**Nanomedicine,
Volume I: Basic Capabilities**

**©
1999 Robert A. Freitas Jr. All Rights
Reserved.**

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

**10.2.4.3 Bekenstein-Bounded
Computation**

A fundamental upper limit on the number of possible quantum
states in a bounded region (e.g., the maximum number of bits that can be coded
in a bounded region) -- is given by the Bekenstein Bound^{1990}
as:

_{}
{Eqn. 10.10}

within a spherical region of radius R containing energy E
= mc^{2} where m is the enclosed mass, c = 3 x 10^{8} m/sec
(speed of light), and ~~h~~ = h / 2 p where h
= 6.63 x 10^{-34} joule-sec (Planck's constant). Maximum processing
speed 'I is then bounded by the minimum time for a state transition, which cannot
be less than the time required for light to cross the region of radius R, or:

_{}
{Eqn. 10.11}

Thus in theory, a single carbon atom of mass m = 2 x 10^{-26}
kg and radius R ~ 0.15 nm could be impressed with up to I_{Bek} ~ 10^{8}
bits and could process information up to 'I_{Bek} ~ 10^{26}
bits/sec in an optimally-designed quantum computer. For a 1 micron^{3}
computer of mass ~10^{-15} kg, I_{Bek} ~ 10^{22} bits
maximum storage capacity and 'I_{Bek} ~ 10^{37} bits/sec maximum
processing capacity. These values are not the least upper limits; Schiffer and
Bekenstein^{1991} estimate that
the Bekenstein Bound probably overestimates I and 'I by at least a factor of
100, but Likharev^{1992} and Margolus
and Levitin^{2319} have derived
similar limits. In 1998, proposed reversible quantum computer systems would
perform significantly below the Bekenstein Bound.^{1993,1994}

Last updated on 24 February 2003