Laboratoire de Physique Théorique
Toulouse - UMR 5152

Imagine you are supposed to keep the memory in your computer with its millions of bytes in a quantum superposition of two very different contents, such as the memory full of zeros and the memory full of ones. For how long you can you do this in principle, if at all ?

The answer to this most formidable open challenge in quantum information processing is : it depends on how many bits differ in the two states --- but not only. In fact, a researcher of the Laboratory has recently shown that quantum mechanics predicts a metric which determines the distance between the states of a quantum memory, just as the metric tensor in Einstein’s field equations determines the distance between two space-time points. The larger this distance, the smaller the life-time of the superposition. The metric tensor generalizes the so-called "Hamming distance" well-known in classical information theory, which just counts the number of differing bits, and which corresponds to a "flat" space. This limit is reached for bits that do not interact. In general, however, quantum mechanical interference leads to the metric of a curved space evolving in time, resulting in a rich pattern of time dependent decoherences, all controlled by a small number of matrix elements of the metric tensor.

Besides the conceptual implications of this new theory, important applications for the optimization of the physical lay-out of quantum memories are expected, as well as for the coherence preserving coding of quantum algorithms.

You can watch a movie of the decoherences in a small quantum memory, exposed to quantum fluctuations of the electromagnetic field.

The corresponding paper, Decoherence in a System of Many Two-Level Atoms has been published in Physical Review Letters, 96 230502 (2006). The corresponding author in the laboratory is Daniel Braun.