1202.1016 (Andrzej Grudka et al.)

Long distance quantum communication over noisy networks    [PDF]

Andrzej Grudka, Michal Horodecki, Pawel Horodecki, Pawel Mazurek, Lukasz Pankowski, Anna Przysiezna

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.

View original: http://arxiv.org/abs/1202.1016