Metabolic quantum limit and holographic bound to the information capacity of magnetoencephalography

Abstract

Magnetoencephalography, the noninvasive measurement of magnetic fields produced by brain activity, utilizes quantum sensors like superconducting quantum interference devices or atomic magnetometers. Here we derive a fundamental, technology-independent bound on the information that such measurements can convey. Using the energy resolution limit of magnetic sensing together with the brain's metabolic power, we obtain a universal expression for the maximum information rate, which depends only on geometry, metabolism, and Planck's constant, and the numerical value of which is 2.6 Mbit/s. At the high bandwidth limit we arrive at a bound scaling linearly with the area of the current source boundary. We thus demonstrate a biophysical holographic bound for metabolically powered information conveyed by the magnetic field. For the geometry and metabolic power of the human brain the geometric bound is 6.6 Gbit/s.

Figures (1)

• Figure 1: (a) The first 30 eigenvalues of ${\cal K}_\Omega$ normalized by $\mu_0^2$, for $a=8~{\rm cm}$ and $d=1.3~{\rm cm}$. (b) Partial information obtained from \ref{['bound2']} by letting the sum over $\ell$ extend from 1 to $m=1,2,...,30$, and generalizing the ERL to be in the range from $\hbar$ (the fundamental limit) up to $10^4\hbar$. It is seen that the more sensitive the sensor, the more spatial modes of ${\cal K}_\Omega$ are required to saturate $I_W$.