Filters, Superpositions and Entanglements
Superpositions are not necessarily entanglements.
A superposition is what happens at a beam splitter.
An entanglement is what happens in a non-linear crystal.
Zeilinger et al, don't use beamsplitters to make entangled
particle pairs. Superpositions and entanglements are different.
Wavefunction collapse can be alot like tapping a computer
programmer on the shoulder while s/he is in deep superposition
of many associated concepts; destoying their concentration.
Decoherence is a loss of the ability to make meaningful
distinguishments, or the loss of the ability
to maintain a record of a past event (entanglement) and
this diffusion or dispersion does not destroy all record
of the past event but makes it increasingly unrecoverable
in a theromdynamic sense, which itself can probably be modelled
as a damping in an impulse-response (Green's functions) sense,
like a pair of bells having clanged against each other
and that correlated ringings of each bell, fading like a memory of
the past as the energy of the event disperses within the bell.
Single-moded spatio-temporal solitons (light-bullets)
are recognized for their ability to resist such dispersion
and are proposed for this reason as candidates for qubits
which resist decoherence. Other possibilities for
decoherence resistent qubits might be BE condensates,
superconductors, and superfluids, and extremely stabilized
laser-light (non-interaction experiments); all of which
effectively seem to homogenize their component units to the
point where they act in extreme unison (coherence).
Pure coherence, unadulterated, is apparently not possible
in any finitely bounded system. But we none-the-less have
computers, which function almost completely as if this
idealism of both continuity and closure were attainable in a
The Zen master will tap the meditating student on the shoulder
to remind him that closures are indeed just as much a part of
life as coherence. Decisions have to be made.
An electric battery represents distinguishment. Its potential
energy is meaningless without continuity (a circuit).
But shorting out the terminals of the battery and explosively
releasing all its energy is also meaningless.
We build an electric circuit with resistance (decoherence) and
yet it can still have meaning, but that meaning is generally
derived from outside the energy economy of that circuit.
The battery's energy is eventually depleted and it fails
to serve its purpose to make some form of distinguishment.
In order for its purpose to survive, the energy must
be replenished from the outside, but not with excessive
greed (we live off the land and should respect the Time
it takes to feed us and itself).
Decoherence is not without distinguishment.
We use circuits with large resistances as "space heaters"
and from this we derive a distinguishment or contrast of
heat and cold on those cold winter nights, but as with
anything else, the 'burning of space'
(or land like the rainforests) is not without its consequences.
Contrast is as important as brightness, but these two
should not be confused with each other.
I like the idea of portraying this in terms of ideal mirrors,
which reflect all the colors in a specific direction, as opposed
to white paper which also reflects all the colors equally, though
not with specific direction (diffuse). Is the mirror, when
crushed into many pieces, the same as the white paper ?
The mirror appears gray because it is really black in the
regions where light is not reflected. And black and white
and grey are merely distinguished by relative brightness.
"Superpositions" are distinguished from "filters" by their
ability to add as well as subtract. Filters only subtract.
When two systems are superposed and then separated, their
former superposition becomes an entanglement.
A filter can exist without a superposition; as in the
spatial filters in holography.
A superposition cannot exist without the concept of a filter
(in terms of destructive interference); as in non-spatial filters
in holography (thick holographic filters using Bragg selectivity,
filtering in the time-like domain using convolution instead
of multiplication of the impulse response and signal in the
Entanglement cannot exist without superpositions and filters;
as in the more recent quadrature mirror "filters" or wavelet
analysis, .... (Indeed it should be called
"analysis" as it is very similar to what a psychoanalyst
does in terms of a patient's _subjective_ spatio-temporal
memories. The analyst essentially unravels the [en]tangled
threads of space-time in a patient's memories (historical
threads) and reweaves them into a more "flat" or "euclidean"
road map. Similarly, the entangled space-time histories
are unravelled in a _physical_ signal by multi-resolution
analysis of both it's static (deterministic) and dynamic
It should be understood here that the distinction of "spatial"
and "temporal" in the above cases are in terms of space-like
and time-like functional domains. The different definitions
of "time" that can arise and the many further implications
are developed elsewhere.
The chinese-box-like hierarchy is derivable from analogous
systems in other fields like linguistics, politics, economics,
etc., where the same hierarchy is more evident.
The overall model is suggestive that a generalized communication
theory abstracting the communicated units and associatively derived
information, as well as the inherent uncertainties, can work
across the normal boundaries of soft and hard sciences.
 Anton Zeilinger et al, Quantum Teleportation, Quantum Non-demolition,...