Long distance quantum communication over noisy networks

Details Long distance quantum communication over noisy networks Long distance quantum communication over noisy networks

2012-02-05

arxiv.org/abs/1202.1016v1

Physics

Quantum Physics

10 pages, 10 figures

Scientific paper

The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long distance entanglement sharing and communication exploits networks, whose nodes share EPR pairs. In [Perseguers et al., Phys. Rev. A 78,062324 (2008)] an important isomorphism between storing quantum information in dimension D and transmission of quantum information in D+1 network has been put forward. It implies that fault tolerant quantum computing allows in principle for long distance quantum communication. However, in fault-tolerant schemes, one usually considers creating known encoded states. However the process of encoding and decoding is exposed to error. We show that during this stage fidelity drops by a constant factor related to the volume of circuit that replaces a gate, while going to an upper level of concatenation. This shows explicitly, that it is possible to obtain long distance entanglement in 2D network. For 3D networks, much simpler schemes are possible, e.g. due to existence of Kitaev topological quantum memory, which uses 2D lattice. Again, we consider explicitly the encoding and decoding stages. In [Dennis et al. J. Math. Phys. 43, 4452 (2002)] such scheme was provided in terms of gates. Here we propose a very simple scheme, based solely on syndrome measurements. It is then showed that the scheme is equivalent to teleporting the state to be encoded through some virtual EPR pair existing within the rest of qubits. We then present numerical simulation of performance of such encoding/decoding scheme.

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