Tradeoffs for reliable quantum information storage in 2D systems. (English) Zbl 1197.81083
Horodecki, Ryszard (ed.) et al., Quantum cryptography and computing. Theory and implementation. Selected papers based on the presentations at the workshop, Gdansk, Poland, September 9–12, 2009. Amsterdam: IOS Press (ISBN 978-1-60750-546-4/hbk; 978-1-60750-547-1/ebook). NATO Science for Peace and Security Series D: Information and Communication Security 26, 125-137 (2010).
Summary: We ask whether there are fundamental limits on storing quantum information reliably in a bounded volume of space. To investigate this question, we study quantum error correcting codes specified by geometrically local commuting constraints on a 2D lattice of finite-dimensional quantum particles. For these 2D systems, we derive a tradeoff between the number of encoded qubits \(k\), the distance of the code \(d\), and the number of particles \(n\). It is shown that \(kd^2=O(n)\) where the coefficient in \(O(n)\) depends only on the locality of the constraints and dimension of the Hilbert spaces describing individual particles. We show that the analogous tradeoff for the classical information storage is \(k(\sqrt{d})=O(n)\).
For the entire collection see [Zbl 1194.81015].
For the entire collection see [Zbl 1194.81015].
MSC:
81P68 | Quantum computation |
81P40 | Quantum coherence, entanglement, quantum correlations |
81Q93 | Quantum control |
81P70 | Quantum coding (general) |
94B60 | Other types of codes |