Physics Help
Physical Information
Physical information
From Wikipedia, the free encyclopedia.
Physical information refers generally to the
information that is contained in a physical system. First, what is information?
Information itself may be loosely defined as "that
which distinguishes one thing from another." The information that is contained
in a thing can thus be said to be the identity of the particular thing,
itself, that is, all of its properties, all that makes it distinct from other
(real or potential) things.
For physical systems, we must distinguish between classical
information and quantum information. Quantum information specifies the complete
quantum state vector (equivalently, wavefunction) of a system, whereas classical
information, roughly speaking, only picks out a quantum state if one is already
given a prespecified set of distinguishable (orthogonal) quantum states to
choose from; such a set forms a basis for the vector space of all possible
(pure) quantum states. Quantum information can thus be considered to consist of
(1) a choice of basis such that the actual quantum state is equal to one of the
basis vectors, plus (2) the classical information specifying which of these
basis vectors is the actual one.
Note that the amount of classical information in a quantum
system gives the maximum amount of information that can actually be measured and
extracted from that quantum system for use by external classical (decoherent)
systems, since only basis states are operationally distinguishable from each
other. The impossibility of differentiating between non-orthogonal states is a
fundamental principle of quantum mechanics, equivalent to Heisenberg's
uncertainty principle. Because of its more general utility, the remainder of
this article will deal primarily with classical information, although quantum
information theory does also have some potential applications (quantum
computing, quantum cryptography, quantum teleportation) that are currently being
actively explored by both theoreticians and experimentalists [1].
An amount of (classical) information may be quantified as
follows [2]. For a system S, defined abstractly in such a way that it has
N distinguishable states (orthogonal quantum states) that are consistent
with its description, the amount of information I(S) contained in
the system's state can be said to be log(N). The logarithm is selected
for this definition since it has the advantage that this measure of information
content is additive when concatenating independent, unrelated subsystems; e.g.,
if subsystem A has I(A)=N distinguishable states (log(N)
information content) and an independent subsystem B has I(B)=M
distinguishable states (log(M) information content), then the
concatenated system has NM distinguishable states and an information
content I(AB) = log(NM) = log(N) + log(M) =
I(A) + I(B). We expect information to be additive
from our everyday associations with the meaning of the word, e.g., that two
pages of a book can contain twice as much information as one page.
The base of the logarithm used in this definition is
arbitrary, since it affects the result by only a multiplicative constant, which
determines the unit of information that is implied. If the log is taken base 2,
the unit of information is the binary digit or bit (so named by John Tukey); if
we use a natural logarithm instead, we might call the resulting unit the "nat."
In magnitude, a nat is apparently identical to Boltzmann's constant k or
the ideal gas constant R, although these particular quantities are
usually reserved to measure physical information that happens to be entropy, and
that are expressed in physical units such as Joules per Kelvin, or kilocalories
per mole per Kelvin.
An easy way to understand physical entropy itself is as
follows: Entropy is simply that part of the (classical) physical information
contained in a system whose identity (as opposed to amount) is unknown. This
informal characterization fits von Neumann's formal definition of the entropy of
a mixed quantum state, as well as Shannon's definition of the entropy of a
probability distribution over classical states [2].
Even when the exact state of a system is known, we can say
that the information in the system is still effectively entropy if that
information is effectively incompressible, that is, if there are no known or
feasibly determinable correlations or redundancies between different pieces of
information within the system. Note that this definition can be viewed as
equivalent to the previous one (unknown information) if we take a
meta-perspective and say that for observer A to know the state of system
B means simply that there is a definite correlation between the state of
observer A and the state of system B; this correlation could be
used by a meta-observer to compress his description of the joint system AB
[3].
-
Michael A. Nielsen and Isaac L. Chuang, Quantum
Computation and Quantum Information, Cambridge University Press, 2000.
-
Michael P. Frank, "Physical Limits of Computing",
Computing in Science and Engineering, 4(3):16-25, May/June 2002.
-
W. H. Zurek, "Algorithmic randomness, physical entropy,
measurements, and the demon of choice," in [4], pp. 393-410, and reprinted in
[5], pp. 264-281.
-
J. G. Hey, ed., Feynman and Computation: Exploring the
Limits of Computers, Perseus, 1999.
-
Harvey S. Leff and Andrew F. Rex, Maxwell's Demon 2:
Entropy, Classical and Quantum Information, Computing, Institute of
Physics Publishing, 2003.
Home | Up | Wavefunctions | Quantum Entanglement | Harmonic Oscillators | Magnetism | Electricity
Electromagnetic Radiation | Temperature | Entropy | Physical Information
Physics Help, made by MultiMedia | Free content and software
This guide is licensed under the GNU
Free Documentation License. It uses material from the Wikipedia.
|
