on syndrome measurements on 2D Kitaev topological quantum memory. Our procedure constitutes an alternative scheme of state injection that can be used for universal quantum computation on 2D Kitaev code. It is shown that the encoding scheme is equivalent to teleporting the state, from a specific node into a whole two-dimensional network, through some virtual EPR pair existing within the rest of network qubits. We present an analytic lower bound on fidelity of the encoding and decoding procedure, using as our main tool a modified metric on space-time lattice, deviating from a taxicab metric at the first and the last time slices.
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Authors (7)
-
Paweł Mazurek
- Uniwersytet Gdański Wydział Fizyki
-
Andrzej Grudka
- Uniwersytet AM w Poznaniu Wydział Fizyki
-
Michał Horodecki
- Uniwersytet Gdański Wydział Fizyki
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Justyna Łodyga
- UM w Poznaniu Wydział Fizyki
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Łukasz Pankowski
- Uniwersytet Gdański Wydział Fizyki
-
Anna Przysiężna
- Uniwersytet Gdański Wydział Fizyki
Cite as
Full text
- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1103/PhysRevA.90.062311
- License
- Copyright (2014 American Physical Society)
Keywords
Details
- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
PHYSICAL REVIEW A
no. 90,
edition 6,
pages 1 - 13,
ISSN: 2469-9926 - Language:
- English
- Publication year:
- 2014
- Bibliographic description:
- Mazurek P., Grudka A., Horodecki M., Horodecki P., Łodyga J., Pankowski Ł., Przysiężna A.: Long-distance quantum communication over noisy networks without long-time quantum memory// PHYSICAL REVIEW A. -Vol. 90, iss. 6 (2014), s.1-13
- DOI:
- Digital Object Identifier (open in new tab) 10.1103/physreva.90.062311
- Verified by:
- Gdańsk University of Technology
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